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 Journal of Fluid MechanicsJournal Prestige (SJR): 1.591 Citation Impact (citeScore): 3Number of Followers: 183      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0022-1120 - ISSN (Online) 1469-7645 Published by Cambridge University Press  [387 journals]
• Transition to turbulence when the Tollmien–Schlichting and bypass
routes coexist
• Authors: Stefan Zammert; Bruno Eckhardt
Abstract: Plane Poiseuille flow, the pressure-driven flow between parallel plates, shows a route to turbulence connected with a linear instability to Tollmien–Schlichting (TS) waves, and another route, the bypass transition, that can be triggered with finite-amplitude perturbation. We use direct numerical simulations to explore the arrangement of the different routes to turbulence among the set of initial conditions. For plates that are a distance $2H$ apart, and in a domain of width $2\unicode[STIX]{x03C0}H$ and length $2\unicode[STIX]{x03C0}H$ , the subcritical instability to TS waves sets in at $Re_{c}=5815$ and extends down to $Re_{TS}\approx 4884$ . The bypass route becomes available above $Re_{E}=459$ with the appearance of three-dimensional, finite-amplitude travelling waves. Below $Re_{c}$ , TS transition appears for a tiny region of initial conditions that grows with increasing Reynolds number. Above $Re_{c}$ , the previously stable region becomes unstable via TS waves, but a sharp transition to the bypass route can still be identified. Both routes lead to the same turbulent state in the final stage of the transition, but on different time scales. Similar phenomena can be expected in other flows where two or more routes to turbulence compete.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.724
Issue No: Vol. 880 (2019)

• A new time scale for turbulence modulation by particles
• Authors: Izumi Saito; Takeshi Watanabe, Toshiyuki Gotoh
Abstract: A new time scale for turbulence modulation by particles is introduced. This time scale is inversely proportional to the number density and the radius of particles, and can be regarded as a counterpart of the phase relaxation time, an important time scale in cloud physics, which characterizes the interaction between turbulence and cloud droplets by condensation–evaporation. Scaling analysis and direct numerical simulations of dilute inertial particles in homogeneous isotropic turbulence suggest that turbulence modulation by particles with a fixed mass-loading parameter can be expressed as a function of the Damköhler number, which is defined as the ratio of the turbulence large-eddy turnover time to the new time scale.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.775
Issue No: Vol. 880 (2019)

• Bifurcation analysis of the primary instability in the flow around a
flexibly mounted circular cylinder
• Authors: Daiane I. Dolci; Bruno S. Carmo
Abstract: The nonlinear character of the primary bifurcation is investigated for the flow around a flexibly mounted circular cylinder. We have considered the cases in which the cylinder can oscillate in the transverse direction only and in both transverse and in-line directions. Low and high values of mass ratio ( $m^{\ast }=5$ and 50) were studied, and reduced velocity ( $V_{r}$ ) values are chosen inside ( $V_{r}=9$ ) and outside ( $V_{r}=5$ and $V_{r}=13$ ) the lock-in range for low Reynolds numbers. For each combination of $m^{\ast }$ and $V_{r}$ , a global linear stability analysis was applied to find the critical Reynolds number $Re_{c}$ of the fluid–structure system. For $V_{r}$ in the lock-in range, the values of $Re_{c}$ were noticeably less than the critical Reynolds number of the flow around a fixed circular cylinder (
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.754
Issue No: Vol. 880 (2019)

• Acoustic theory of the many-bladed contra-rotating propeller: physics of
the wake interaction noise critical sources
• Authors: A. B. Parry; M. J. Kingan
Abstract: In the theory of interaction noise from contra-rotating propellers with many blades, the usual far-field radiation formulae can be re-cast as a double integral, over a source surface, which can be evaluated asymptotically solely in terms of the contributions from critical points. The paper shows that these critical points have a particularly interesting physical meaning. They relate to locations on an event line, running between hub and tip, that represent the locus of the wake–blade interactions at a fixed point in time. The event line rotates at the speed of the spinning interaction tone but does not coincide with the radial variation in either the wake location or the rear blade leading edge. At the precise critical locations on the event line, it is shown that the Mach number of the event line is unity in the direction of the observer (the sonic condition) and the tangent to the event line – at a fixed time – is normal to a line drawn between it and the observer (the normal-edge condition). The zero-mode case is also considered, for which we show that, even though the event line rotates at infinite speed, there can still exist locations that satisfy the sonic and normal-edge conditions. The paper also discusses the physical meaning of the lower-order boundary solutions from the hub and tip.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.755
Issue No: Vol. 880 (2019)

• The structure and dynamics of backflow in turbulent channels
• Authors: J. I. Cardesa; J. P. Monty, J. Soria, M. S. Chong
Abstract: A statistical description of flow regions with negative streamwise velocity is provided based on simulations of turbulent plane channels in the Reynolds number range $547\leqslant Re_{\unicode[STIX]{x1D70F}}\leqslant 2003$ . It is found that regions of backflow are attached and their density per surface area – in wall units – is an increasing function of $Re_{\unicode[STIX]{x1D70F}}$ . Their size distribution along the three coordinates reveals that, even though in the mean they appear to be circular in the wall-parallel plane, they tend to become more elongated in the spanwise direction after reaching a certain height. Time-tracking of backflow regions in a $Re_{\unicode[STIX]{x1D70F}}=934$ simulation showed they convect downstream at the mean velocity corresponding to $y^{+}\approx 12$ , they seldom interact with other backflow events, their statistical signature extends in the streamwise direction for at least $300$ wall units, and they result from a complex interaction between regions of high and low spanwise vorticity far beyond the viscous sublayer. This could explain why some statistical aspects of these near-wall events do not scale in viscous units; they are dependent on the $Re_{\unicode[STIX]{x1D70F}}$ -dependent dynamics further away from the wall.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.774
Issue No: Vol. 880 (2019)

• Rotation of a superhydrophobic cylinder in a viscous liquid
• Authors: Ehud Yariv; Michael Siegel
Abstract: The hydrodynamic quantification of superhydrophobic slipperiness has traditionally employed two canonical problems – namely, shear flow about a single surface and pressure-driven channel flow. We here advocate the use of a new class of canonical problems, defined by the motion of a superhydrophobic particle through an otherwise quiescent liquid. In these problems the superhydrophobic effect is naturally measured by the enhancement of the Stokes mobility relative to the corresponding mobility of a homogeneous particle. We focus upon what may be the simplest problem in that class – the rotation of an infinite circular cylinder whose boundary is periodically decorated by a finite number of infinite grooves – with the goal of calculating the rotational mobility (velocity-to-torque ratio). The associated two-dimensional flow problem is defined by two geometric parameters – namely, the number $N$ of grooves and the solid fraction $\unicode[STIX]{x1D719}$ . Using matched asymptotic expansions we analyse the large- $N$ limit, seeking the mobility enhancement from the respective homogeneous-cylinder mobility value. We thus find the two-term approximation, $$\begin{eqnarray}\displaystyle 1+{\displaystyle \frac{2}{N}}\ln \csc {\displaystyle \frac{\unicode[STIX]{x03C0}\unicode[STIX]{x1D719}}{2}}, & & \displaystyle \nonumber\end{eqnarray}$$ for the ratio of the enhanced mobility to the homogeneous-cylinder mobility. Making use of conformal-mapping techniques and inductive arguments we prove that the preceding approximation is actually exact for $N=1,2,4,8,\ldots$ . We conjecture that it is exact for all $N$ .
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.776
Issue No: Vol. 880 (2019)

• Instabilities in non-ideal fluids
• Authors: J.-C. Robinet; X. Gloerfelt
Pages: 1 - 4
Abstract: The recent study of Ren et al. (J. Fluid Mech., vol. 871, 2019, pp. 831–864) investigated the hydrodynamic linear stability of a compressible boundary layer over an insulated flat plate for a non-ideal gas (supercritical $\text{CO}_{2}$ ). In particular, the authors showed that in the transcritical regime (across the pseudo-critical line) the flow is strongly convectively unstable due to the co-existence of two unstable modes: Mode I, related to Tollmien–Schlichting instabilities and a new inviscid two-dimensional mode (Mode II) with a spatial growth rate one order of magnitude larger than Mode I for high Eckert numbers. In contrast to the transcritical regime, in the sub- and supercritical regimes, Mode II does not exist. Only Mode I drives the instabilities: viscous and two-dimensional for the subcritical regime and inflectional and three-dimensional for the supercritical regime.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.719
Issue No: Vol. 880 (2019)

• Pressure–strain terms in Langmuir turbulence
• Authors: Brodie C. Pearson; Alan L. M. Grant, Jeff A. Polton
Pages: 5 - 31
Abstract: This study investigates the pressure–strain tensor ( $\unicode[STIX]{x1D72B}$ ) in Langmuir turbulence. The pressure–strain tensor is determined from large-eddy simulations (LES), and is partitioned into components associated with the mean current shear (rapid), the Stokes shear and the turbulent–turbulent (slow) interactions. The rapid component can be parameterized using existing closure models, although the coefficients in the closure models are particular to Langmuir turbulence. A closure model for the Stokes component is proposed, and it is shown to agree with results from the LES. The slow component of $\unicode[STIX]{x1D72B}$ does not agree with existing ‘return-to-isotropy’ closure models for five of the six components of the Reynolds stress tensor, and a new closure model is proposed that accounts for these deviations which vary systematically with Langmuir number, $La_{t}$ , and depth. The implications of these results for second- and first-order closures of Langmuir turbulence are discussed.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.701
Issue No: Vol. 880 (2019)

• Contrasts between momentum and scalar transport over very rough surfaces
• Authors: Qi Li; Elie Bou-Zeid
Pages: 32 - 58
Abstract: Large-eddy simulations are conducted to contrast momentum and passive scalar transport over large, three-dimensional roughness elements in a turbulent channel flow. Special attention is given to the dispersive fluxes, which are shown to be a significant fraction of the total flux within the roughness sublayer. Based on pointwise quadrant analysis, the turbulent components of the transport of momentum and scalars are found to be similar in general, albeit with increasing dissimilarity for roughnesses with low frontal blockage. However, strong dissimilarity is noted between the dispersive momentum and scalar fluxes, especially below the top of the roughness elements. In general, turbulence is found to transport momentum more efficiently than scalars, while the reverse applies to the dispersive contributions. The effects of varying surface geometries, measured by the frontal density, are pronounced on turbulent fluxes and even more so on dispersive fluxes. Increasing frontal density induces a general transition in the flow from a wall bounded type to a mixing layer type. This transition results in an increase in the efficiency of turbulent momentum transport, but the reverse occurs for scalars due to reduced contributions from large-scale motions in the roughness sublayer. This study highlights the need for distinct parameterizations of the turbulent and dispersive fluxes, as well as the importance of considering the contrasts between momentum and scalar transport for flows over very rough surfaces.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.687
Issue No: Vol. 880 (2019)

• Formation of a hidden cavity below droplets impacting on a granular
substrate
• Authors: Song-Chuan Zhao; Rianne de Jong, Devaraj van der Meer
Pages: 59 - 72
Abstract: Droplet impact on a granular layer results in various morphologies of the liquid–grain mixture. Some are concentrated and highly curved, some are extended and flatter. No matter how the morphology looks from the top, it is generally believed that its bottom is tightly connected to the concavely deformed granular target. In this paper we report the discovery of a hidden cavity below a droplet residual, formed upon impact on packings of hydrophilic grains and exposed by X-ray tomography. Its occurrence in the parameter space is explored. We elucidate the mechanism leading to this counterintuitive phenomenon using a dual-curvature model and an energy criterion. This research may shed new light onto the ongoing discussion about the origin of the so-called fossilized raindrop impressions.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.742
Issue No: Vol. 880 (2019)

• Tuning the dispersion of reactive solute by steady and oscillatory
electroosmotic–Poiseuille flows in polyelectrolyte-grafted
micro/nanotubes
Pages: 73 - 112
Abstract: This paper extends the analysis of solute dispersion in electrohydrodynamic flows to the case of band broadening in polyelectrolyte-grafted (soft) capillaries by accounting for the effects of ion partitioning, irreversible catalytic reaction and pulsatile flow actuation. In the Debye–Hückel limit, we present the benchmark solutions of electric potential and velocity distribution pertinent to steady and oscillatory mixed electroosmotic–pressure-driven flows in soft capillaries. Afterwards, the mathematical models of band broadening based on the Taylor–Aris theory and generalized dispersion method are presented to investigate the late-time asymptotic state and all-time evolution of hydrodynamic dispersion, respectively. Also, to determine the heterogeneous dispersion behaviour of solute through all spatiotemporal stages and to relax the constraint of small zeta potentials, a full-scale numerical simulation of time-dependent solute transport in soft capillaries is presented by employing the second-order-accurate finite difference method. Then, by inspecting the dispersion of passive tracer particles in Poiseuille flows, we examine the accuracy of two analytical approaches against the simulation results of a custom-built numerical algorithm. Our findings from hydrodynamic dispersion in Poiseuille flows reveal that, compared to rigid capillaries, more time is required to approach the longitudinal normality and transverse uniformity of injected solute in soft capillaries. For the case of dispersion in mixed electrohydrodynamic flows, it is found that the characteristics of the soft interface, including the thickness, permittivity, fixed charge density and friction coefficient of the polymer coating layer, play a significant role in determining the Taylor diffusion coefficient, advection speed and dispersion rate of solutes in soft capillaries.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.628
Issue No: Vol. 880 (2019)

• Reattachment streaks in hypersonic compression ramp flow: an
input–output analysis
• Authors: Anubhav Dwivedi; G. S. Sidharth, Joseph W. Nichols, Graham V. Candler, Mihailo R. Jovanović
Pages: 113 - 135
Abstract: We employ global input–output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock–boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat-flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favourably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base-flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.702
Issue No: Vol. 880 (2019)

• Pattern formation on time-dependent domains
• Authors: M. Ghadiri; R. Krechetnikov
Pages: 136 - 179
Abstract: In the quest to understand the dynamics of distributed systems on time-dependent spatial domains, we study experimentally the response to domain deformations by Faraday wave patterns – standing waves formed on the free surface of a liquid layer due to its vertical vibration – chosen as a paradigm owing to their historical use in testing new theories and ideas. In our experimental set-up of a vibrating water container with controlled positions of lateral walls and liquid layer depth, the characteristics of the patterns are measured using the Fourier transform profilometry technique, which allows us to reconstruct an accurate time history of the pattern three-dimensional landscape and reveal how it reacts to the domain dynamics on various length and time scales. Analysis of Faraday waves on growing, shrinking and oscillating domains leads to a number of intriguing results. First, the observation of a transverse instability – namely, when a two-dimensional pattern experiences an instability in the direction orthogonal to the direction of the domain deformation – provides a new facet to the stability picture compared to the one-dimensional systems in which the longitudinal (Eckhaus) instability accounts for pattern transformation on time-varying domains. Second, the domain evolution rate is found to be a key factor dictating the patterns observed on the path between the initial and final domain aspect ratios. Its effects range from allowing the formation of complex sequences of patterns to impeding the appearance of any new pattern on the path. Third, the shrinkage–growth process turns out to be generally irreversible on a horizontally evolving domain, but becomes reversible in the case of a time-dependent liquid layer depth, i.e. when the dilution and convective effects of the domain flow are absent. These experimentally observed enigmatic effects of the domain size variations in time are complemented here with appropriate theoretical insights elucidating the dynamics of two-dimensional pattern evolution, which proves to be more intricate compared to one-dimensional systems.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.659
Issue No: Vol. 880 (2019)

• Development of gravity currents on slopes under different interfacial
instability conditions
• Authors: Antoine Martin; M. Eletta Negretti, E. J. Hopfinger
Pages: 180 - 208
Abstract: We present experimental results on the development of gravity currents moving onto sloping boundaries with slope angles $\unicode[STIX]{x1D703}=7^{\circ }$ , $10^{\circ }$ and $15^{\circ }$ . Different regimes of flow development are observed depending on the slope angle and on the initial velocity and density profiles, characterized by the Richardson number $J_{i}=\unicode[STIX]{x1D6FF}_{i}{g_{0}}^{\prime }/\unicode[STIX]{x0394}u_{i}^{2}$ , where $\unicode[STIX]{x1D6FF}_{i}$ , $\unicode[STIX]{x0394}u_{i}$ and $g_{0}^{\prime }$ are, respectively, the velocity interface thickness, the maximum velocity difference and reduced gravity at the beginning of the slope. For $J_{i}>0.7$ and the larger slope angle, the flow strongly accelerates, reaches a maximum at the beginning of the Kelvin–Helmholtz instability, then decelerates and re-accelerates again. For $0.3 PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.713 Issue No: Vol. 880 (2019) • Numerical investigation of shear-flow free-surface turbulence and air entrainment at large Froude and Weber numbers • Authors: Xiangming Yu; Kelli Hendrickson, Bryce K. Campbell, Dick K. P. Yue Pages: 209 - 238 Abstract: We investigate two-phase free-surface turbulence (FST) associated with an underlying shear flow under the condition of strong turbulence (SFST) characterized by large Froude ($Fr$) and Weber ($We$) numbers. We perform direct numerical simulations of three-dimensional viscous flows with air and water phases. In contrast to weak FST (WFST) with small free-surface distortions and anisotropic underlying turbulence with distinct inner/outer surface layers, we find SFST to be characterized by large surface deformation and breaking accompanied by substantial air entrainment. The interface inner/outer surface layers disappear under SFST, resulting in nearly isotropic turbulence with${\sim}k^{-5/3}$scaling of turbulence kinetic energy near the interface (where$k$is wavenumber). The SFST air entrainment is observed to occur over a range of scales following a power law of slope$-10/3$. We derive this using a simple energy argument. The bubble size spectrum in the volume follows this power law (and slope) initially, but deviates from this in time due to a combination of ongoing broad-scale entrainment and bubble fragmentation by turbulence. For varying$Fr$and$We$, we find that air entrainment is suppressed below critical values$Fr_{cr}$and$We_{cr}$. When PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.695 Issue No: Vol. 880 (2019) • Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis • Authors: Christoph Wenzel; Tobias Gibis, Markus Kloker, Ulrich Rist Pages: 239 - 283 Abstract: A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter$\unicode[STIX]{x1D6FD}_{K}$calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness$\unicode[STIX]{x1D6FF}_{99}$and the skin-friction coefficient$c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar$\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same$\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same$\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium. PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.670 Issue No: Vol. 880 (2019) • Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer • Authors: Tobias Gibis; Christoph Wenzel, Markus Kloker, Ulrich Rist Pages: 284 - 325 Abstract: A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzel et al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter$\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption,$\unicode[STIX]{x1D6EC}_{c}$values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form$\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$with the kinematic (incompressible) displacement thickness$\unicode[STIX]{x1D6FF}_{K}^{\ast }$is shown to be a valid parameter of the form$\unicode[STIX]{x1D6EC}_{c}$and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale,$\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.672 Issue No: Vol. 880 (2019) • The evolution of a front in turbulent thermal wind balance. Part 2. Numerical simulations • Authors: Matthew N. Crowe; John R. Taylor Pages: 326 - 352 Abstract: In Crowe & Taylor (J. Fluid Mech., vol. 850, 2018, pp. 179–211) we described a theory for the evolution of density fronts in a rotating reference frame subject to strong vertical mixing using an asymptotic expansion in small Rossby number,$Ro$. We found that the front reaches a balanced state where vertical diffusion is balanced by horizontal advection in the buoyancy equation. The depth-averaged buoyancy obeys a nonlinear diffusion equation which admits a similarity solution corresponding to horizontal spreading of the front. Here we use numerical simulations of the full momentum and buoyancy equations to investigate this problem for a wide range of Rossby and Ekman numbers. We examine the accuracy of our asymptotic solution and find that many aspects of the solution are valid for$Ro=O(1)$. However, the asymptotic solution departs from the numerical simulations for small Ekman numbers where the dominant balance in the momentum equation changes. We trace the source of this discrepancy to a depth-independent geostrophic flow that develops on both sides of the front and we develop a modification to the theory described in Crowe & Taylor (2018) to account for this geostrophic flow. The refined theory closely matches the numerical simulations, even for$Ro=O(1)$. Finally, we develop a new scaling for the intense vertical velocity that can develop in thin bands at the edges of the front. PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.688 Issue No: Vol. 880 (2019) • On Langmuir circulation in 1 : 2 and 1 : 3 resonance • Authors: L. Cui; W. R. C. Phillips Pages: 353 - 387 Abstract: This paper is concerned with the nonlinear dynamics of spanwise periodic longitudinal vortex modes (Langmuir circulation (LC)) that arise through the instability of two-dimensional periodic flows (waves) in a non-stratified uniformly sheared layer of finite depth. Of particular interest is the excitation of the vortex modes either in the absence of interaction or in resonance, as described by nonlinear amplitude equations built upon the mean field Craik–Leibovich (CL) equations. Since Y-junctions in the surface footprints of Langmuir circulation indicate sporadic increases (doubling) in spacing as they evolve to the scale of sports stadiums, interest is focused on bifurcations that instigate such changes. To that end, surface patterns arising from the linear and nonlinear excitation of the vortex modes are explored, subject to two parameters: a Rayleigh number${\mathcal{R}}$present in the CL equations and a symmetry breaking parameter$\unicode[STIX]{x1D6FE}$in the mixed free surface boundary conditions that relax to those at the layer bottom where$\unicode[STIX]{x1D6FE}=0$. Looking first to linear instability, it is found as$\unicode[STIX]{x1D6FE}$increases from zero to unity, that the neutral curves evolve from asymmetric near onset to almost symmetric. The nonlinear dynamics of single modes is then studied via an amplitude equation of Ginzburg–Landau type. While typically of cubic order when the bifurcation is supercritical (as it is here) and the neutral curves are parabolic, the Ginzburg–Landau equation must instead here be of quartic order to recover the asymmetry in the neutral curves. This equation is then subjected to an Eckhaus instability analysis, which indicates that linearly unstable subharmonics mostly reside outside the Eckhaus boundary, thereby excluding them as candidates for excitation. The surface pattern is then largely unchanged from its linear counterpart, although the character of the pattern does change when$\unicode[STIX]{x1D6FE}\ll 1$as a result of symmetry breaking. Attention is then turned to strong resonance between the least stable linear mode and a sub-harmonic of it, as described by coupled nonlinear amplitude equations of Stuart-Landau type. Both 1 : 2 and 1 : 3 resonant interactions are considered. Phase plots and bifurcation diagrams are employed to reveal classes of solution that can occur. Dominant over much of the${\mathcal{R}}$-$\unicode[STIX]{x1D6FE}$range considered are non-travelling pure... PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.697 Issue No: Vol. 880 (2019) • Supersonic turbulent boundary layer drag control using spanwise wall oscillation • Authors: Jie Yao; Fazle Hussain Pages: 388 - 429 Abstract: Spanwise wall oscillation has been extensively studied to explore possible drag control methods, mechanisms and efficacy – particularly for incompressible flows. We performed direct numerical simulation for fully developed turbulent channel flow to establish how effective spanwise wall oscillation is when the flow is compressible and also to document its drag reduction (${\mathcal{D}}{\mathcal{R}}$) trend with Mach number. Drag reduction${\mathcal{D}}{\mathcal{R}}$is first investigated for three different bulk Mach numbers$M_{b}=0.3$,$0.8$and$1.5$at a fixed bulk Reynolds number$Re_{b}=3000$. At a given velocity amplitude$A^{+}$($=12$),${\mathcal{D}}{\mathcal{R}}$at$M_{b}=0.3$agrees with the strictly incompressible case; at PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.727 Issue No: Vol. 880 (2019) • Capillary ripples in thin viscous films • Authors: Maziyar Jalaal; Carola Seyfert, Jacco H. Snoeijer Pages: 430 - 440 Abstract: Capillary ripples in thin viscous films are important features of coating and lubrication flows. Here, we present experiments based on digital holographic microscopy, measuring with nanoscale resolution the morphology of capillary ripples ahead of a viscous drop spreading on a prewetted surface. Our experiments reveal that upon increasing the spreading velocity, the amplitude of the ripples first increases and subsequently decreases. Above a critical spreading velocity, the ripples even disappear completely and this transition is accompanied by a divergence of the ripple wavelength. These observations are explained quantitatively using linear wave analysis, beyond the usual lubrication approximation, illustrating that new phenomena arise when the capillary number becomes of the order of unity. PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.734 Issue No: Vol. 880 (2019) • Dynamics of rapidly depressurized multiphase shock tubes • Authors: D. Zwick; S. Balachandar Pages: 441 - 477 Abstract: Rapid depressurization is a fluid phenomenon that occurs in many industrial and natural applications. Its behaviour is often complicated by the formation, propagation and interaction of waves. In this work, we perform computer simulations of the rapid depressurization of a gas–solid mixture in a shock tube. Our problem set-up mimics previously performed experiments, which have been historically used as a laboratory surrogate for volcanic eruptions. The simulations are carried out with a discontinuous Galerkin compressible fluid solver with four-way coupled Lagrangian particle tracking capabilities. The results give an unprecedented look into the complex multiphase physics at work in this problem. Different regimes have been characterized in a regime map that highlights the key observations. While the mean flow behaviour is in good agreement with experiments, the simulations show unexpected accelerations of the particle front as it expands. Additionally, a new lifting mechanism for gas bubble (void) growth inside the gas–solid mixture is detailed. PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.710 Issue No: Vol. 880 (2019) • A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow • Authors: Shengqi Zhang; Zhenhua Xia, Yipeng Shi, Shiyi Chen Pages: 478 - 496 Abstract: Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number$Ra$and channel height$H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different$Ro$can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers. PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.715 Issue No: Vol. 880 (2019) • Laser-induced forward transfer of viscoplastic fluids • Authors: Maziyar Jalaal; Martin Klein Schaarsberg, Claas-Willem Visser, Detlef Lohse Pages: 497 - 513 Abstract: Laser-induced forward transfer (LIFT) is a nozzle-free printing technology that can be used for two- and three-dimensional printing. In LIFT, a laser pulse creates an impulse inside a thin film of material that results in the formation of a liquid jet. We experimentally study LIFT of viscoplastic materials by visualizing the process of jetting with high-speed imaging. The shape of the jet depends on the laser energy, focal height, surface tension and material rheology. We theoretically identify the characteristic jetting velocity and how it depends on the control parameters, and define non-dimensional groups to classify the regimes of jetting. Based on the results, we propose the optimal conditions for printing with LIFT technology. PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.731 Issue No: Vol. 880 (2019) • Slickwater hydraulic fracture propagation: near-tip and radial geometry solutions • Authors: Brice Lecampion; Haseeb Zia Pages: 514 - 550 Abstract: We quantify the importance of turbulent flow on the propagation of hydraulic fractures (HF) accounting for the addition of friction reducing agents to the fracturing fluid (slickwater fluid). The addition in small quantities of a high molecular weight polymer to water is sufficient to drastically reduce friction of turbulent flow. The maximum drag reduction (MDR) asymptote is always reached during industrial-like injections. The energy required for pumping is thus drastically reduced, allowing for high volume high rate hydraulic fracturing operations at a reasonable cost. We investigate the propagation of a hydraulic fracture propagating in an elastic impermeable homogeneous solid under a constant (and possibly very high) injection rate accounting for laminar and turbulent flow conditions with or without the addition of friction reducers. We solve the near-tip HF problem and estimate the extent of the laminar boundary layer near the fracture tip as a function of a tip Reynolds number for slickwater. We obtain different propagation scalings and transition time scales. This allows us to easily quantify the growth of a radial HF from the early-time turbulent regime(s) to the late-time laminar regimes. Depending on the material and injection parameters, some propagation regimes may actually be bypassed. We derive both accurate and approximate solutions for the growth of radial HF in the different limiting flow regimes (turbulent smooth, rough, MDR) for the zero fracture toughness limit (corresponding to the early stage of propagation of a radial HF). We also investigate numerically the transition(s) between the early-time MDR regime to the late-time laminar regimes (viscosity and toughness) for slickwater fluid. Our results indicate that the effect of turbulent flow on high rate slickwater HF propagation is limited and matters only at early times (at most during the first minutes for industrial hydraulic fracturing operations). PubDate: 2019-12-10T00:00:00.000Z DOI: 10.1017/jfm.2019.716 Issue No: Vol. 880 (2019) • ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$Re$++++++++++++ ++++++++ ++++&rft.title=Journal+of+Fluid+Mechanics&rft.issn=0022-1120&rft.date=2019&rft.volume=880&rft.spage=551&rft.epage=593&rft.aulast=Sahu&rft.aufirst=Tulsi&rft.au=Tulsi+Ram+Sahu&rft.au=Mohd+Furquan,+Sanjay+Mittal&rft_id=info:doi/10.1017/jfm.2019.699">Numerical study of flow-induced vibration of a circular cylinder with attached flexible splitter plate at low$Re$• Authors: Tulsi Ram Sahu; Mohd Furquan, Sanjay Mittal Pages: 551 - 593 Abstract: Flow-induced vibration (FIV) of an elastically mounted circular cylinder with an attached splitter plate in uniform flow is studied numerically via a stabilized space–time finite element method. The Reynolds number based on the cylinder diameter$D$and the free-stream speed is restricted to 150. The ratio of the density of the body to that of the fluid, for the major part of the study, is 10. Two different reduced speeds are defined to quantify the compliance of the elastic support and flexibility of the splitter plate, respectively:$U_{s}^{\ast }$based on the natural frequency of the spring–mass system and$U_{p}^{\ast }$based on the fundamental natural frequency of the plate. Flow past a stationary cylinder ($U_{s}^{\ast }=0$) with a flexible splitter plate of length$3.5D$is studied at different values of$U_{p}^{\ast }$. The vibration response of the plate exhibits lock-in with various eigenmodes of the plate in different ranges of$U_{p}^{\ast }$. The onsets of these lock-in regions are abrupt and hysteretic. The elastically mounted cylinder, without the splitter plate, undergoes large-amplitude vortex-induced vibration (VIV) for$4
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.699
Issue No: Vol. 880 (2019)

• Steepened Mach waves near supersonic jets: study of azimuthal structure
and generation process using conditional averages
• Authors: Pierre Pineau; Christophe Bogey
Pages: 594 - 619
Abstract: The azimuthal structure and the generation process of steepened acoustic waves are investigated in the near field of temporal round jets at Mach numbers of 2 and 3. Initially, the shear layers of the jets are in a laminar state and display instability waves whose main properties are close to those predicted from linear temporal analysis. Then, they transition to a turbulent state and generate high-intensity Mach waves displaying sharp compressions typical of those recorded for jets producing crackle noise. These waves are first shown to be poorly reproduced when only the axisymmetric mode is considered, but to be well captured with the first five azimuthal modes. Their generation process is investigated by performing conditional averages of the flow and acoustic fields triggered by the detection of intense positive pressure peak close to the jets. No steepened waves are visible in the conditionally averaged pressure profiles when the procedure involves only one azimuthal mode at a time. However, sharp compressions are obtained based on the first five modes taken together. In that case, the steep compressions are correlated over a limited portion of the jet circumference and are steeper as more azimuthal modes are considered. Moreover, a direct link is established between the steepened waves and the supersonic convection of large-scale coherent flow structures located in the supersonic core of the jets. This indicates that these waves constitute an extreme, nonlinear case of Mach wave radiation by these structures. In addition, the capacity of flow structures to generate sharp, steepened waves is related to their shapes. More particularly, flow structures with a large extent in the radial direction are shown to produce stronger and steeper Mach waves than those that are elongated in the flow direction.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.729
Issue No: Vol. 880 (2019)

• Bacterial spinning top
• Authors: Kenta Ishimoto
Pages: 620 - 652
Abstract: We have investigated the dynamics of a monotrichous bacteria cell near a wall boundary, taking elastic hook flexibility into consideration. Combining theoretical linear stability analysis and direct numerical computations via the boundary element method, we have found that the elastohydrodynamic coupling between the hook elasticity and cell rotational motion enables a stable vertical spinning behaviour like a low-Reynolds-number spinning top. The forwardly rotated flagellum, which generates the force exertion pushing towards the cell body, typically destabilizes the vertical upright position and leads to a boundary-following motion. In contrast, the backward rotation of the flagellum, generating a force pulling the cell body, contributes to stable upright behaviour in a large range of hook rigidity. Further numerical investigations have demonstrated that the non-spherical geometry of the cell body and boundary adhesive interactions affect the bacterial dynamics, leading to complex behaviours such as horizontal spinning and unstable vertical spinning motions, both of which are experimentally observed in Pseudomonas aeruginosa bacteria. These results highlight the rich diversity of bacterial surface motility emerging from mechanical boundary interactions coupled with the cell swimming and hook flexibility.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.714
Issue No: Vol. 880 (2019)

• Atomization of acoustically forced liquid sheets
• Authors: Sandip Dighe; Hrishikesh Gadgil
Pages: 653 - 683
Abstract: Atomization of a smooth laminar liquid sheet produced by the oblique impingement of two liquid jets and subjected to transverse acoustic forcing in quiescent ambient is investigated. The acoustic forcing perturbs the liquid sheet perpendicular to its plane, thereby setting up a train of sinuous waves propagating radially outwards from the impingement point. These sheet undulations grow as the wave speed decreases towards the edge of the sheet and the sheet characteristics, like intact length and mean drop size, reduce drastically as compared to the natural breakup. Our observations show that the effect of the acoustic field is perceptible over a continuous range of forcing frequencies. Beyond a certain forcing frequency, called the cutoff frequency, the effect of the external acoustic field ceases. The cutoff frequency is found to be an increasing function of the Weber number. Our measurements of the characteristics of spatially amplifying sinuous waves show that the instabilities responsible for the natural sheet breakup augment in the presence of external forcing. Combining the experimental observations and measurements, we conclude that the linear theory of aerodynamic interaction (Squire’s theory) (Squire, Brit. J. Appl. Phys., vol. 4 (6), 1953, pp. 167–169) predicts the important features of this phenomenon reasonably well.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.732
Issue No: Vol. 880 (2019)

• Numerical study of a turbulent separation bubble with sweep
• Authors: G. N. Coleman; C. L. Rumsey, P. R. Spalart
Pages: 684 - 706
Abstract: Direct numerical simulation (DNS) is used to study a separated and rapidly reattached turbulent boundary layer over an idealized $35^{\circ }$ infinite swept wing. The separation and reattachment are induced by a transpiration profile at fixed distance above the layer, with the pressure gradient applied to a well-defined, fully developed, zero-pressure-gradient (ZPG) collateral state. To isolate the influence of the sweep, results are compared with one of our earlier DNS of an unswept flow, with the same chordwise transpiration distribution and appropriate upstream momentum thickness. The independence principle (IP) traditionally proposed for swept wings, which is exact for laminar flows, is found to be close to valid in some regions (bridging the separation/reattachment zone) and to fail in others (in the ZPG layers upstream and downstream of the separation). This is assessed primarily through the skin friction and integral thicknesses. The regions in which the IP is approximately valid correspond to regions of diminished Reynolds-stress divergence, compared to the pressure-gradient magnitude. The mean-velocity profiles exhibit significant skewing as the flow develops, while the velocity magnitude departs only slightly from the ZPG logarithmic profile, even above the separation zone. Implications for Reynolds-averaged turbulence modelling are discussed.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.736
Issue No: Vol. 880 (2019)

• Gelatine cavity dynamics of high-speed sphere impact
• Authors: Akihito Kiyama; Mohammad M. Mansoor, Nathan B. Speirs, Yoshiyuki Tagawa, Tadd T. Truscott
Pages: 707 - 722
Abstract: We investigate the impact and penetration of a solid sphere passing through gelatine at various impact speeds up to $143.2~\text{m}~\text{s}^{-1}$ . Tests were performed with several concentrations of gelatine. Impacts for low elastic Froude number $\mathit{Fr}_{e}$ , a ratio between inertia and gelatine elasticity, resulted in rebound. Higher $\mathit{Fr}_{e}$ values resulted in penetration, forming cavities with prominent surface textures. The overall shape of the cavities resembles those observed in water-entry experiments, yet they appear in a different order with respect to increasing inertia: rebound, quasi-seal, deep-seal, shallow-seal and surface-seal. Remarkably, similar to the $We$ – $Bo$ phase diagram in water-entry experiments, the elastic Froude number $\mathit{Fr}_{e}$ and elastic Grashof number $\mathit{Gr}_{e}$ (a ratio between gravity and gelatine elasticity) classify all five different phenomena into distinguishable regimes. We find that $\mathit{Fr}_{e}$ can be a good indicator to describe the cavity length $H$ , particularly in the shallow-seal regime. Finally, the evolution of cavity shape, pinch-off depth, and lower cavity radius are investigated for different
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.696
Issue No: Vol. 880 (2019)

• The role of rotary motion on vortices in reverse flow
• Authors: Luke R. Smith; Yong Su Jung, James D. Baeder, Anya R. Jones
Pages: 723 - 742
Abstract: The physics of a rotary wing in forward flight are highly complex, particularly when flow separation is involved. The purpose of this work is to assess the role of three-dimensional (3-D) vortex dynamics, with a focus on Coriolis forces, in the evolution of vortices in the reverse flow region of a rotating wing. High-fidelity numerical simulations were performed to recreate the flow about a representative rotating wing in forward flight. A vorticity transport analysis was performed to quantify and compare the magnitudes of 2-D flow physics, vortex tilting and Coriolis effects in the resulting flow fields. Three-dimensional vortex dynamics was found to have a very small impact on the growth and behaviour of vortices in the reverse flow region; in fact, the rate of vortex growth was successfully modelled using a simple 2-D vortex method. The small role of 3-D physics was attributed to the Coriolis and vortex tilting terms being approximately equal and opposite to one another. This ultimately lead to vortex behaviour that more closely resembled a surging wing as opposed to a conventional rotating wing, a feature unique to the reverse flow region.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.728
Issue No: Vol. 880 (2019)

• Energy budget in internal wave attractor experiments
• Authors: Géraldine Davis; Thierry Dauxois, Timothée Jamin, Sylvain Joubaud
Pages: 743 - 763
Abstract: The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.741
Issue No: Vol. 880 (2019)

• Effect of excitation frequency on flow characteristics around a square
cylinder with a synthetic jet positioned at front surface
• Authors: Yuan Qu; Jinjun Wang, Lihao Feng, Xi He
Pages: 764 - 798
Abstract: The flow over a square cylinder controlled by a slot synthetic jet positioned at the front surface is investigated experimentally at different excitation frequencies. The Reynolds number based on the free-stream velocity and the side length of the square cylinder is 1000. The flow visualization was conducted using the laser-induced fluorescence technique. The velocity fields upstream and downstream of the square cylinder were measured synchronously with the two-dimensional time-resolved particle image velocimetry technique. Both the evolution of vortex structures and the characteristic frequencies of upstream and downstream flow fields are presented. The flow dynamics vary significantly with the excitation frequency at a fixed stroke length. During one excitation cycle, the synthetic jet vortex pair deflects to one side and later swings to the other side at a quite small excitation frequency of $f_{e}/f_{0}=0.6$ , while it only deflects toward one side and does not turn to the other side at $f_{e}/f_{0}=1.0$ . Compared with the natural case, the wake characteristics for the above two cases are not changed much by the synthetic jet adopted. At a moderate excitation frequency of $f_{e}/f_{0}=2.0$ , the synthetic jet deflects upwards and downwards alternatively. The upstream flow field has a dominant frequency identical to half of the excitation frequency. Under the perturbations of the synthetic jet, two wake vortex pairs are formed per shedding cycle with a shedding frequency equal to that of the square cylinder without control. At a higher excitation frequency of $f_{e}/f_{0}=3.4$ , the synthetic jet keeps deflecting to one side, and the upstream flow field is governed by the excitation frequency. The flow separation on the deflected side is suppressed effectively, and no periodic vortex shedding can be observed in the wake. Statistically, the velocity profiles also change with control. The recirculation bubble length in the wake is shortened, and the time-averaged velocity fluctuation is weakened remarkably. The control effects of the synthetic jet and the continuous jet are compared in this paper when placed at the front surface of a square cylinder.
PubDate: 2019-12-10T00:00:00.000Z
DOI: 10.1017/jfm.2019.703
Issue No: Vol. 880 (2019)

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