Stationary Regimes and Parametrization of Ekman Friction in the Karman Model of Flow Induced by External Vortical Body Force

Pub Date : 2024-07-02 DOI:10.1134/s0001433824700166
S. V. Kostrykin, I. G. Yakushkin
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Abstract

Using numerical simulation of the Karman model of viscous fluid flow under the action of an external vortex body force, two different stationary modes were extracted and studied in detail: with small (Batchelor regime) and with substantial (Stewartson regime) secondary circulation. The diagram of stationary regimes is plotted in the space of flow parameters—Rossby and small Ekman numbers. For the flow decaying to the stationary one in the Batchelor regime, a theoretical model is proposed based on which a stationary solution to the problem can be obtained, as well as a parameterization of the Ekman friction coefficient, the Ekman pumping velocity, and the stationary pressure in terms of average flow characteristics (vorticity and divergence). For the Stewartson regime, a parameterization of the stationary flow is proposed and a numerical investigation of the decay rate is conducted. The results of the theoretical analysis have been compared with numerical calculations and found to be in good agreement.

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外部涡体力诱导的卡曼模型中的静止状态和埃克曼摩擦参数化
摘要 通过对外部涡体力作用下粘性流体流动的 Karman 模型进行数值模拟,提取并详细研究了两种不同的静止模式:小循环(Batchelor 模式)和大循环(Stewartson 模式)。在流动参数--罗斯比和小埃克曼数的空间中绘制了静止状态图。对于在 Batchelor 模式中衰减到静止模式的流动,提出了一个理论模型,在此基础上可以得到问题的静止解,并根据平均流动特性(涡度和发散)对埃克曼摩擦系数、埃克曼泵送速度和静止压力进行了参数化。对于 Stewartson 体系,提出了静止流的参数化,并对衰减率进行了数值研究。将理论分析结果与数值计算结果进行了比较,发现两者非常吻合。
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