Turbulent diffusion in the geostrophic inverse cascade
Turbulent diffusion in the geostrophic inverse cascade
复制标题
地转逆级联中的湍流扩散
DOI：
10.1017/s0022112002001763
复制
发表时间：
2002
影响因子：
3.7
通讯作者：
G. Vallis
中科院分区：
文献类型：
--
作者：
K. S. Smith;Giulio Boccaletti;C. Henning;I. Marinov;C. Tam;I. Held;G. Vallis
在地球大气和海洋中的大规模横向湍流热传输问题的部分动机，部分由湍流传输本身的问题，我们试图更好地了解各种类型的充分发展的二维湍流平流被动示踪剂的运输。考虑的湍流类型对应于流函数和平流场之间的各种关系。每种湍流都有两个二次不变量，并且每一个都可以形成一个逆叶栅。这些叶栅可以通过例如摩擦、背景涡度梯度或平均温度梯度来改变或停止。我们专注于三个物理上可实现的情况下：经典的二维湍流，表面准地转湍流，浅水准地转湍流在尺度大的变形半径相比。在每个模型中，我们假设示踪剂方差由大尺度平均示踪剂梯度维持，而湍流能量通过随机强迫在小尺度产生，并通过线性阻力耗散。我们预测的频谱形状，涡尺度和平衡能量所造成的逆级联，并使用预期的速度和长度尺度来预测综合示踪剂通量。当线性阻力使叶栅停止时，所得到的扩散系数是阻力系数的递减函数，但在每种情况下具有不同的依赖性。当β显著时，我们发现示踪剂混合尺度与含能（或喷流）尺度之间存在明显区别，前者取决于β，但几乎与阻力无关，后者由阻力系数和β的组合设定。我们的预测是通过高分辨率的光谱模拟测试。我们发现，在所有情况下，被动标量扩散梯度下降的扩散系数是很好地预测从湍流现象获得的混合长度和速度尺度的估计。
Motivated in part by the problem of large-scale lateral turbulent heat transport in the Earth's atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed two-dimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical two-dimensional turbulence, surface quasi-geostrophic turbulence, and shallow-water quasi-geostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a large-scale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes. When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When β is significant, we find a clear distinction between the tracer mixing scale, which depends on β but is nearly independent of drag, and the energy-containing (or jet) scale, set by a combination of the drag coefficient and β. Our predictions are tested via high- resolution spectral simulations. We find in all cases that the passive scalar is diffused down-gradient with a diffusion coefficient that is well-predicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.