Mechanics of Fluids

Fluid mechanics in fluids at rest.

Using readily available experimental thermophoretic particle-velocity data it is shown, contrary to current teachings, that for the case of compressible flows independent dye- and particle-tracer velocity measurements of the local fluid velocity at a point in a flowing fluid do not generally result in the same fluid velocity measure. Rather, tracer-velocity equality holds only for incompressibl...

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, v...

Microcantilever mechanics in flowing viscous fluids

A general kinetic theory of liquids; quantum mechanics of fluids.

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Differential Invariants of Lie Pseudogroups in Mechanics of Fluids

We present bases of differential invariants for Lie pseudogroups admitted by the main models of fluid mechanics. Among them infinite-dimensional parts of symmetry groups of Navier-Stokes equations in general (V.O. Bytev, 1972) and rotationally-symmetric (L.V. Kapitanskij, 1979) cases; stationary gas dynamics equations (M. Munk, R. Prim, 1947); stationary incompressible ideal magnetohydrodynamic...