Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere
Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere
复制标题
单位球面上双射流柯尔莫哥洛夫型流的增强耗散率
DOI：
10.1007/s00021-022-00718-y
复制
发表时间：
2022
影响因子：
1.3
通讯作者：
Miura Tatsu-Hiko
中科院分区：
文献类型：
--
作者：
Maekawa Yasunori;Miura Tatsu-Hiko
研究了二维单位球面上由二次带状球谐函数给出的定常解的双喷流Kolmogorov型流动的增强耗散。基于Ibrahim，Maekawa和Masoudi提出的伪谱有界法和魏提出的修正的Gearhart-Prüss型定理，我们得到了线性化算子沿虚轴方向预解的估计，并证明了当粘性系数足够小时，线性化方程的解在速度上迅速衰减.
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 and a modified version of the Gearhart–Prüss type theorem shown by Wei , 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 ratewhen the viscosity coefficientis sufficiently small as in the case of the plane Kolmogorov flow.