标题： 波与平均流相互作用的多尺度动力学：从非线性WKB理论到天气和气候模型中的重力波参数化 显示英文标题

标题： Multi-Scale Dynamics of the Interaction Between Waves and Mean Flows: From Nonlinear WKB Theory to Gravity-Wave Parameterizations in Weather and Climate Models

摘要： 小尺度波与大尺度流之间的相互作用可以通过一种多尺度理论来描述，该理论是天气和气候模型中新型次网格尺度重力波（GW）参数化方法的基础。 此处回顾了该理论的发展。 它适用于所有有趣的大气分层区域，即也适用于中间大气中出现的中等强度分层，从而扩展了准地转理论推导的经典假设。 在强波幅情况下，会出现一个完全非线性的理论，而对于弱GW幅值，则由一个准线性理论进行补充。 后者允许扩展到谱描述，这构成了避免由于焦散线引起的不稳定性（例如来自GW反射）的数值实现基础。 讨论了能量和位涡的守恒性质，以及GW对大尺度流产生影响的条件。 描述了该理论在大气模型中GW参数化的数值实现，并讨论了与经典GW参数化相比该方法的后果。 尽管比后者更昂贵，但它表现出显著增强的真实性，同时比需要解析所有相关GW的方法要高效得多。 所报告的理论及其实施可能还对其他波-平均相互作用的高效且具有概念洞察力的描述具有兴趣，包括那些焦散线形成带来特殊挑战的情况。 显示英文摘要

摘要： The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The development of this theory is reviewed here. It applies to all interesting regimes of atmospheric stratification, i.e. also to moderately strong stratification as occurring in the middle atmosphere, and thereby extends classic assumptions for the derivation of quasi-geostrophic theory. At strong wave amplitudes a fully nonlinear theory arises that is complemented by a quasilinear theory for weak GW amplitudes. The latter allows the extension to a spectral description that forms the basis of numerical implementations that avoid instabilities due to caustics, e.g. from GW reflection. Conservation properties are discussed, for energy and potential vorticity, as well as conditions under which a GW impact on the larger-scale flow is possible. The numerical implementation of the theory for GW parameterizations in atmospheric models is described, and the consequences of the approach are discussed, as compared to classic GW parameterizations. Although more costly than the latter, it exhibits significantly enhanced realism, while being considerably more efficient than an approach where all relevant GWs are to be resolved. The reported theory and its implementation might be of interest also for the efficient and conceptually insightful description of other wave-mean interactions, including those where the formation of caustics presents a special challenge.