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Special Section Articles

# Large Eddy Simulations of a Stratified Shear Layer

[+] Author and Article Information
Hieu T. Pham

Mechanical and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92092
e-mail: h8pham@ucsd.edu

Sutanu Sarkar

Fellow ASME
Mechanical and Aerospace Engineering,
University of California,
San Diego,
La Jolla, CA 92092
e-mail: sarkar@ucsd.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 2, 2013; final manuscript received December 15, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060913 (Apr 28, 2014) (11 pages) Paper No: FE-13-1287; doi: 10.1115/1.4026416 History: Received May 02, 2013; Revised December 15, 2013

## Abstract

The performance of the large eddy simulation (LES) approach in predicting the evolution of a shear layer in the presence of stratification is evaluated. The LES uses a dynamic procedure to compute subgrid model coefficients based on filtered velocity and density fields. Two simulations at different Reynolds numbers are simulated on the same computational grid. The fine LES simulated at a low Reynolds number produces excellent agreement with direct numerical simulations (DNS): the linear evolution of momentum thickness and bulk Richardson number followed by an asymptotic approach to constant values is correctly represented and the evolution of the integrated turbulent kinetic energy budget is well captured. The model coefficients computed from the velocity and the density fields are similar and have a value in range of $0.01-0.02$. The coarse LES simulated at a higher Reynolds number Re = 50,000 shows acceptable results in terms of the bulk characteristics of the shear layer, such as momentum thickness and bulk Richardson number. Analysis of the turbulent budgets shows that, while the subgrid stress is able to remove sufficient energy from the resolved velocity fields, the subgrid scalar flux and thereby the subgrid scalar dissipation are underestimated by the model.

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## Figures

Fig. 1

Snapshots of the density field at various times in the DNS of a stratified shear layer [7]. Development of Kelvin–Helmholtz billows in (a) breakdown of the billows into turbulence in (b) and the late-time layer of decaying turbulence in (c) are important characteristics of a turbulent stratified shear layer.

Fig. 2

Evolution of length scales at center of the shear layer in the LES models: (a) Kolmogorov scale η and Ozmidov scale LO and (b) energy-containing scale LEN and Ellison scale LE. Solid lines and dash lines denote the fine (low-Re) and coarse (high-Re) LES models, respectively. The scales are normalized by the horizontal grid spacing Δx=0.12.

Fig. 3

Comparison of wavenumber spectra between the DNS and the LES cases at t=180 and z=0: (a) velocity fields and (b) density fields. The energy spectrum are plotted against the streamwise wavenumber kx.

Fig. 4

Snapshots of the density field at various times in the fine (low-Re) LES. Similar to results of DNS, the LES captures the Kelvin–Helmholtz billows, their breakdown into turbulence, and the decay of turbulence.

Fig. 5

Temporal evolution of (a) the momentum thickness δθ and (b) the bulk Richardson number Rib is similar between the DNS and the fine (low-Re) LES

Fig. 6

Comparison of integrated turbulent kinetic energy budget over the computational domain in (a) the DNS and (b) the fine (low-Re) LES

Fig. 7

Budgets of (a) the turbulent kinetic energy and (b) the density variance 〈ρ'2〉 at t=120 in the fine (low-Re) LES

Fig. 8

(a) Dynamic subgrid coefficient Cd and (b) horizontally averaged eddy viscosity at various times in the fine (low-Re) LES

Fig. 9

(a) Dynamic subgrid coefficient Cθ and (b) horizontally averaged eddy diffusivity at various times in the fine (low-Re) LES

Fig. 10

Snapshots of the density field at various times in the coarse (high-Re) LES. The development of Kelvin–Helmholtz billows and the evolution of turbulence are well captured.

Fig. 11

Comparison of (a) the momentum thickness δθ and (b) the bulk Richardson number Rib between the fine (low-Re) and the coarse (high-Re) LES cases

Fig. 12

Budgets of (a) the turbulent kinetic energy K and (b) the density variance 〈ρ'2〉 at t=120 in the coarse (high-Re) LES

Fig. 13

(a) Difference in the eddy viscosity and eddy diffusivity at z=0 between the fine (low-Re) and coarse (high-Re) LES cases and (b) evolution of squared shear rate S2 and squared buoyancy frequency N2 at the same location

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