Modulational instability of nonuniformly damped, broad-banded waves: Applications to waves in sea ice

Stuhlmeier, Raphael, Heffernan, Conor, Alberello, Alberto ORCID: https://orcid.org/0000-0001-7957-4012 and Părău, Emilian ORCID: https://orcid.org/0000-0001-5134-2068 (2024) Modulational instability of nonuniformly damped, broad-banded waves: Applications to waves in sea ice. Physical Review Fluids, 9. ISSN 2469-990X

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Abstract

This paper sets out to explore the modulational (or Benjamin-Feir) instability of a monochromatic wave propagating in the presence of damping such as that induced by sea ice on the ocean surface. The fundamental wave motion is modelled using the spatial Zakharov equation, to which either uniform or nonuniform (frequency-dependent) damping is added. By means of mode truncation the spatial analog of the classical Benjamin-Feir instability can be studied analytically using dynamical systems techniques. The formulation readily yields the free surface and its envelope, giving insight into the physical implications of damping on the modulational instability. The evolution of an initially unstable mode is also studied numerically by integrating the damped, spatial Zakharov equation, in order to complement the analytical theory. This sheds light on the effects of damping on spectral broadening arising from this instability.

Item Type:	Article
Additional Information:	Funding information: R.S. and C.H. gratefully acknowledge the support of EPSRC Grant No. EP/V012770/1. A.A. and E.P. gratefully acknowledge the support of EPSRC Grant No. EP/Y02012X/1.
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User:	LivePure Connector
Date Deposited:	24 Sep 2024 12:55
Last Modified:	26 Sep 2024 00:02
URI:	https://ueaeprints.uea.ac.uk/id/eprint/96794
DOI:	10.1103/PhysRevFluids.9.094802

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