Linear theory has long been used to study mountain waves and has been successful in describing much of their behaviour. In the simplest theoretical context, that of two-dimensional steady-state flow with constant Brunt–Väisälä frequency (N) and horizontal wind speed (U), finite-amplitude effects are relatively minor until wave breaking occurs. However, in more complex environmental profiles, significant finite-amplitude effects occur below the wave-breaking threshold. We constructed a linearized version of a fully nonlinear time-dependent model, thereby facilitating direct comparisons between linear and finite-amplitude solutions in cases with upstream profiles representative of typical real-world events. Beginning with the simplest profile that includes a tropopause, namely an environment with constant upstream wind speed and two layers of constant static stability, we progressively investigate more complex profiles that include vertical wind shear typical of the midlatitude westerlies. Our results demonstrate that, even without wave breaking, finite-amplitude effects can play an important role in modulating the mountain-wave amplitude and gravity-wave drag. The modulation is a function of the tropopause height and is most pronounced when the cross-ridge flow increases strongly with height.

中文翻译：

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有限振幅效应在不间断山波中重要吗？

长期以来，线性理论一直被用于研究山波，并成功地描述了它们的大部分行为。在最简单的理论背景下，具有恒定布伦特-维萨莱频率 ( N ) 和水平风速 ( U)，在发生波浪破碎之前，有限幅度效应相对较小。然而，在更复杂的环境剖面中，在破波阈值以下会发生显着的有限幅度效应。我们构建了一个完全非线性时间相关模型的线性化版本，从而在具有代表典型现实世界事件的上游剖面的情况下促进线性和有限幅度解之间的直接比较。从包括对流层顶的最简单剖面开始，即具有恒定上游风速和两层恒定静态稳定性的环境，我们逐步研究更复杂的剖面，包括中纬度西风带典型的垂直风切变。我们的结果表明，即使没有波浪破碎，有限幅度效应可以在调节山波幅度和重力波阻力方面发挥重要作用。这种调制是对流层顶高度的函数，当横脊气流随高度强烈增加时最为明显。