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Baroclinic tidal conversion: note on a paper of L.R.M. Maas

Published online by Cambridge University Press:  12 August 2022

Carl Wunsch Open the ORCID record for Carl Wunsch [Opens in a new window]  and
Jared Wunsch Open the ORCID record for Jared Wunsch [Opens in a new window]
Carl Wunsch*
Affiliation:
Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA
Jared Wunsch
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: [email protected]
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Abstract

Maas (J. Fluid Mech., vol. 684, 2011, pp. 5–24) showed that, for an oscillating two-dimensional barotropic tide flowing over sub-critical topography of compact support, some topographic forms existed that produced non-radiating baroclinic disturbances. The problem is related to ‘stealth’ and ‘cloaking’ problems. Here Maas's result is derived using a simpler approach, not involving complicated mappings, but formally restricted to perturbation topography. Wider results come from the discussion of nearly compact support topographic disturbances provided by Schwartz functions with weak high-wavenumber radiation and by exploiting both a known functional equation formulation and Fourier methods. The problem is extended to disturbances on uniform slopes. A variety of non-radiating topographies can be found, although they are mathematically delicate and unlikely to be found in nature. Topography with weak radiation at high wavenumber is a much wider class of structures. Application of these solutions would lie with the ability to estimate dissipation over and near the topography from motions observed at a distance.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A47
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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