13 citations · 34 across the 10 of their papers we have counts for
10 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…
Exponential asymptotics and higher-order Stokes phenomenon in singularly perturbed ODEs
Josh Shelton, Samuel Crew, Philippe H. Trinh
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has a…
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…
Exponential asymptotics and the generation of free-surface flows by submerged line vortices
Josh Shelton, Philippe H. Trinh
There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface…
Exponential asymptotics for steady parasitic capillary ripples on steep gravity waves
Josh Shelton, Philippe H. Trinh
In this paper we develop an asymptotic theory for steadily travelling gravity-capillary waves under the small-surface tension limit. In an accompanying work [Shelton et al. (2021),…
On the structure of parasitic gravity-capillary waves in the small surface tension limit
Josh Shelton, Paul Milewski, Philippe H. Trinh
In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed a…