论文标题
低模式流中斜压扭矩的扰动分析
Perturbation analysis of baroclinic torque in low-Mach-number flows
论文作者
论文摘要
在本文中，我们预示着低液体流动中的斜压扭矩的一系列扩展，因此可以通过分析进行任何浮力项的准确性和普遍性，并可以构建和验证新型的浮力项。我们首先证明，引入浮力项的目的是近似斜压扭矩，并且可以直接地通过其卷曲偏离斜压扭矩来测量任何浮力项的准确性。然后引入了一种常规的扰动方法，以用于低模式流中流体力压力的椭圆形方程，从而产生了一系列泊松方程，其溶液导致斜角扭矩的串联表示和新型的浮力项。通过浮力术语的错误定义以及斜压扭矩的串联表示，经典的引力和离心浮力项以及其他先前提出的浮力项。最后，数值模拟证实，随着密度变化的降低或我们新提出的浮力项的增加顺序，具有新型浮力项之一的简化方程可以融合到原始的低模式数字方程。
In this paper, we propse a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed and validated. We first demonstrate that the purpose of introducing a buoyancy term is to approximate the baroclinic torque, and straightforwardly the accuracy of any buoyancy term could be measured by the deviation of its curl from the baroclinic torque. Then a regular perturbation method is introduced for the elliptic equation of the hydrodynamic pressure in low-Mach-number flows, resulting in a sequence of Poisson equations, whose solutions lead to the series representation of the baroclinic torque and the new types of buoyancy terms. With the error definition of buoyancy terms and the series representation of the baroclinic torque, the classical gravitational and centrifugal buoyancy term, as well as some other previously proposed buoyancy terms are revisited. Finally, numerical simulations confirm that, with a decreasing density variation or an increasing order of our newly proposed buoyancy term, the simplified equations with one of the new types of buoyancy terms can converge to the original low-Mach-number equations.
