This article reviews theory and applications of Koopman modes in fluid mechanics.
Koopman mode decomposition is based on the surprising fact, discovered in, that normal …

This book comprises seven chapters, an appendix, a bibliographical section 98 references,
and an index. Exercises are provided at the end of each chapter. The stated goal of the book …

We present two interesting features of vortex rings in incompressible, Newtonian fluids that
involve their Hamiltonian structure. The first feature is for the Hamiltonian model of …

Pure reconstruction phases—geometric and dynamic—are computed in the N-point-vortex
model in the plane, for the cases $ N= 3$ and $ N= 4$. The phases are computed relative to …

We study a growing biological tissue as an open biphasic mixture with mass exchange
between phases. The solid phase is identified with the matrix of a porous medium, while the …

We consider the evolution of an incompressible two-dimensional perfect fluid as the
boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially …

A vortex patch is a desingularization of a point vortex in which the vorticity is a bounded
function over a finite, nonzero area A of the plane. It can thus be viewed as the …

We derive formulas for the long time evolution of passive interfaces in three “canonical”
incompressible, inviscid, two-dimensional flow models. The point vortex models, introduced …