The evolution of the critical layer of a Rossby wave
The evolution of the critical layer of a Rossby wave
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罗斯贝波临界层的演化
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
K. Stewartson
中科院分区：
文献类型：
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作者：
K. Stewartson
摘要 考虑受均匀剪切力作用的罗斯贝波的演化，波的强度用参数 ∊ ≪ 1 来表征。在该过程的第一阶段，当 t ∼ 1 时，在 y = 0 线附近的层（称为临界层）外的各处都建立了稳定流，其中涡度振荡幅度逐渐增大。然而，跨层的速度跳跃是稳定的，并且与强迫振荡具有相同的波长。在较大的时间 (∊ 1/2 t ∼ 1) 下，速度跳跃振荡缓慢，并产生高次谐波。通过考虑模型方程可以看出，当 ∊1/2 t → ∞ 时，速度跳跃趋于零，但会引起垂直于层的速度的剧烈振荡。讨论了该理论与 Benney-Bergeron-Davis 理论的关系，并简要考虑了粘度的影响。
Abstract The evolution of a Rossby wave forced on a uniform shear is considered, the strength of the wave being characterised by a parameter ∊ ≪ 1. In the first stage of the process, when t ∼ 1, a steady flow is established everywhere outside a layer near the line y = 0, known as the critical layer, in which the vorticity oscillates with increasing amplitude. The velocity jump across the layer is however steady and of the same wavelength as the forcing oscillation. At larger times (∊ 1/2 t ∼ 1) the velocity jump oscillates slowly and higher harmonics are generated. It is shown by considering a model equation that as ∊1/2 t → ∞ the velocity jump tends to zero but that violent oscillations in the velocity normal to the layer are induced. The relation of this theory with the Benney-Bergeron-Davis theory is discussed and the effect of viscosity briefly considered.