大尺度气旋性涡旋中眼的形成
Formation of eyes in large-scale cyclonic vortices
摘要：
我们提出了稳定的，层流，轴对称对流的Boussinesq流体在一个浅的，旋转的，圆柱形的域的数值模拟。流动由施加的垂直热通量驱动，并由域的背景旋转形成。其几何形状受到热带气旋的启发，全球流动模式由一个浅的漩涡和r-z平面内的极向流组成，该极向流主要在底部边界附近向内，沿上表面向外。我们的数值实验证实，正如Oruba等人2017年所建议的那样，在漩涡中心形成了一个眼睛，这让人想起热带气旋中所看到的，其特征是极向流方向的局部逆转。我们建立了流动的比例定律，并绘制出眼睛形成或不形成的条件。我们证明了在首阶时，速度与V=（αg β）^{1/2}H成比例，其中g是重力，α是膨胀系数，β是背景温度梯度，H是区域的深度.我们还表明，控制流动的两个最重要的参数是Re=VH/ν和Ro=V/ΩH，其中Ω是背景旋转速率，ν是粘度。普朗特数和纵横比也起着重要的作用，如果次要的话。最后，也是最重要的，我们建立了眼睛形成所需的标准。这些包括一个下界Re，上，下界Ro，和一个上界埃克曼数。
英文摘要：
We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the domain. The geometry is inspired by that of tropical cyclones and the global flow pattern consists of a shallow, swirling vortex combined with a poloidal flow in the r-z plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested by Oruba et al 2017, an eye forms at the centre of the vortex which is reminiscent of that seen in a tropical cyclone and is characterised by a local reversal in the direction of the poloidal flow. We establish scaling laws for the flow and map out the conditions under which an eye will, or will not, form. We show that, to leading order, the velocity scales with V=(αg β)^{1/2}H, where g is gravity, αthe expansion coefficient, βthe background temperature gradient, and H is the depth of the domain. We also show that the two most important parameters controlling the flow are Re=VH/νand Ro=V/ΩH, where Ωis the background rotation rate and νthe viscosity. The Prandtl number and aspect ratio also play an important, if secondary, role. Finally, and most importantly, we establish the criteria required for eye formation. These consist of a lower bound on Re, upper and lower bounds on Ro, and an upper bound on Ekman number.
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