scholarly journals A Second-Moment Closure Model of Langmuir Turbulence

2013 ◽  
Vol 43 (4) ◽  
pp. 673-697 ◽  
Author(s):  
Ramsey R. Harcourt
Keyword(s):  
Reynolds Stress ◽  
Momentum Flux ◽  
Stokes Drift ◽  
Moment Closure ◽  
Langmuir Turbulence ◽  
Stress Equation ◽  
Second Moment ◽  
Stability Functions ◽  
Second Moment Closure ◽  
The Stability

Abstract The Reynolds stress equation is modified to include the Craik–Leibovich vortex force, arising from the interaction of the phase-averaged surface wave Stokes drift with upper-ocean turbulence. An algebraic second-moment closure of the Reynolds stress equation yields an algebraic Reynolds stress model (ARSM) that requires a component of the vertical momentum flux to be directed down the gradient of the Stokes drift, in addition to the conventional component down the gradient of the ensemble-averaged Eulerian velocity. For vertical and horizontal component fluctuations, the momentum flux must be closed using the form , where the coefficient is generally distinct from the eddy viscosity or eddy diffusivity . Rational expressions for the stability functions , , and are derived for use in second-moment closure models where the turbulent velocity and length scales are dynamically modeled by prognostic equations for and . The resulting second-moment closure (SMC) includes the significant effects of the vortex force in the stability functions, in addition to source terms contributing to the and equations. Additional changes are made to the way in which is limited by proximity to boundaries or by stratification. The new SMC model is tuned to, and compared with, a suite of steady-state large-eddy simulation (LES) solutions representing a wide range of oceanic wind and wave forcing conditions. Comparisons with LES show the modified SMC captures important processes of Langmuir turbulence, but not without notable defects that may limit model generality.

scholarly journals An Improved Second-Moment Closure Model of Langmuir Turbulence

2015 ◽  
Vol 45 (1) ◽  
pp. 84-103 ◽  
Author(s):  
Ramsey R. Harcourt
Keyword(s):  
Surface Defects ◽  
Solid Wall ◽  
Vertical Component ◽  
Force Production ◽  
Reynolds Stress Model ◽  
Moment Closure ◽  
Langmuir Turbulence ◽  
Near Surface ◽  
Second Moment ◽  
Second Moment Closure

AbstractA prior second-moment closure (SMC) model of Langmuir turbulence in the upper ocean is modified by introduction of inhomogeneous pressure–strain rate and pressure–scalar gradient closures that are similar to the high Reynolds number, near-wall treatments for solid wall boundaries. This repairs several near-surface defects in the algebraic Reynolds stress model (ARSM) of the prior SMC by redirecting Craik–Leibovich (CL) vortex force production of turbulent kinetic energy out of the surface-normal vertical component and into a horizontal one, with an associated reduction in near-surface CL production of vertical momentum flux. A surface-proximity function introduces a new closure parameter that is tuned to previous results from large-eddy simulations (LES), and a numerical SMC model based on stability functions from the new ARSM produces improved comparisons with mean profiles of momentum and TKE components from steady-state LES results forced by aligned wind and waves. An examination of higher-order quasi-homogeneous closures and a numerical simulation of Langmuir turbulence away from the boundaries both show the near-surface inhomogeneous closure to be both necessary for consistency and preferable for simplicity.

Modeling the Rapid Part of the Pressure-Diffusion Process in the Reynolds Stress Transport Equation

2004 ◽  
Vol 126 (4) ◽  
pp. 634-641 ◽  
Author(s):  
Kazuhiko Suga
Keyword(s):  
Diffusion Process ◽  
Reynolds Stress ◽  
Moment Closure ◽  
Turbulence Energy ◽  
Second Moment ◽  
Recirculating Flow ◽  
Pressure Diffusion ◽  
Two Component ◽  
Recirculating Flows ◽  
Second Moment Closure

Modeling the pressure-diffusion process is discussed to improve the prediction of turbulent recirculating flows by a second moment closure. Since the recent DNS research of a turbulent recirculating flow by Yao et al. [Theore. Comput. Fluid Dynamics 14 (2001) 337–358] suggested that the pressure-diffusion process of the turbulence energy was significant in the recirculating region, the present study focuses on the rapid part of the process consisting of the mean shear. This rapid pressure-diffusion model is developed for the Reynolds stress equation using the two-component-limit turbulence condition and added to a low Reynolds number two-component-limit full second moment closure for evaluation. Its effects are discussed through applications of turbulent recirculating flows such as a trailing-edge and a back-step flows. Encouraging results are obtained though some margins to be improved still remain.

Assessment of a Reynolds Stress Closure Model for Appendage-Hull Junction Flows

1995 ◽  
Vol 117 (4) ◽  
pp. 557-563 ◽  
Author(s):  
Hamn-Ching Chen
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Moment Closure ◽  
Superior Performance ◽  
Navier Stokes ◽  
Second Moment ◽  
Eddy Viscosity Model ◽  
Second Moment Closure

A multiblock numerical method, for the solution of the Reynolds-Averaged Navier-Stokes equations, has been used in conjunction with a near-wall Reynolds stress closure and a two-layer isotropic eddy viscosity model for the study of turbulent flow around a simple appendage-hull junction. Comparisons of calculations with experimental data clearly demonstrate the superior performance of the present second-order Reynolds stress (second-moment) closure over simpler isotropic eddy viscosity models. The second-moment solutions are shown to capture the most important features of appendage-hull juncture flows, including the formation and evolution of the primary and secondary horseshoe vortices, the complex three-dimensional separations, and interaction among the hull boundary layer, the appendage wake and the root vortex system.

scholarly journals Computation of Flow and Heat Transfer in Rotating Two-Pass Square Channels by a Reynolds Stress Model

1999 ◽  
Author(s):  
Hamn-Ching Chen ◽  
Yong-Jun Jang ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
Secondary Flows ◽  
Moment Closure ◽  
Closure Model ◽  
Second Moment ◽  
Flow And Heat Transfer ◽  
Second Moment Closure ◽  
Near Wall

A multiblock numerical method has been employed for the calculation of three-dimensional flow and heat transfer in rotating two-pass square channels with smooth walls. The finite-analytic method solves Reynolds-Averaged Navier-Stokes equations in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model and a two-layer k–ε isotropic eddy viscosity model. Comparison of second-moment and two-layer calculations with experimental data clearly demonstrate that the secondary flows in rotating two-pass channels have been strongly influenced by the Reynolds stress anisotropy resulting from the Coriolis and centrifugal buoyancy forces as well as the 180° wall curvatures. The near-wall second-moment closure model provides the most reliable heat transfer predictions which agree well with measured data.

Nonlinear second moment closure consistent with shear and strain flows

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 825-831
Author(s):  
Dirk G. Pfuderer ◽  
Claus Eifert ◽  
Johannes Janicka
Keyword(s):  
Moment Closure ◽  
Second Moment ◽  
Second Moment Closure
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