ROME: A Pseudo‐Spectral Algorithm for Time‐Dependent Shear Flows in Stratified Environments

Abstract

Abstract Parameterizations of small‐scale mixing are important in modeling the behavior of the World Ocean. These microstructure mixing processes do not exist in isolation, however, and larger‐scale processes can affect their fluxes, which is an important consideration for general circulation models. We have developed a new pseudo‐spectral hydrodynamic model, the “Rocking Ocean Modeling Environment,” which is able to simulate the effects of some large‐scale processes, such as shear and internal waves. The code induces a time‐dependent shear forcing across a small domain that can accurately resolve the micro‐scale. This configuration presents a challenge for modeling via Fourier‐based algorithms because the typical evolution of such a flow is incompatible with the periodic boundary conditions at the vertical extremities of the computational domain. This complication is addressed by reformulating the governing equations in a new, temporally varying “tilting” coordinate system associated with the background flow as has been done in the past in the field of homogenous turbulence. The code is applied to one such process which is known to show substantial differences in turbulent environments: salt fingers. We simulate salt fingers in the presence of constant and oscillating shear in order to quantify the mixing of heat and salt by these systems under the impacts of large‐scale internal waves. Generally, it is shown that the application of shear can reduce fluxes by a factor of 2 or 3 for typical amplitudes of near‐inertial waves and that the impact of shear decreases as the frequency of the applied shear increases.

Keywords

• double‐diffusive convection
• microstructure
• salt fingering
• shear
• numerical simulations
• pseudospectral methods