Vortex design problem

Vortex design problem

In this investigation we propose a computational approach for solution of optimal control problems for vortex systems with compactly supported vorticity. The problem is formulated as PDE–constrained optimization in which the solutions are found using a gradient–based descent method. Recognizing such Euler flows as free– boundary problems, the proposed approach relies on shape differentiation co...

Design of Hydrofoil Assisted Catamarans using a Non-Linear Vortex Lattice Method

Extensive experimental investigations of hydrofoil-assisted catamarans have identified the main hydrodynamic parameters affecting the performance of these vessels. Design principles of existing vessels are discussed in the light of these hydrodynamic findings. The experience gained from experimental testing has provided the basis for the development of a non-linear vortex lattice method for des...

On the Cauchy problem for axi-symmetric vortex rings

We consider the classical Cauchy problem for the 3d Navier-Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry. We show that natural approximations of the problem obtained by smoothing the initial data satisfy good a-priori estimates which enable us to conclude that the original pro...

Multiple Solutions for an Elliptic Problem Related to Vortex Pairs

On polygonal relative equilibria in the N-vortex problem

Helmholtz’s equations provide the motion of a system of N vortices which describes a planar incompressible fluid. A relative equilibrium is a particular solution of these equations for which the distances between the particles are invariant during the motion. In this article, we are interested in relative equilibria formed of concentric regular polygons of vortices. We show that in the case of ...