论文标题
分层剪切流中密度阶梯的湍流破坏
Turbulent disruption of density staircases in stratified shear flows
论文作者
论文摘要
已广泛研究了由分层和湍流引起的阶梯状“密度楼梯”分布的形成，并且可以通过通过“ Phillips机制”增加分层而增加了湍流通量的降低，可以通过足够稳定的分层湍流来解释。但是，除了在双重扩散过程很重要的区域，导致热盐阶梯酶的区域外，这种密度阶梯通常不经常观察到。使用降低的阶模型来进化速度和密度梯度，我们分析了分层和剪切的湍流中的楼梯形成。在假定惯性缩放$ε\ sim u^3/l $的假设下，动能耗散率$ε$，其中$ u $和$ u $和$ l $是特征性的速度和长度尺度，我们确定批量richardson号码$ \ \ \ \ \ \ text {ri} _ {ri} _ {b} $ and the prand $ \ prand $ \ prand prand $ {prand prand}可以潜在地形成并表明菲利普斯机制仅在足够小的湍流prandtl数字的极限下生存。对于相关的海洋参数，发现系统不容易到楼梯的一系列湍流prandtl数字是$ \ text {pr} _t \ simeq 0.5-0.7 $。由于几项研究表明，稳定分层的湍流和海洋内饰中的湍流prandtl数通常高于此阈值，因此该结果支持经验观察，即在存在环境湍流的情况下，海洋室内不受欢迎的楼梯。我们还表明，我们的分析对于$ε$（例如更强大的缩放$ε\ sim \ sim u^{2} n $，我们的分析是可靠的，其中$ n $是浮力频率的特征值），从而支持我们的剪切式主导和浮力为浮力的动力和强度的湍流机制以及稳固的分层和强大的分层。
Formation of step-like 'density staircase' distributions induced by stratification and turbulence has been widely studied and can be explained by the 'instability' of a sufficiently strongly stably stratified turbulent flow due to the decrease of the turbulent density flux with increasing stratification via the 'Phillips mechanism'. However, such density staircases are not often observed in ocean interiors, except in regions where double diffusion processes are important, leading to thermohaline staircases. Using reduced order models for the evolution of velocity and density gradients, we analyse staircase formation in stratified and sheared turbulent flows. Under the assumption of inertial scaling $ε\sim U^3/L$ for the kinetic energy dissipation rate $ε$, where $U$ and $L$ are characteristic velocity and length scales, we determine ranges of bulk Richardson numbers $\text{Ri}_{b}$ and turbulent Prandtl numbers $\text{Pr}_{T}$ for which staircases can potentially form and show that the Phillips mechanism only survives in the limit of sufficiently small turbulent Prandtl numbers. For relevant oceanic parameters, a range of turbulent Prandtl numbers above which the system is not prone to staircases is found to be $\text{Pr}_T \simeq 0.5 - 0.7$. Since several studies indicate that the turbulent Prandtl number in stably stratified turbulence and in ocean interiors is usually above this threshold, this result supports the empirical observation that staircases are not favoured in ocean interiors in the presence of ambient turbulence. We also show that our analysis is robust to other scalings for $ε$ (such as the more strongly stratified scaling $ε\sim U^{2}N$, where $N$ is a characteristic value of the buoyancy frequency), supporting our results in both shear-dominated and buoyancy-dominated turbulent regimes as well as in weakly and strongly stratified regimes.
