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首页> 外文会议>NATO ARW and IUTAM Symposium Sep 2-7, 2001 Zakopane, Poland >Advection―diffusion of a passive scalar in the flow of a decaying vortex
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Advection―diffusion of a passive scalar in the flow of a decaying vortex

机译：对流-被动标量在衰减涡流中的扩散

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摘要

We have shown the existence of a similarity solution of the advection―diffusion equation representing the evolution of the initially uniform gradient of a passive scalar in the flow field of a diffusing Gaussian vortex. As a special case, Sc = 1 gives the solution of the Navier-Stokes equation obtained by Abernathy &e Pearson (1984) and Moore (1985) where the diffusing quantity is the background vorticity perpendicular to the axis of the central vortex. The solution yields a quantitative description of the process of spiral wind-up (Bassom & Gilbert 1998, 1999), giving accelerated diffusion due to the reduction of radial scale and the enhancement of the concentration gradients. Such a situation occurs when a flame sheet or another chemical reaction front is wrapped around a diffusing vortex. Marble (1985) studied the case when the initial fuel concentration is given by a step function. The similarity solution (9) and the analogous solutions for higher Fourier modes can be added to approximate the evolution of any initial concentration profile. Both small and large Sc regimes are of practical interest.
机译：我们已经证明了对流扩散方程的相似解的存在，该方程代表了扩散高斯涡流场中被动标量的初始均匀梯度的演化。作为特殊情况，Sc = 1给出了由Abernathy＆e Pearson（1984）和Moore（1985）获得的Navier-Stokes方程的解，其中扩散量是垂直于中心涡旋轴的背景涡度。该解决方案给出了螺旋缠绕过程的定量描述（Bassom＆Gilbert 1998，1999），由于径向尺度的减小和浓度梯度的增加，给出了加速的扩散。当火焰片或其他化学反应前沿包裹在扩散涡流周围时，会发生这种情况。 Marble（1985）研究了由阶跃函数给出初始燃料浓度的情况。可以添加相似解（9）和更高傅里叶模式的类似解，以近似任何初始浓度分布的演变。大型和小型Sc制度都具有实际意义。

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