Projects per year
Abstract
We present new numerical solutions for nonlinear standing water waves when the effects of both gravity and surface tension are considered. For small values of the surface tension parameter, solutions are shown to exhibit highly oscillatory capillary waves (parasitic ripples), which are both time- and space-periodic, and which lie on the surface of an underlying gravity-driven standing wave. Our numerical scheme combines a time-dependent conformal mapping together with a shooting method, for which the residual is minimised by Newton iteration. Previous numerical investigations typically clustered gridpoints near the wave crest, and thus lacked the fine detail across the domain required to capture this phenomenon of small-scale parasitic ripples. The amplitude of these ripples is shown to be exponentially small in the zero surface tension limit, and their behaviour is linked to (or explains) the generation of an elaborate bifurcation structure.
Original language | English |
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Article number | R6 |
Number of pages | 13 |
Journal | Journal of Fluid Mechanics |
Volume | 972 |
Early online date | 4 Oct 2023 |
DOIs | |
Publication status | Published - 10 Oct 2023 |
Bibliographical note
Funding.JSandPHTacknowledgesupportbytheEngineeringandPhysicalSciences Research Council (EPSRC grant no. EP/V012479/1). J S is additionally supported by the Engineering and Physical Sciences Research Council (EPSRC grant no. EP/W522491/1).Keywords
- capillary waves
- surface gravity waves
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
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Exponential asymptotics for multi-dimensional systems in fluid mechanics
Trinh, P. (PI)
Engineering and Physical Sciences Research Council
1/04/21 → 31/05/25
Project: Research council
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Maths Research Associates 2021
Milewski, P. (PI)
Engineering and Physical Sciences Research Council
1/10/21 → 30/06/24
Project: Research council