Implementation of the LANS-alpha turbulence model in a primitive equation ocean model

Abstract

This paper presents the first numerical implementation and tests of the Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model in a primitive equation ocean model. The ocean model in which we work is the Los Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of LANS-alpha as POP-alpha. Two versions of POP-alpha are presented: the full POP-alpha algorithm is derived from the LANS-alpha primitive equations, but requires a nested iteration that makes it too slow for practical simulations; a reduced POP-alpha algorithm is proposed, which lacks the nested iteration and is two to three times faster than the full algorithm. The reduced algorithm does not follow from a formal derivation of the LANS-alpha model equations. Despite this, simulations of the reduced algorithm are nearly identical to the full algorithm, as judged by globally averaged temperature and kinetic energy, and snapshots of temperature and velocity fields. Both POP-alpha algorithms can run stably with longer timesteps than standard POP. Comparison of implementations of full and reduced POP-alpha algorithms are made within an idealized test problem that captures some aspects of the Antarctic Circumpolar Current, a problem in which baroclinic instability is prominent. Both POP-alpha algorithms produce statistics that resemble higher-resolution simulations of standard POP. A linear stability analysis shows that both the full and reduced POP-alpha algorithms benefit from the way the LANS-alpha equations take into account the effects of the small scales on the large. Both algorithms (1) are stable; (2) make the Rossby Radius effectively larger; and (3) slow down Rossby and gravity waves.

Submitted to J. Computational Physics March 21, 2007

References in corpus (8)

• The Camassa-Holm equations as a closure model for turbulent channel flow
• The Navier-Stokes-alpha model of fluid turbulence
• Regularization modeling for large-eddy simulation
• Direct Numerical Simulations of the Navier-Stokes Alpha Model
• Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion
• Efficient form of the LANS-alpha turbulence model in a primitive-equation ocean model
• The Euler-Poincare Equations in Geophysical Fluid Dynamics
• A Dynamic model for the Lagrangian Averaged Navier-Stokes-$\alpha$ Equations

Cited by in corpus (13)

• Analysis of a General Family of Regularized Navier-Stokes and MHD Models
• A framework for the evaluation of turbulence closures used in mesoscale ocean large-eddy simulations
• Rotating shallow water flow under location uncertainty with a structure-preserving discretization
• Efficient form of the LANS-alpha turbulence model in a primitive-equation ocean model
• Stochastic Closures for Wave--Current Interaction Dynamics
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• A consistent stochastic large-scale representation of the Navier-Stokes equations
• Stochastic Variational Formulations of Fluid Wave-Current Interaction
• The Equivalence of the Lagrangian-Averaged Navier-Stokes-α Model and the Rational LES model in Two Dimensions
• Geometric Lagrangian averaged Euler-Boussinesq and primitive equations
• A derivation of the NS-alpha model and preliminary application to plane channel flow
• On spectral scaling laws for averaged turbulence on the sphere
• A turbulence model for smoothed particle hydrodynamics