Internal Travelling Waves in the Limit of a Discontinuously Stratified Fluid
Internal Travelling Waves in the Limit of a Discontinuously Stratified Fluid
复制标题
不连续分层流体极限内的行波
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
G. James
中科院分区：
文献类型：
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作者：
G. James
在光滑分层逼近不连续两层剖面的奇异极限情况下，我们考虑了理想分层流体中的内行波。我们的分析涉及小幅度的二维波，它在有限深度的无限大的水平条带中传播。光滑或不连续层结问题被描述为统一的空间演化问题，其中层结ρ起函数参数的作用。向量场相对于ρ不是光滑的，但具有一定的弱连续性。当弗劳德数接近临界值时，我们将问题归结为中心流形上的一个问题，该中心流形上的平凡状态与ρ无关(对于通常的拓扑结构)。考虑较弱的拓扑结构，证明了中心流形在ρ中的连续性。然后用ℝ2中的一个常微分方程来描述小解，该常微分方程解连续地依赖于ρ中的
Ck Norm。
Abstract We consider internal travelling waves in a perfect stratified fluid, in the singular limit case when smooth stratifications approach a discontinuous two-layer profile. Our analysis concerns two-dimensional waves of small amplitude, propagating in an infinite horizontal strip of finite depth. The problems with smooth or discontinuous stratification are formulated as a unifying spatial evolution problem, where the stratification ρ plays the role of a functional parameter. The vector field is not smooth with respect to ρ, but has some weak continuity. When the Froude number is close to a critical value, we reduce the problem to one on a center manifold in a neighborhood of the trivial state independent of ρ (for the usual topology). Considering a weaker topology, we prove the continuity in ρ of the center manifold. Then the small solutions are described by an ordinary differential equation in ℝ2, which depends continuously on ρ in the
Ck norm.