5 papers · 1 filter
On the stability of large-amplitude gravity-capillary surface waves
Josh Shelton, Adam Rook
We consider the stability of periodic gravity-capillary waves of finite amplitude for small values of the surface tension. Linear stability with respect to both superharmonic and s…
An enthalpy-based model for the physics of ice crystal icing
Timothy Peters, Josh Shelton, Hui Tang +1
Ice crystal icing (ICI) in aircraft engines is a major threat to flight safety. Due to the complex thermodynamic and phase-change conditions involved in ICI, rigorous modelling of…
Time-dependent nonlinear gravity-capillary surface waves with viscous dissipation and wind forcing
Josh Shelton, Paul Milewski, Philippe H. Trinh
We develop a time-dependent conformal method to study the effect of viscosity on steep surface waves. When the effect of surface tension is included, numerical solutions are found…
A model ODE for the exponential asymptotics of nonlinear parasitic capillary ripples
Josh Shelton, Philippe Trinh
In this work, we develop a linear model ODE to study the parasitic capillary ripples present on steep Stokes waves when a small amount of surface tension is included in the formula…
Pathological exponential asymptotics for a model problem of an equatorially trapped Rossby wave
Josh Shelton, S. Jonathan Chapman, Philippe H. Trinh
We examine a misleadingly simple linear second-order eigenvalue problem (the Hermite-with-pole equation) that was previously proposed as a model problem of an equatorially-trapped…