Systems of Hydrodynamic Type that Approximate Two-Dimensional Ideal Fluid Equations

The problem of modelling 2D isotropic turbulence in a periodic rectangular domain excited by the forcing pattern of prescribed spatial scale is considered. This setting could be viewed as the simplest analogue of the large scale quasi-2D circulation of the ocean and the atmosphere. Since the direct numerical simulation (DNS) of this problem is usually not possible due to the high computational costs we explore several possibilities to construct coarse approximation models and corresponding subgrid closures (deterministic or stochastic). The necessity of subgrid closures is especially important when the forcing scale is close to the cutoff scale of the coarse model that leads to the significant weakening of the inverse energy cascade and large scale component of the system dynamics. The construction of closures is based on the a priori analysis of the DNS solution and takes into account the form of a spatial approximation scheme used in a particular coarse model. We show that the statistics of a coarse model could be significantly improved provided a proper combination of deterministic and stochastic closures is used. As a result we are able to restore the shape of the energy spectra of the model. In addition the lagged auto correlations of the model solution as well as its sensitivity to external perturbations fit the characteristics of the DNS model much better.

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2D turbulence closures for the barotropic jet instability simulation

Perezhogin

2020

Russian Journal of Numerical Analysis and Mathematical Modelling

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In the present work the possibility of turbulence closure applying to improve barotropic jet instability simulation at coarse grid resolutions is considered. This problem is analogous to situations occurring in eddy-permitting ocean models when Rossby radius of deformation is partly resolved on a computational grid. We show that the instability is slowed down at coarse resolutions. As follows from the spectral analysis of linearized equations, the slowdown is caused by the small-scale normal modes damping arising due to numerical approximation errors and nonzero eddy viscosity. In order to accelerate instability growth, stochastic and deterministic kinetic energy backscatter (KEBs) parameterizations and scale-similarity model were applied. Their utilization led to increase of the growth rates of normal modes and thus improve characteristic time and spatial structure of the instability.

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Systems of Hydrodynamic Type that Approximate Two-Dimensional Ideal Fluid Equations

Cited by 3 publications

References 20 publications

Dynamic Meteorology Research in Russia, 2015–2018

Dynamic Meteorology Research in Russia, 2015–2018

Stochastic and deterministic kinetic energy backscatter parameterizations for simulation of the two-dimensional turbulence

2D turbulence closures for the barotropic jet instability simulation

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