I am a postdoctoral researcher in Mathematics at the University of Bath, working on nonlinear water waves and perturbation methods. The problems I study typically contain features that are beyond-all-orders of the asymptotic limit considered. An example of this is in the small-surface-tension limit of surface water waves, where highly oscillatory parasitic ripples appear in the wave profile. These are responsible for the generation of ellaborate bifurcation structures that exist under the same limit. I am interested in the effects of surface tension, vorticity, viscosity, and time dependence on nonlinear surface waves, and developing perturbation methods to solve unresolved problems in applied mathematics.
Currently, I am developing formulations for time-dependent surface waves that include vorticity and vortices within the fluid. Recently, new exact solutions have been found in simple formulations of this problem when the effects of gravity, surface tension, and time-dependence are neglected.
My methedology allows for the incorporation of these effects, and for the solution stability to be studied (both linear stability of subharmonic perturbations, and nonlinear stability in an initial-value problem).
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J. Shelton, S. Crew, & P. Trinh |
- Exponential asymptotics and higher-order Stokes phenomenon in singularly perturbed ODEs. |
SIAP. (accepted) |
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T. Peters, J. Shelton, H. Tang, & P. Trinh |
- An enthalpy-based model for the physics of ice crystal icing. |
J. Fluid Mech. (accepted) |
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J. Shelton |
- Time-periodic generalised solitary waves with a hydraulic fall. |
J. Fluid Mech. (Focus on Fluids paper; accepted) |
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J. Shelton, P. Trinh |
- A model ODE for the exponential asymptotics of nonlinear parasitic capillary ripples. |
IMA J. Appl Math. (2024) |
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J. Shelton, S. J. Chapman, & P. Trinh |
- Exponential asymptotics for a model problem of an equatorially trapped Rossby wave. |
SIAP. (2024) |
| (4) |
J. Shelton, P. Milewski, & P. Trinh |
- On the structure of parasitic gravity-capillary standing waves in the small surface tension limit. |
J. Fluid Mech. (2023) |
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J. Shelton & P. Trinh |
- Exponential asymptotics and the generation of free-surface flows by submerged line vortices. |
J. Fluid Mech. (2023) |
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J. Shelton & P. Trinh |
- Exponential asymptotics for steady parasitic capillary ripples on steep gravity waves. |
J. Fluid Mech. (2022) |
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J. Shelton, P. Milewski, & P. Trinh |
- On the structure of steady parasitic gravity-capillary waves in the small surface tension limit. |
J. Fluid Mech. (2021) |
