Raphael Stuhlmeier, Conor Heffernan, Alberto Alberello, Emilian Părău
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Modulational instability of nonuniformly damped, broad-banded waves: Applications to waves in sea ice
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.
期刊介绍:
Physical Review Fluids is APS’s newest online-only journal dedicated to publishing innovative research that will significantly advance the fundamental understanding of fluid dynamics. Physical Review Fluids expands the scope of the APS journals to include additional areas of fluid dynamics research, complements the existing Physical Review collection, and maintains the same quality and reputation that authors and subscribers expect from APS. The journal is published with the endorsement of the APS Division of Fluid Dynamics.