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 …

Vortex crystals is one name in use for the subject of vortex patterns that move without
change of shape or size. Most of what is known pertains to the case of arrays of parallel line …

We prove the existence of many different symmetry types of relative equilibria for systems of
identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry …

With some basis now in statistical mechanics, we turn to fluid mechanics. We want a
representation of a fluid's flow compatible with our Monte Carlo tools. We will develop these …

We describe the instantaneous streamline patterns that occur on the surface of a two-
dimensional sphere in the presence of point vortices of general strength for cases in which …

The dynamic behavior of baroclinic point vortices in two-layer quasi-geostrophic flow
provides a compact model for studying the transport of heat in a variety of geophysical flows …

Mathematics develops both due to demands of other sciences and due to its internal logic.
The latter fact explains the attention of mathematicians to many problems, which are in close …

We consider the motion of a point vortex on the surface of a sphere with solid boundaries.
This problem is of interest in oceanography, where coherent vortex structures can persist for …

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane
can be expressed in Hamiltonian form, where the resulting equations of motion are …

We give a geometric account of the relative motion or the shape dynamics of $ N $ point
vortices on the sphere exploiting the $\mathsf {SO}(3) $-symmetry of the system. The main …