Axisymmetric deformation of compressible, nearly incompressible, and incompressible thin layers between two rigid surfaces

The Incompressible Laminar Axisymmetric Wake

Spaces of Incompressible Surfaces

The homotopy type of the space of PL homeomorphisms of a Haken 3 manifold was computed in [H1], and with the subsequent proof of the Smale conjecture in [H2], the computation carried over to diffeomorphisms as well. These results were also obtained independently by Ivanov [I1,I2]. The main step in the calculation in [H1], though not explicitly stated in these terms, was to show that the space o...

Limits Of Incompressible Surfaces

One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not contradictory result that although one can sometimes embed arbitrarily many surfaces in a 3-manifold it is impossible to ever embed an infinite number of such surfa...

Vortex stretching in incompressible and compressible fluids

where u is determined from ω nonlocally, through the solution of the elliptic system given by (2) and (3). A similar formulation applies to smooth isentropic compressible flows, if one replaces the vorticity ω in (4) by ω/ρ. This formulation is very convenient for many theoretical purposes, as well as for better understanding a variety of fluid phenomena. At an intuitive level, it reflects the ...

Variational Principles for Compressible and Incompressible Systems

Some of the results of a previous paper 1 on the relations between adiabatic and incompressible systems are the establishing of a variational energy principle for incompressible systems and consequently of comparison theorems for stability of adiabatic and incompressible perturbations of the same equilibrium state. In this paper we extend these analyses to the most general compressible regimes ...