Spectral Methods for Coastal-Trapped Waves and Instabilities in a Background Flow

TL;DR

This paper introduces a spectral numerical method to identify coastal-trapped waves and instabilities in non-hydrostatic flows with complex topography, validated against previous results and realistic simulations.

Contribution

A novel spectral approach for solving eigenvalue problems related to coastal-trapped waves in non-hydrostatic models with complex topography.

Findings

Method reliably identifies coastal-trapped wave solutions.

Results are consistent with previous numerical and analytical studies.

Successfully applied to realistic Southeast Greenland shelf simulations.

Abstract

Here we present a numerical method for finding non-hydrostatic coastal-trapped wave and instability solutions to the non-hydrostatic Boussinesq equations in the presence of a background flow and complicated coastal topography. We use spectral methods to discretise the two-dimensional eigenvalue problem and solve the resulting discrete problem by standard methods. Our approach is applied to three examples and shown to be consistent with previous numerical and analytical results. In particular, we show that our method is able to reliably identify coastal-trapped wave solutions that correspond to waves seen in realistic simulations of the Southeast Greenland shelf.