2026/06/08 by Matthew N. Crowe, Edward R. Johnson
Earth and Planetary Sciences · Physics and Astronomy · #Oceanographic and Atmospheric Processes #Ocean Waves and Remote Sensing #Nonlinear Waves and Solitons
paper · doi:10.1175/jpo-d-25-0141.1
Abstract This paper considers coastal-trapped waves and instabilities in the nonhydrostatic Boussinesq equations in the presence of a background flow and complicated coastal topography, using a spectral method to discretize the two-dimensional eigenvalue problem and solve the resulting discrete problem by standard methods. Our approach is applied to several examples and demonstrated to be consistent with previous numerical and analytical results. Further, we are able to reliably identify previously unseen coastal-trapped wave modes using a realistic coastal geometry, thereby confirming predictions made by Gelderloos et al. based on recent simulations of the southeast Greenland shelf. Significance Statement The term “coastal-trapped waves” describes a family of waves that move along coastlines with wavelengths of hundreds to thousands of kilometers. These waves can have significant effects on coastal regions by modifying ocean currents or causing sea level rises and floods. This work describes a computational method for studying and predicting coastal-trapped waves based on the offshore sea depth, wave size, and water properties. We present four examples that demonstrate the effectiveness of this approach and verify that our results agree with previous theoretical and numerical theory. We also show that our method can be used to identify new waves in a realistic model of the southeast Greenland shelf, thus confirming predictions made by other authors. All scripts and data used in this work are available in a publicly accessible repository.