Dynamics of vorticity defects in shear
Dynamics of vorticity defects in shear
复制标题
剪切涡度缺陷的动力学
DOI：
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发表时间：
1997
影响因子：
3.7
通讯作者：
W. Young
中科院分区：
文献类型：
--
作者：
N. Balmforth;D. del;W. Young
匹配的渐近展开被用来获得一个减少描述的非线性和粘性演化的小，局部涡缺陷嵌入在库埃特流。这种涡度亏损近似类似于Vlasov方程，以及用于研究强迫Rossby波临界层及其二次不稳定性的其他简化描述。本文发展了涡度亏损近似的线性稳定性理论。得到了无粘缺陷和粘性缺陷简正模的色散关系。奈奎斯特方法用于获得不稳定的必要和充分条件，并定性地了解基本状态的变化如何改变稳定性。线性初值问题的明确解决与拉普拉斯变换，所得到的解决方案表现出瞬态增长和最终衰减的流函数与连续谱。扩展计划可以推广到处理非库埃特，但单调，速度剖面涡缺陷。
Matched asymptotic expansions are used to obtain a reduced description of the nonlinear and viscous evolution of small, localized vorticity defects embedded in a Couette flow. This vorticity defect approximation is similar to the Vlasov equation, and to other reduced descriptions used to study forced Rossby wave critical layers and their secondary instabilities. The linear stability theory of the vorticity defect approximation is developed in a concise and complete form. The dispersion relations for the normal modes of both inviscid and viscous defects are obtained explicitly. The Nyquist method is used to obtain necessary and sufficient conditions for instability, and to understand qualitatively how changes in the basic state alter the stability properties. The linear initial value problem is solved explicitly with Laplace transforms; the resulting solutions exhibit the transient growth and eventual decay of the streamfunction associated with the continuous spectrum. The expansion scheme can be generalized to handle vorticity defects in non-Couette, but monotonic, velocity profiles.