Large-eddy simulation of free-surface turbulence

In this paper we investigate the large-eddy simulation (LES) of the interaction between a turbulent shear flow and a free surface at low Froude numbers. The benchmark flow field is first solved by using direct numerical simulations (DNS) of the Navier–Stokes equations at fine (1282 × 192 grid) resolution, while the LES is performed at coarse resolution. Analysis of the ensemble of 25 DNS datasets shows that the amount of energy transferred from the grid scales to the subgrid scales (SGS) reduces significantly as the free surface is approached. This is a result of energy backscatter associated with the fluid vertical motions. Conditional averaging reveals that the energy backscatter occurs at the splat regions of coherent hairpin vortex structures as they connect to the free surface. The free-surface region is highly anisotropic at all length scales while the energy backscatter is carried out by the horizontal components of the SGS stress only. The physical insights obtained here are essential to the efficacious SGS modelling of LES for free-surface turbulence. In the LES, the SGS contribution to the Dirichlet pressure free-surface boundary condition is modelled with a dynamic form of the Yoshizawa (1986) expression, while the SGS flux that appears in the kinematic boundary condition is modelled by a dynamic scale-similarity model. For the SGS stress, we first examine the existing dynamic Smagorinsky model (DSM), which is found to capture the free-surface turbulence structure only roughly. Based on the special physics of free-surface turbulence, we propose two new SGS models: a dynamic free-surface function model (DFFM) and a dynamic anisotropic selective model (DASM). The DFFM correctly represents the reduction of the Smagorinsky coefficient near the surface and is found to capture the surface layer more accurately. The DASM takes into account both the anisotropy nature of free-surface turbulence and the dependence of energy backscatter on specific coherent vorticity mechanisms, and is found to produce substantially better surface signature statistics. Finally, we show that the combination of the new DFFM and DASM with a dynamic scale-similarity model further improves the results.

[1]  Leonhard Kleiser,et al.  Subgrid‐scale energy transfer in the near‐wall region of turbulent flows , 1994 .

[2]  Maria Vittoria Salvetti,et al.  A Priori Tests of a New Dynamic Subgrid-Scale Model for Finite-Difference Large-Eddy Simulations , 1995 .

[3]  P. Moin,et al.  A dynamic localization model for large-eddy simulation of turbulent flows , 1995, Journal of Fluid Mechanics.

[4]  C. Meneveau,et al.  Scale-Invariance and Turbulence Models for Large-Eddy Simulation , 2000 .

[5]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[6]  Kunio Kuwahara,et al.  Direct numerical simulation of three‐dimensional open‐channel flow with zero‐shear gas–liquid interface , 1993 .

[7]  J. Ferziger,et al.  Evaluation of subgrid-scale models using an accurately simulated turbulent flow , 1979, Journal of Fluid Mechanics.

[8]  P. Moin,et al.  A dynamic subgrid‐scale model for compressible turbulence and scalar transport , 1991 .

[9]  C. Meneveau,et al.  On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet , 1994, Journal of Fluid Mechanics.

[10]  Lian Shen,et al.  Turbulent diffusion near a free surface , 2000, Journal of Fluid Mechanics.

[11]  C. G. Speziale.  Galilean invariance of subgrid-scale stress models in the large-eddy simulation of turbulence , 1985, Journal of Fluid Mechanics.

[12]  Wei Liu,et al.  Energy transfer in numerically simulated wall‐bounded turbulent flows , 1994 .

[13]  P. Moin,et al.  Subgrid-scale backscatter in turbulent and transitional flows , 1991 .

[14]  A. Leonard.  Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows , 1975 .

[15]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[16]  Parviz Moin,et al.  Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence , 1995, Journal of Fluid Mechanics.

[17]  Ronald Adrian,et al.  Subgrid‐scale energy transfer and near‐wall turbulence structure , 1996 .

[18]  R. A. Antonia,et al.  Conditional Sampling in Turbulence Measurement , 1981 .

[19]  John Kim,et al.  On the structure of wall‐bounded turbulent flows , 1983 .

[20]  Laurie T. Fialkowski,et al.  Large-Wave Simulation (LWS) of Free-Surface Flows Developing Weak Spilling Breaking Waves , 2000 .

[21]  Valerio De Angelis,et al.  Direct numerical simulation of near-interface turbulence in coupled gas-liquid flow , 1996 .

[22]  Ron F. Blackwelder,et al.  On the wall structure of the turbulent boundary layer , 1976, Journal of Fluid Mechanics.

[23]  Steven A. Orszag,et al.  Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow , 1995, Journal of Fluid Mechanics.

[24]  M. Salvetti,et al.  Large-eddy simulation of free-surface decaying turbulence with dynamic subgrid-scale models , 1997 .

[25]  N. Mangiavacchi.  Dynamics of a turbulent jet interacting with a free surface. , 1994 .

[26]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[27]  A. Volodin,et al.  Stability of an incompressible two-dimensional wake , 1983 .

[28]  J. Koseff,et al.  A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows , 1993 .

[29]  David T. Walker,et al.  Shear-free turbulence near a flat free surface , 1996, Journal of Fluid Mechanics.

[30]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[31]  梶島 岳夫.  乱流の数値シミュレーション = Numerical simulation of turbulent flows , 2003 .

[32]  G. Yadigaroglu,et al.  Numerical investigation of the entrainment and mixing processes in neutral and stably-stratified mixing layers , 1999 .

[33]  J. Ferziger,et al.  Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows , 1983 .

[34]  Xiang Zhang,et al.  The surface layer for free-surface turbulent flows , 1999, Journal of Fluid Mechanics.

[35]  Robert L. Street,et al.  On Simulation of Turbulent Nonlinear Free-Surface Flows , 1999 .

[36]  J. Andrzej Domaradzki,et al.  Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence , 1990 .

[37]  A. Yoshizawa.  Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling , 1986 .

[38]  Sanjoy Banerjee,et al.  A numerical study of free-surface turbulence in channel flow , 1995 .

[39]  T. F. Swean,et al.  Length scales and the energy balance for turbulence near a free surface , 1993 .