二维分布涡运动的广义Helmholtz-Kirchhoff模型
Generalized Helmholtz-Kirchhoff model for two dimensional distributed vortex motion
摘要：
将二维斯托克斯方程改写为一个耦合的非线性常微分方程组。这些方程描述了涡量膨胀矩相对于厄米函数和涡量集中中心的演化。我们证明了这种扩展的收敛性，并表明，在零粘度和零核心尺寸的限制，我们正式恢复亥姆霍兹基尔霍夫模型的点涡的演变。本展开式系统地考虑了粘性和有限涡核尺寸的影响。我们还表明，我们的展开的低阶截断导致将流动表示为相互作用的高斯（即Oseen）涡系，先前的实验工作已证明这是对许多重要物理流动的精确近似[9]。
英文摘要：
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite functions and of the centers of vorticity concentrations. We prove the convergence of this expansion and show that in the zero viscosity and zero core size limit we formally recover the Helmholtz-Kirchhoff model for the evolution of point-vortices. The present expansion systematically incorporates the effects of both viscosity and finite vortex core size. We also show that a low-order truncation of our expansion leads to the representation of the flow as a system of interacting Gaussian (i.e. Oseen) vortices which previous experimental work has shown to be an accurate approximation to many important physical flows [9].
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