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Implementation of the LANS-$$\alpha$$ turbulence model in a primitive equation ocean model. (English) Zbl 1220.86001
Summary: 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 with 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, snapshots of temperature and velocity fields, and temperature variance. 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) have an effective Rossby deformation radius that is larger than the deformation radius of the unmodeled equations; and (3) reduce the propagation speeds of the modeled Rossby and gravity waves relative to the unmodeled waves at high wave numbers.

##### MSC:
 86A05 Hydrology, hydrography, oceanography 76D05 Navier-Stokes equations for incompressible viscous fluids 76U05 General theory of rotating fluids
POP
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