On the propagation of mountain waves: linear theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915879538655232 |
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| author | Constantin, Adrian Weber, Jörg |
| author_facet | Constantin, Adrian Weber, Jörg |
| contents | We derive and establish a solution concept for the linear mountain wave problem in two dimensions. After linearizing the governing equations and a change of variables, the problem can be stated as a Dirichlet boundary value problem for a Helmholtz equation in terms of the vertical wind profile in the upper half-plane, with altitude-dependent potential (the Scorer parameter). To single out the correct solution, we have to make use of a radiation condition which is, due to the different physical situation, different from the classical Sommerfeld radiation condition for electromagnetic or acoustic waves. We rigorously develop a transform method and construct the physically correct solution, following Lyra's monotonicity criterion for mountain waves. In this procedure, we clearly recognize the two typical types of mountain waves: vertically propagating waves and trapped lee waves. This paper is the first rigorous work on Helmholtz-like equations in the upper half-plane subject to such a non-classical radiation condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the propagation of mountain waves: linear theory Constantin, Adrian Weber, Jörg Analysis of PDEs Mathematical Physics We derive and establish a solution concept for the linear mountain wave problem in two dimensions. After linearizing the governing equations and a change of variables, the problem can be stated as a Dirichlet boundary value problem for a Helmholtz equation in terms of the vertical wind profile in the upper half-plane, with altitude-dependent potential (the Scorer parameter). To single out the correct solution, we have to make use of a radiation condition which is, due to the different physical situation, different from the classical Sommerfeld radiation condition for electromagnetic or acoustic waves. We rigorously develop a transform method and construct the physically correct solution, following Lyra's monotonicity criterion for mountain waves. In this procedure, we clearly recognize the two typical types of mountain waves: vertically propagating waves and trapped lee waves. This paper is the first rigorous work on Helmholtz-like equations in the upper half-plane subject to such a non-classical radiation condition. |
| title | On the propagation of mountain waves: linear theory |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2509.26125 |