Low Rossby limiting dynamics for stably stratified flow with Finite Froude number

On the Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence

A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The Karman-Howarth equation for the dynamics of the two-point correlation function of potential vorticity reveals the possibility of inertial-range dynamics in certain regimes in the Rossby, Froude, Prandtl and Reynolds number parameters. For the case of large Rossby and Froude numbers, and for the case of quasi-geostrophic dynamics, a linear scaling law with 2/3 prefactor is derived for the third-order mixed correlation between po…

稳定层化湍流中的不确定性增长

Uncertainty Growth in Stably Stratified Turbulence

研究了统计稳态稳定层化三维湍流中的不确定性增长和混沌动力学，通过双模拟和去相关诊断量化初始微扰的发散，发现层化强度增加会单调降低李雅普诺夫指数，但不确定性增长仍保持与各向同性湍流相似的时间序列。

剪切驱动分层湍流中的能量传递、间歇性和混合

Energy transfer, Intermittency and Mixing in Shear-Driven Stratified Turbulence

通过直接数值模拟研究不同弗劳德数下分层剪切湍流的能量传递、间歇性和混合，发现中间分层区间出现垂直剪切水平流并增强混合，能谱正向传递为主，强分层增强间歇性，混合系数约为0.1。

Bounds on solutions of the rotating, stratified, incompressible, non-hydrostatic, three-dimensional Boussinesq equations

We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations describe the interplay between velocity and buoyancy in a rotating frame. A hierarchy of dynamical variables is introduced whose members $Ω_{m}(t)$ ($1 \leq m < \infty$) are made up from the respective sum of the $L^{2m}$-norms of vorticity and the density gradient. Each $Ω_{m}(t)$ has a lower bound in terms of the inverse Rossby number, $Ro^{-1}$, that turns out to be crucial to the argument. For convenience, the $Ω_{m}$…