43 citations · 292 across the 26 of their papers we have counts for
10 papers · 1 filter
Spatially quasi-periodic water waves of finite depth
Jon Wilkening, Xinyu Zhao
We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-per…
Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values
Jon Wilkening, Xinyu Zhao
We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent…
Numerical Algorithms for Water Waves with Background Flow over Obstacles and Topography
David M. Ambrose, Roberto Camassa, Jeremy L. Marzuola +3
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a peri…
Quasi-periodic traveling gravity-capillary waves
Jon Wilkening, Xinyu Zhao
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple p…
Spatially quasi-periodic water waves of infinite depth
Jon Wilkening, Xinyu Zhao
We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value proble…
The instability of Wilton ripples
Olga Trichtchenko, Bernard Deconinck, Jon Wilkening
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phe…
Optimizing intermittent water supply in urban pipe distribution networks
Anna M. Lieb, Chris H. Rycroft, Jon Wilkening
In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different ti…
Relative-Periodic Elastic Collisions of Water Waves
Jon Wilkening
We compute time-periodic and relative-periodic solutions of the free-surface Euler equations that take the form of overtaking collisions of unidirectional solitary waves of differe…
Overdetermined Shooting Methods for Computing Standing Water Waves with Spectral Accuracy
Jon Wilkening, Jia Yu
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision.…
Breakdown of self-similarity at the crests of large amplitude standing water waves
Jon Wilkening
We study the limiting behavior of large-amplitude standing waves on deep water using high-resolution numerical simulations in double and quadruple precision. While periodic traveli…