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arXiv · 2109.13435

Rate of the enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere

Yasunori Maekawa·Tatsu-Hiko Miura
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Abstract

We study the enhanced dissipation for the two-jet Kolmogorov type flow which is a stationary solution to the Navier-Stokes equations on the two-dimensional unit sphere given by the zonal spherical harmonic function of degree two. Based on the pseudospectral bound method developed by Ibrahim, Maekawa, and Masmoudi [15] and a modified version of the Gearhart-Pr\"uss type theorem shown by Wei [48], we derive an estimate for the resolvent of the linearized operator along the imaginary axis and show that a solution to the linearized equation rapidly decays at the rate $O(e^{-\sqrt{\nu}\,t})$ when the viscosity coefficient $\nu$ is sufficiently small as in the case of the plane Kolmogorov flow.

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Yasunori Maekawa, Tatsu-Hiko Miura. 2021-09-28. Rate of the enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere. https://doi.org/10.1007/s00021-022-00718-y

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