Related papers: A geometric approach to generalized Stokes conject…
In a companion paper, Grimshaw (Asymptotic Methods in Fluid Mechanics, 2010, pp. 71-120) has demonstrated how techniques of Borel summation can be used to elucidate the exponentially small terms that lie hidden beyond all orders of a…
We provide analysis to determine the effects of gravitational waves on electromagnetic waves, using perturbation theory in general relativity. Our analysis is performed in a completely covariant manner without invoking any coordinates. For…
The aim of this note is to examine the efficacy of a recently developed approach to the recovery of nonlinear water waves from pressure measurements at the seabed, by applying it to the celebrated extreme Stokes wave.
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from…
Granular flows in a narrow pipe are studied numerically by the model taking account of hydrodynamic effects of fluid surrounding particles. In the simulations density waves are observed over the wide range of the Stokes number, which…
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…
Stokes phenomenon refers to the fact that the asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines has an unphysical divergence. An important special case…
Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The…
We establish novel existence results of $3d$ gravity-capillary periodic traveling waves. In particular we prove the bifurcation of multiple, geometrically distinct truly $3d$ Stokes waves having the same momentum of any non-resonant $2d$…
The geometric phase techniques for swimming in viscous flows express the net displacement of a swimmer as a path integral of a field in configuration space. This representation can be transformed into an area integral for simple swimmers…
We consider stratified steady water waves in a two dimensional channel. Our main subject is spectral properties of the Frechet derivatives of steady water Stokes waves. One of main results is the absence of subharmonic water waves in a…
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables…
A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
When studying fluid-body interactions in the low-Froude limit, traditional asymptotic theory predicts a waveless free-surface at every order. This is due to the fact that the waves are in fact exponentially small---that is, beyond all…
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and…
Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of…
The swimming of a sphere by means of radial helical surface waves is studied on the basis of the Stokes equations. Explicit expressions are derived for the matrices characterizing the mean translational and rotational swimming velocities…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…