Efficient form of the LANS-\(\alpha \) turbulence model in a primitive-equation ocean model.

*(English)*Zbl 1220.86002Summary: The Lagrangian-averaged Navier-Stokes alpha (LANS-\(\alpha \)) model is a turbulence parameterization that has been shown to capture some of the most important features of high resolution ocean modeling at lower resolution. The LANS-\(\alpha \) model improves turbulence statistics with an additional nonlinear term and a smoothed advecting velocity. In this work we investigate two smoothing techniques-Helmholtz inversions and filters-and their effect on the LANS-\(\alpha \) model’s results and efficiency. We show that convolution filters are an effective smoothing method; that filters and Helmholtz inversions produce similar trends-statistics like higher-resolution non-LANS-\(\alpha \) simulations-as the smoothing parameter is increased; and that the filter is computationally more efficient.

Filters must be constructed such that a pressure-velocity numerical instability is not excited. We show analytically that certain ranges of filter weights are unstable, and confirm this with numerical experiments. Our stability criterion also guarantees that the kinetic energy is well defined, and that the filtered velocity is smoother that the original velocity.

Simulations of LANS-\(\alpha \) using the largest filter (width nine) in the POP primitive-equation ocean model resemble doubled-resolution simulations of standard POP in statistics such as kinetic energy, eddy kinetic energy, and potential temperature fields. The computational cost of adding LANS-\(\alpha \) with this filter is only 27%, as compared to a factor of 8-10 for a doubling of resolution.

Filters must be constructed such that a pressure-velocity numerical instability is not excited. We show analytically that certain ranges of filter weights are unstable, and confirm this with numerical experiments. Our stability criterion also guarantees that the kinetic energy is well defined, and that the filtered velocity is smoother that the original velocity.

Simulations of LANS-\(\alpha \) using the largest filter (width nine) in the POP primitive-equation ocean model resemble doubled-resolution simulations of standard POP in statistics such as kinetic energy, eddy kinetic energy, and potential temperature fields. The computational cost of adding LANS-\(\alpha \) with this filter is only 27%, as compared to a factor of 8-10 for a doubling of resolution.

##### MSC:

86A05 | Hydrology, hydrography, oceanography |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76U05 | General theory of rotating fluids |

##### Keywords:

Lagrangian-averaged Navier-Stokes alpha model; primitive equation ocean model; geophysical turbulence##### Software:

POP
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\textit{M. R. Petersen} et al., J. Comput. Phys. 227, No. 11, 5717--5735 (2008; Zbl 1220.86002)

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##### References:

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