Internal wave tunnelling through non‐uniformly stratified shear flow
Internal wave tunnelling through non‐uniformly stratified shear flow
复制标题
通过非均匀分层剪切流的内波隧道
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
B. Sutherland
中科院分区：
文献类型：
--
作者：
G. L. Brown;B. Sutherland
摘要我们研究了重力内波在具有垂直变化背景剪切的非均匀分层流体中的传播。为了量化波的传输，我们表明，适当的措施是发送到入射赝能，T通量的比值。在两种情况下，我们推导出波通过分段线性剪切流的传播的T的解析预测。在这两种情况下，流体在剪切深度上是不分层的，而在其他地方是均匀分层的。在一项研究中，密度分布是连续的。这样的基本状态是不稳定的，但随着体理查森数Ri变大，增长率会变得非常小。在无限大的Richardson数（无剪切）的限制下，我们恢复了Sutherland和Yewchuk（2004）的隧穿预测。在弱剪切中，入射波可以微弱地传输，即使相速度匹配剪切层内的流速（临界水平）。然而，当入射波的相速度与剪切的相对侧面上的流速完全匹配时，不发生传输。在强剪切中，Ri ≥ 1，透射峰出现在入射波数和频率接近但不同于与不稳定模式相关的波数和频率的地方。在第二项研究中，背景密度分布是不连续的，代表了曾经均匀分层的流体中混合良好的斑块。在这种情况下，对于具有与剪切层内的流动速度相匹配的相速度的入射波，不发生透射。然而，如果入射波与剪切侧面的界面波共振，则会出现传输尖峰。
Abstract We examine the transmission of internal gravity waves through a non‐uniformly stratified fluid with vertically varying background shear. To quantify wave transmission we show that the appropriate measure is the ratio of the flux of transmitted to incident pseudoenergy, T. We derive an analytic prediction of T for the transmission of waves through a piecewise‐linear shear flow in two cases. In both, the fluid is unstratified over the depth of the shear and uniformly stratified elsewhere. In one study, the density profile is continuous. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number, Ri, becomes large. In the limit of an infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland and Yewchuk (2004). In weak shear, incident waves can transmit weakly, even if the phase speed matches the flow speed within the shear layer (a critical level). However, no transmission occurs when the phase speed of incident waves exactly matches the flow speed on the opposite flank of the shear. In strong shear, with Ri ⋍ 1, a transmission peak occurs where the incident wavenumber and frequency are close to, but different from, those associated with unstable modes. In a second study, the background density profile is discontinuous and representative of a well‐mixed patch within a once uniformly stratified fluid. In this case, no transmission occurs for incident waves with phase speed matching the speed of the flow within the shear layer. However, a transmission spike occurs if the incident waves are resonant with interfacial waves that flank the shear.