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Seminar «Mathematical modeling of geophysical processes: direct and inverse problems»

Seminar Organizing Committee


Corr. RAS V.N.Lykosov (Marchuk Institute of Numerical Mathematics of RAS, RCC MSU)

Doctor of Physics and Mathematics V.M. Stepanenko (RCC MSU, Geographical Faculty of Moscow State University)


A.V.Debolsky (RCC MSU, A.M. Obukhov Institute of Atmospheric Physics of RAS).

Perezhogin P.A. Marchuk Institute of Numerical Mathematics of RAS


The report is devoted to the development of parametrizations of "subgrid" quasi-two-dimensional turbulence and their testing in model problems and in the NEMO ocean model. Various regimes of flow of a two-dimensional fluid are studied, in which the largest deviations of the statistical characteristics of the simulated turbulence from the theoretically expected ones are observed due to the presence of approximation errors. In particular, it is shown that in forced two-dimensional turbulence, excited in a stochastic manner near the grid scale, the reverse energy cascade is poorly reproduced. For this case, an a priori analysis of subgrid forces (the interaction between resolvable and unresolvable scales) was carried out taking into account the numerical approximations of the advective term. It is shown that subgrid forces return kinetic energy on the scale of the inertial interval of the reverse energy cascade. Two parametrizations of OPEC (reverse redistribution of kinetic energy) in Fourier space were constructed, which reproduce the spectrum of energy generation by subgrid forces: stochastic parametrization (based on an autoregressive process) and a negative viscosity model. Both parameterizations are capable of reconstructing the reverse energy cascade at a coarse spatial resolution. The OPEC parametrizations were implemented in the NEMO ocean model and investigated at eddy admitting resolution (1/4 degree). It is shown that OPEC parameterizations are able to increase the vortex activity, restore the meridional heat flux, meridional overturning circulation, and reduce the errors in the mean near-surface fields.

This work was carried out at the INM RAS with the support of the Russian Foundation for Basic Research (19-35-90023, 18-05-60184) and the Moscow Center of Fundamental and Applied Mathematics (Ministry of Education and Science of Russia, agreement 075-15-2019-1624).

 Due to the self-isolation regime, the seminar will be held in the form of a webinar on the Zoom platform.

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For communication on all issues related to the work of the seminar, please contact the Scientific Secretary Andrey Vladimirovich Debolsky at