Moore's asymptotic analysis of vortex-sheet motion predicts that the Kelvin–Helmholtz
instability leads to the formation of a weak singularity in the sheet profile at a finite time. The …

Almost‐sure convergence of a subsequence of the vorticity to a weak solution is proven for
the point‐vortex method for 2‐D, inviscid, incompressible fluid flow. Here “almost‐sure” is …

Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-
up in hydrodynamic instability, wave interactions on the ocean's free surface, the …

Vortex methods have a history as old as finite differences. They have since faced difficulties
stemming from the numerical complexity of the Biot–Savart law, the inconvenience of adding …

We consider an ill-posed Boussinesq equation which arises in shallow water waves and
nonlinear lattices. This equation has growing and decaying modes in the linear as well as …

For the applications of high Reynolds number flows, the vortex method presents the
advantage of being free from numerically dissipative truncation error. In practice, however …

We prove nonlinear stability and convergence of certain boundary integral methods for time-
dependent water waves in a two-dimensional, inviscid, irrotational, incompressible fluid, with …

Coherent vortex structures occur in many types of fluid flow including mixing layers, jets and
wakes. A vortex sheet is a mathematical model for such structures, in which the shear layer …

We present a kernel-free boundary integral method (KFBIM) for solving variable coefficients
partial differential equations (PDEs) in a doubly connected domain. We focus our study on …

Boundary integral numerical methods are among the most accurate methods for interfacial
Stokes flow, and are widely applied. They have the advantage that only the boundary of the …