NUMERICAL STUDY OF THE TRANSIENT MODES OF THE KOLMOGOROV FLOW IN A SQUARE CELL

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Abstract

The problem of two-dimensional flow of a viscous slightly compressible liquid in a square cell under excitation by a static external force periodic in space (Kolmogorov flow) is considered. A new method for determining the flow structure based on the analysis of the vorticity field at various points in time is presented. This method is used to classify the types of flows whose characteristics are obtained by numerical modeling. The main flow modes are distinguished depending on the values of the bottom friction coefficient and the pumping force: laminar, chaotic and vortex modes. Transitional flow types are studied separately: the quasi-periodic regime, which arises through a sequence of bifurcations during the change of laminar and chaotic flow modes, and the regime of alternation, which occurs during the transition from chaotic to vortex flow. Phase diagrams in the space of the amplitude of the external force — the bottom friction coefficient are constructed, making it possible to classify the type of flow according to the values of the bottom friction coefficient and the pumping force.

About the authors

A. O Posudnevskaya

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences; Institute of Design Automation of the Russian Academy of Sciences

Email: posudnevskaia.ao@phystech.edu
Chernogolovka, Russia; Moscow, Russia

S. V Fortova

Institute of Design Automation of the Russian Academy of Sciences

Moscow, Russia

A. N Doludenko

Joint Institute of High Temperatures of the Russian Academy of Sciences

Moscow, Russia

I. V Kolokolov

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences

Chernogolovka, Russia

V. V Lebedev

L.D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences

Chernogolovka, Russia

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