Forced and Unforced Flexural-gravity Solitary Waves

Flexural-gravity waves beneath an ice sheet are investigated. Forced waves generated by a moving load as well as freely propagating solitary waves are considered for the nonlinear problem as proposed by Plotnikov and Toland [2011]. In the unforced case, a Hamiltonian reformulation of the governing equations is presented in three dimensions. A weakly nonlinear analysis is performed to derive a cubic nonlinear Schrödinger equation near the minimum phase velocity in two dimensions. Both steady and time-dependent fully nonlinear computations are presented in the two-dimensional case, and the influence of finite depth is also discussed

Instability of some unsteady viscous flows

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Nearly inviscid Faraday waves

Many powerful techniques from Hamiltonian mechanics are available for the study of ideal hydrodynamics. This article explores some of the consequences of including small viscosity in a study of surface gravity-capillary waves excited by the vertical vibration of a container. It is shown that in this system, as in others, the addition of small viscosity provides a singular perturbation of the ideal fluid system, and that as a result its effects are nontrivial. The relevance of existing studies of ideal fluid problems is discussed from this point of view