Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension.

ABSTRACT: A numerical method is introduced for the computation of time-periodic vortex sheets with surface tension separating two immiscible, irrotational, two-dimensional ideal fluids of equal density. The approach is based on minimizing a nonlinear functional of the initial conditions and supposed period that is positive unless the solution is periodic, in which case it is zero. An adjoint-based optimal control technique is used to efficiently compute the gradient of this functional. Special care is required to handle singular integrals in the adjoint formulation. Starting with a solution of the linearized problem about the flat rest state, a family of smooth, symmetric breathers is found that, at quarter-period time intervals, alternately pass through a flat state of maximal kinetic energy, and a

SUBMITTER: Ambrose DM 

PROVIDER: S-EPMC2840482 | biostudies-literature | 2010 Feb

REPOSITORIES: biostudies-literature