Mountain waves: Linear theory

In this talk, I will discuss the linear theory of mountain waves in two dimensions. After an introduction to the physical relevance and the typically observed wave patterns, we turn to the underlying boundary value problem for the compressible Euler equations coupled to the ideal gas law and the first law of thermodynamics. In particular, we are interested in their linearization at a background state, corresponding to an incoming horizontal wind profile. We show how the linearized equations can be reduced to a Helmholtz-like equation (the Scorer equation, well-known in the applied literature) for the vertical velocity on the upper-half plane. We then present a solution theory for the corresponding boundary value problem. Here, we have to pay special attention to a careful implementation of a physically correct radiation condition that is fundamentally different to typical radiation conditions à la Sommerfeld, which are relevant in the context of electromagnetic and acoustic waves, but physically incorrect for mountain waves. The talk is based on joint work with Adrian Constantin (U Vienna).