5 papers
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…
Automorphisms of Stokes multipliers in higher-order WKBJ theory
Josh Shelton, Samuel Crew, Christopher J. Lustri
We consider the Stokes phenomenon and higher-order Stokes phenomenon (HOSP) of formal asymptotic transseries arising in the WKBJ analysis of linear differential equations and integ…
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…