Simulation of the Arctic—North Atlantic Ocean Circulation with a Two-Equation K-Omega Turbulence Parameterization

Sergey Moshonkin,Vladimir Zalesny,Anatoly Gusev

doi:10.3390/jmse6030095

Sergey Moshonkin, Vladimir Zalesny + Show 1 more

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https://doi.org/10.3390/jmse6030095

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Abstract

The results of large-scale ocean dynamics simulation taking into account the parameterization of vertical turbulent exchange are considered. Numerical experiments were carried out using k − ω turbulence model embedded to the Institute of Numerical Mathematics Ocean general circulation Model (INMOM). Both the circulation and turbulence models are solved using the splitting method with respect to physical processes. We split k − ω equations into the two stages describing transport-diffusion and generation-dissipation processes. At the generation-dissipation stage, the equation for ω does not depend on k. It allows us to solve both turbulence equations analytically that ensure high computational efficiency. The coupled model is used to simulate the hydrophysical fields of the North Atlantic and Arctic Oceans for 1948–2009. The model has a horizontal resolution of 0.25 ∘ and 40 σ -levels along the vertical. The numerical results show the model’s satisfactory performance in simulating large-scale ocean circulation and upper layer dynamics. The sensitivity of the solution to the change in the coefficients entering into the analytical solution of the k − ω model which describe the influence of some physical factors is studied. These factors are the climatic annual mean buoyancy frequency (AMBF) and Prandtl number as a function of the Richardson number. The experiments demonstrate that taking into account the AMBF improves the reproduction of large-scale ocean characteristics. Prandtl number variations improve the upper mixed layer depth simulation.

Highlights

The simulation of momentum, heat and salt vertical turbulent exchange is very important for ocean general circulation models (OGCMs)
The aims of the paper are as follows: 1. to present a new splitting algorithm for solving k − ω turbulence equations that allows to reduce the complete system to the stages of transport-diffusion and generation-dissipation; 2. to find an analytical solution of k − ω equations at the generation-dissipation splitting stage that is impossible for k − kl and k − closures; 3. to demonstrate possibilities of controlling the obtained analytical solution of k − ω equations through its coefficients by means of different physical factors
Our experiments showed the computational efficiency of the algorithm for forward simulation of Arctic—North Atlantic general circulation

Summary

Introduction

The simulation of momentum, heat and salt vertical turbulent exchange is very important for ocean general circulation models (OGCMs). In OGCMs, vertical mixing is parameterized using a second-order differential operator with variable exchange coefficients KU, KT and KS [1,2,3,4,5]. The first approach is more simple and efficient from the computational point of view. This approach is traditionally used in numerical simulation of large-scale ocean circulation [6]. When using the second approach, special attention should be paid to the construction of an effective numerical technique for solving turbulence equations

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