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Environmental Fluid Mechanics    [4 followers]  Follow    
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
     ISSN (Print) 1573-1510 - ISSN (Online) 1567-7419
     Published by Springer-Verlag Homepage  [2187 journals]   [SJR: 0.732]   [H-I: 23]
  • Hele-Shaw beach creation by breaking waves: a mathematics-inspired
    • Abstract: Abstract Fundamentals of nonlinear wave-particle interactions are studied experimentally in a Hele-Shaw configuration with wave breaking and a dynamic bed. To design this configuration, we determine, mathematically, the gap width which allows inertial flows to survive the viscous damping due to the side walls. Damped wave sloshing experiments compared with simulations confirm that width-averaged potential-flow models with linear momentum damping are adequately capturing the large scale nonlinear wave motion. Subsequently, we show that the four types of wave breaking observed at real-world beaches also emerge on Hele-Shaw laboratory beaches, albeit in idealized forms. Finally, an experimental parameter study is undertaken to quantify the formation of quasi-steady beach morphologies due to nonlinear, breaking waves: berm or dune, beach and bar formation are all classified. Our research reveals that the Hele-Shaw beach configuration allows a wealth of experimental and modelling extensions, including benchmarking of forecast models used in the coastal engineering practice, especially for shingle beaches.
      PubDate: 2014-04-17
  • Flow and turbulence characteristics in a suburban street canyon
    • Abstract: Abstract Flow and turbulence data collected during a yearlong experiment in a street-canyon configuration located in suburban terrain are analyzed. The instrumentation included 13 sonic anemometers deployed on two masts within the street canyon and on three masts on the building roofs. Flow patterns were classified as being in the wake-interference regime. The in-canyon flow and turbulence structure showed a strong dependence on the above-roof wind direction. While channeling along the street dominates for most wind directions, recirculation patterns develop for narrow sectors with above-roof wind directions perpendicular to the street. For these cross-flow scenarios, different scaling velocities were tested and the influence of upwind fetch and stability was investigated in more detail. Similar to previous studies, our findings confirmed that it is difficult to identify a single velocity scale that unifies both mean flow and turbulence properties inside the canyon. Turbulence properties scaled best with the friction velocity at the upwind roof but scaling with mean wind speeds measured at the upwind roof or at an operational meteorological station 5-km away from the study area, resulted in comparable or even better statistics for the mean flow parameters. Turbulence kinetic energy in the shear-layer region at roof layer varied depending on upwind fetch and stability. As turbulence is transported from the shear layer into the canyon region, the in-canyon turbulence characteristics also varied as a function of these two parameters.
      PubDate: 2014-04-05
  • On thermally forced flows in urban street canyons
    • Abstract: Abstract During sunny days with periods of low synoptic wind, buoyancy forces can play a critical role on the air flow, and thus on the dispersion of pollutants in the built urban environments. Earlier studies provide evidence that when a surface inside an urban street canyon is at a higher temperature than that of local ambient air, buoyancy forces can modify the mechanically-induced circulation within the canyons (i.e., gaps between buildings). The aspect ratio of the urban canyon is a critical factor in the manifestation of the buoyancy parameter. In this paper, computational fluid dynamics simulations are performed on urban street canyons with six different aspect ratios, focusing on the special case where the leeward wall is at a greater temperature than local ambient air. A non-dimensional measure of the influence of buoyancy is used to predict demarcations between the flow regimes. Simulations are performed under a range of buoyancy conditions, including beyond those of previous studies. Observations from a field experiment and a wind tunnel experiment are used to validate the results.
      PubDate: 2014-04-03
  • Influence of seafloor topography on the depositional behavior of
           bi-disperse turbidity currents: a three-dimensional, depth-resolved
           numerical investigation
    • Abstract: Abstract We discuss the results of direct numerical simulations of bi-disperse turbidity currents interacting with a flat bottom wall and a Gaussian bump, respectively, with a focus on the final deposit profiles of the coarse and fine particles. We identify regions of reduced and enhanced deposition, as a result of the presence of the bump. Coarse particles are predominantly deposited towards the sides of the bump, as a result of the bi-section and lateral deflection of the current by the bump. In contrast, for fine particles the influence of the bump is felt more in its far wake. We furthermore employ Lagrangian markers in order to track the coarse and fine particles in the current, and to investigate their deposit locations as function of their location of origin. By comparing the final deposit maps, we observe that the bump has the strongest influence on those particles originating in the central lock sections.
      PubDate: 2014-04-01
  • Effect of initial excess density and discharge on constant flux gravity
           currents propagating on a slope
    • Abstract: Abstract The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, $(g_o^{\prime } Q)^{1/3}$ , which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.
      PubDate: 2014-04-01
  • Dynamics of the head of gravity currents
    • Abstract: Abstract The present work experimentally investigates the dynamics of unsteady gravity currents produced by lock-release of a saline mixture into a fresh water tank. Seven different experimental runs were performed by varying the density of the saline mixture in the lock and the bed roughness. Experiments were conducted in a Perspex flume, of horizontal bed and rectangular cross section, and recorded with a CCD camera. An image analysis technique was applied to visualize and characterize the current allowing thus the understanding of its general dynamics and, more specifically, of the current head dynamics. The temporal evolution of both head length and mass shows repeated stretching and breaking cycles: during the stretching phase, the head length and mass grow until reaching a limit, then the head becomes unstable and breaks. In the instants of break, the head aspect ratio shows a limit of 0.2 and the mass of the head is of the order of the initial mass in the lock. The average period of the herein called breaking events is seen to increase with bed roughness and the spatial periodicity of these events is seen to be approximately constant between runs. The rate of growth of the mass at the head is taken as a measure to assess entrainment and it is observed to occur at all stages of the current development. Entrainment rate at the head decreases in time suggesting this as a phenomenon ruled by local buoyancy and the similarity between runs shows independence from the initial reduced gravity and bed roughness.
      PubDate: 2014-04-01
  • Visualization of the internal flow properties and the material exchange
           interface in an entraining viscous Newtonian gravity current
    • Abstract: Abstract In order to simulate a simple entraining geophysical flow, a viscous Newtonian gravity current is released from a reservoir by a dam-break and flows along a rigid horizontal bed until it meets a layer of entrainable material of finite depth, identical to the current. The goal is to examine the entrainment mechanisms by observing the interaction between the incoming flow and the loose bed. The sole parameter varied is the initial volume of the gravity current, thus altering its height and velocity. The gravity current plunges or spills into the entrainable bed and the velocity of the flow front becomes linear with time. The bed material is directly affected: motion is generated in the fluid far downstream of, and in that lying beneath the encroaching front. Shear bands are identified, separating horizontal flow downstream from flow with a strong vertical component close to the step. Downstream of the step the flow is horizontal and stratified, with no slip on the bottom boundary and very low shear near the surface. Between these two regions may lie transitional zones with linear velocity profiles, separated by horizontal bands of high shear; the number of transitional zones in the cross-section varies with the initial volume of the dam-break.
      PubDate: 2014-04-01
  • Turbulent entrainment into fluid mud gravity currents
    • Abstract: Abstract The entrainment of ambient water into non-Newtonian fluid mud gravity currents was investigated in this study. Constant volume release gravity currents were generated in a lock-exchange tank for a wide range of experimental conditions. A technique similar to the so-called light attenuation technique was used to find the boundary of the current, allowing for the calculation of both temporal and bulk entrainment parameters (in terms of the temporal and bulk entrainment velocities, respectively). It was found that the temporal entrainment velocity is dependent on different parameters in the different propagation phases. The slumping phase begins with an adjustment zone (henceforth, non-established zone) in which the temporal entrainment velocity is not a function of the current front velocity, followed by the established zone in which the temporal entrainment velocity is a function of the current front velocity. This dependence of the temporal entrainment velocity on the current front velocity carries through to the inertia-buoyancy phase. As expected, temporal entrainment velocity in the viscous-buoyancy phase was negligible in comparison to average entrainment velocity in the other phases. It is observed that the temporal entrainment characteristics in the non-established zone is governed by the competition between the entrainment-inhibiting density stratification effects and the entrainment-favouring effects of the Kelvin–Helmholtz billows that are quantified by the Richardson number and the Reynolds number of the gravity current, respectively. In the established zone, Reynolds number effects were observed to dominate over Richardson number effects in dictating temporal entrainment characteristics. A parameterization for the temporal entrainment velocity for non-Newtonian fluid mud gravity currents is developed based upon the experimental observations. This study also found that the bulk entrainment characteristics for the non-Newtonian fluid mud gravity currents can be parameterized by the Newtonian bulk entrainment parameterizations that rely solely on a bulk Richardson number. Interestingly, it was found that the non-Newtonian characteristics of the gravity current have little to no effect on the entrainment of the Newtonian ambient fluid.
      PubDate: 2014-04-01
  • A simplified approach to address turbulence modulation in turbidity
           currents as a response to slope breaks and loss of lateral confinement
    • Abstract: Abstract Turbidity currents traversing canyon-fan systems flow over bed slopes that decrease in the downstream direction. This slope decrease eventually causes turbidity currents to decelerate and enter a net-depositional mode. When the slope decrease is relatively rapid in the downstream direction, the turbidity current undergoes a concomitantly rapid and substantial transition. Similar conditions are found when turbidity currents debouch to fan systems with loss of lateral confinement. In this work a simplified approach to perform direct numerical simulation of continuous turbidity currents undergoing slope breaks and loss of lateral confinement is presented and applied to study turbulence modulation in the flow. The presence of settling sediment particles breaks the top–bottom symmetry of the flow, with a tendency to self-stratify. This self-stratification damps turbulence, particularly near the bottom wall, affecting substantially the flow’s ability to transport sediment in suspension. This work reports results on two different situations: turbidity currents driven by fine and coarser sediment flowing through a decreasing slope. In the case of fine sediment, after the reduction in the slope of the channel, the flow remains turbulent with only a modest influence on turbulence statistics. In the case of coarse sediments, after the change in slope, turbulence is totally suppressed.
      PubDate: 2014-04-01
  • Gravity currents with double stratification: a numerical and analytical
    • Abstract: Abstract We consider high-Reynolds-number Boussinesq gravity current and intrusion systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a rectangular lock; the height ratio of the fluids $H$ , the stratification parameter of the ambient $S$ , and the internal stratification parameter of the current, $\sigma $ , are quite general. We perform two-dimensional Navier–Stokes simulation and compare the results with those of a previously-published one-layer shallow-water model. The results provide insights into the behavior of the system and enhance the confidence in the approximate model while also revealing its limitations. The qualitative predictions of the model are confirmed, in particular: (1) there is an initial “slumping” stage of propagation with constant speed $u_N$ , after which $u_N$ decays with time; (2) for fixed $H$ and $S$ , the increase of $\sigma $ causes a slower propagation of the current; (3) for some combinations of the parameters $H,S, \sigma $ the fluid released from the lock lacks initially (or runs out quickly of) buoyancy “driving power” in the horizontal direction, and does not propagate like a gravity current. There is also a fair quantitative agreement between the predictions of the model and the simulations concerning the spread of the current.
      PubDate: 2014-04-01
  • A review of gravity currents formed by submerged single-port discharges in
           inland and coastal waters
    • Abstract: Abstract In this paper, the authors review the current state of the science on the dynamics of gravity currents generated by positively and negatively buoyant jet discharges from submerged round outfalls (i.e., a point source) in inland and coastal waters. Specifically, this article focuses on describing gravity currents occurring at both the bottom boundary and the free surface of the receiving fluid. The manmade discharge operations generating both types of gravity currents and their significance to sustainability of the surrounding hydro-environment are first described. The authors then summarize the flow regimes characteristics of these discharges before becoming gravity currents and how those flow regimes influence the dynamics of the gravity currents. The gravity current dynamics in the calm receiving waters are then analyzed. This analysis is followed by an analysis of the influence of the hydrodynamic forces (e.g., currents, turbulence, waves) on the dynamics of gravity currents. Finally, the authors review quantitative modeling approaches for different forms of gravity current, and identify the current knowledge gaps and research needs.
      PubDate: 2014-04-01
  • Gravity currents with tailwaters in Boussinesq and non-Boussinesq systems:
           two-layer shallow-water dam-break solutions and Navier–Stokes
    • Abstract: Abstract We consider the dam-break initial stage of propagation of a gravity current of density $\rho _{c}$ released from a lock (reservoir) of height $h_0$ in a channel of height $H$ . The channel contains two-layer stratified fluid. One layer, called the “tailwater,” is of the same density as the current and is of thickness $h_T (< h_0)$ , and the other layer, called the “ambient,” is of different density $\rho _{a}$ . Both Boussinesq ( $\rho _{c}/\rho _{a}\approx 1$ ) and non-Boussinesq systems are investigated. By assuming a large Reynolds number, we can model the flow with the two-layer shallow-water approximation. Due to the presence of the tailwater, the “jump conditions” at the front of the current are different from the classical Benjamin formula, and in some circumstances (clarified in the paper) the interface of the current matches smoothly with the horizontal interface of the tailwater. Using the method of characteristics, analytical solutions are derived for various combinations of the governing parameters. To corroborate the results, two-dimensional direct numerical Navier–Stokes simulations are used, and comparisons for about 80 combinations of parameters in the Boussinesq and non-Boussinesq domains are performed. The agreement of speed and height of the current is very close. We conclude that the model yields self-contained and fairly accurate analytical solutions for the dam-break problem under consideration. The results provide reliable insights into the influence of the tailwater on the propagation of the gravity current, for both heavy-into-light and light-into-heavy motions. This is a significant extension of the classical gravity-current theory from the particular $h_T=0$ point to the $h_T > 0$ domain.
      PubDate: 2014-04-01
  • LES of lock-exchange compositional gravity currents: a brief review of
           some recent results
    • Abstract: Abstract Three-dimensional 3-D Large eddy simulation (LES) has become a powerful tool to investigate evolution and structure of gravity currents, especially for cases (e.g., high Reynolds number flows, flows with massive separation) where 3-D Direct numerical simulation using non-dissipative viscous solvers is computationally too expensive. In this paper we briefly review some important results obtained based on high-resolution 3-D LES of bottom-propagating compositional Boussinesq currents in lock-exchange configurations. LES was used to provide a detailed description of the structure of the current, to discuss the role of the large-scale coherent structures, and to predict the evolution of the front velocity over the different stages of the current propagation. Three main types of lock-exchange flows are considered: (1) currents with a high volume of release (HVR) and a low volume of release (LVR) propagating in a channel with a smooth horizontal bed; (2) HVR and LVR currents propagating in a horizontal channel containing a porous layer; and (3) currents propagating in a horizontal channel containing an array of bottom obstacles (2-D dunes and ribs). The simulations are performed using non-dissipative numerical algorithms and sub-grid scale models that predict a zero eddy viscosity in regions where the turbulence is negligible. Experimental data is used to validate LES predictions. LES results show that in most cases the evolution of the front velocity is consistent with that predicted based on shallow-flow theory. LES flow fields are then used to estimate important quantities (e.g., bed friction velocity, sediment entrainment capacity) that are very difficult to obtain from experiments and to understand how the structure and evolution of the current change because of the additional drag induced by obstacles present within the channel or at the channel bed. The paper also discusses how the evolution and structure of the current change as the Reynolds number is increased to values that are relevant for gravity currents encountered in geosciences and environmental engineering applications.
      PubDate: 2014-04-01
  • Curvature-induced secondary flow in submarine channels
    • Abstract: Abstract The curvature-driven secondary flow in sinuous submarine channels has been a subject of considerable interest and controversy. Here, results from numerical model studies involving saline flow in laboratory-scale channels are presented. A 3D finite volume model of density and turbidity currents is used and simulations are run with different inflow discharges and channel-axis slopes. The simulation results show strong influence of bend wave length, channel gradient, confinement and cross sectional shape on the structure of secondary flow in submarine channels. Major findings are: (i) reversal of secondary flow in submarine channels is strongly associated with a tight bend characterized by a smaller wave length to width ratio or larger wave number, (ii) for the same inflow condition and planform characteristics, a trapezoidal channel cross section is more favorable to secondary flow reversal than a rectangular cross section, (iii) lateral convection resulting from the interaction between in-channel and overbank flows leads to the reversal of secondary flow in an unconfined channel at a lower channel slope than in a confined channel with the same dimensions, (iv) flow discharge has only nominal effect on the secondary flow in submarine channels.
      PubDate: 2014-04-01
  • Waves and turbulence in katabatic winds
    • Abstract: Abstract The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $(\overline{\hbox {Ri}_\mathrm{g} } >1)$ , but sometimes at smaller values $(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $\hbox {z/L}<1$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $\hbox {z/L}>1$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $\overline{\hbox {Ri}_\mathrm{g} }$ was identified. Eddy diffusivities of momentum $\hbox {K}_\mathrm{M}$ and heat $\hbox {K}_\mathrm{H}$ were dependent on wave activities, notably when $\overline{\hbox {Ri}_\mathrm{g} } > 1$ . The ratio $\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$ dropped well below unity at high $\overline{\hbox {Ri}_\mathrm{g} }$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.
      PubDate: 2014-04-01
  • Direct numerical simulations of boundary condition effects on the
           propagation of density current in wall-bounded and open channels
    • Abstract: Abstract The propagation of density current under different boundary conditions is investigated using high resolution direct numerical simulations (DNS). A revised Kleiser and Schumann influence-matrix method is used to treat the general Robin type velocity boundary conditions and the related “tau” error corrections in the numerical simulations. Comparison of the simulation results reveals that the boundary conditions change the turbulent flow field and therefore the propagation of the front. This paper mainly focuses on the effects of boundary conditions and initial depth of the dense fluid. The differences in energy dissipation and overall front development in wall-bounded and open channels are examined. Through DNS simulations, it is evident that with the decrease of initial release depth ratio ( $D/H$ ), the effect of the top boundary becomes less important. In wall-bounded channels, there are three distinctive layers in the vertical distribution of energy dissipation corresponding to the contributions from bottom wall, interface, and top wall, respectively. In open channels, there are only two layers with the top one missing due to the shear free nature of the boundary. It is found that the energy dissipation distribution in the bottom layer is similar for cases with the same $D/H$ ratio regardless the top boundary condition. The simulation results also reveal that for low Reynolds number cases, the energy change due to concentration diffusion cannot be neglected in the energy budget. To reflect the real dynamics of density current, the dimensionless Froude number and Reynolds number should be defined using the release depth $D$ as the length scale.
      PubDate: 2014-04-01
  • Numerical simulation of water mixing and renewals in the Barcelona harbour
           area: the winter season
    • Abstract: Abstract In the present paper, we use numerical simulation to investigate currents, mixing and water renewal in Barcelona harbour under typical conditions of wind forcing for the winter season. This site is of particular importance due to the interplay between touristic and commercial activities, requiring detailed and high-definition studies of water quality within the harbour. We use Large Eddy Simulation (LES) which directly resolves the anisotropic and energetic large scales of motion and parametrizes the small, dissipative, ones. Small-scale turbulence is modelled by the anisotropic Smagorinsky model (ASM) to be employed in presence of large cell anisotropy. The complexity of the harbour is modelled using a combination of curvilinear, structured, non-staggered grid and the immersed boundary method. Boundary conditions for wind and currents at the inlets of the port are obtained from in-situ measurements. Analysis of the numerical results is carried out based on both instantaneous and time-averaged velocity fields. First- and second-order statistics, such as turbulent kinetic energy and horizontal and vertical eddy viscosities, are calculated and their spatial distribution is discussed. The study shows the presence of intense current in the narrow and elongated part of the harbour together with sub-surface along-shore elongated rolling structures (with a time scale of a few hours), and they contribute to the vertical water mixing. Time-averaged velocity field reveals intense upwelling and downwelling zones along the walls of the harbour. The analysis of second-order statistics shows strong inhomogeneity of turbulent kinetic energy and horizontal and vertical eddy viscosities in the horizontal plane, with larger values in the regions characterized by stronger currents. The water renewal within the port is quantified for particular sub-domain regions, showing that the complexity of the harbour is such that certain in-harbour basins have a water renewal of over five days, including the yacht marina area. The LES solution compares favourably with available current-meter data. The LES solution is also compared with a RANS solution obtained in literature for the same site under the same forcing conditions, the comparison demonstrating a large sensitivity of properties to model resolution and frictional parametrization.
      PubDate: 2014-03-27
  • Instabilities in non-rotating and rotating shallow shear flows
    • Abstract: Abstract Numerical simulations for the wave radiation effect on the linear and nonlinear instabilities of rotating and non-rotating shallow flows are conducted using shallow-water equations. At a low convective Froude number, the results of the instabilities is a string of eddies. The coalescence between the neighbouring eddies decides the transverse mixing of the shallow shear flow. At a higher convective Froude number, the development of the shear flow is characterized by wave radiation and the production of shocklets. The radiation of waves in the non-rotating shallow flow is a phenomenon analogous to the radiation of sound in gas dynamics. In the rotating flow on the other hand, the shallow-flow instabilities are intensified due to rotational interference within a window of instability over a narrow range of Rossby numbers.
      PubDate: 2014-03-18
  • Spreading of oil on water in the surface-tension regime
    • Abstract: Abstract The third stage of oil spreading on water, in which surface-tension force promotes spreading against the resisting viscous effect, is investigated using a similarity solution in combination with an integral boundary-layer technique to solve the unidirectional oil-spreading dynamics problem in the last stage of spreading. The thin layer is assumed to be supplied by oil from a bulk boundary. Using a constitutive equation for oil-film surface tension versus oil-film thickness, analytical solutions near the bulk boundary and near the edge are developed. Using the asymptotic solutions to initiate integration, the differential equations for the oil thickness, oil velocity, and boundary-layer profiles are integrated starting from the leading edge and bulk boundary, which after matching provide a complete solution. The results for the spreading-law prefactors are found to differ by about 10 % from published theoretical results using the same constitutive equation. Using an empirical constitutive equation for oil-film surface tension versus distance from the bulk boundary leads to a spreading-law prefactor that is in excellent agreement with the published experimental result and published theoretical work providing and using the same empirical constitutive equation.
      PubDate: 2014-03-06
  • Preface
    • PubDate: 2014-01-18
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