THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS  

作　　者：许兰喜 关芳芳 Lanxi XU;Fangfang GUAN(College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing,100029,China)

机构地区：[1]College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing,100029,China

出　　处：《Acta Mathematica Scientia》2024年第3期1036-1045,共10页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(21627813)。

摘　　要：The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

关 键 词：plane parallel shear flows energy method energy functional nonlinear stability Reynolds number 

分 类 号：O35[理学—流体力学]