Hamiltonian representation of equations of hydrodynamics and its use in describing wave movements in currents with shear
Abstract
A procedure for the Hamiltonian formulation of the equations of motion is proposed for hydrodynamictype media. It is shown that if the relations, besides the Euler equations, have a linearly functional dependence on the hydrodynamic velocity v, then the Klebsch representation establishing the relationship between v and the canonical variables may be found in a general form. The fundamental aspects of the formulation are illustrated for a uniform incompressible fluid with a shear flow. The normal variables of the problem are found for the special case of a semiinfinite medium and a bilinear flow profile. For the onedimensional case, the nonlinear long waves are described using the BenjaminOno and Riemann equations. Estimates are presented for characteristic values of the parameters of the atmospheric boundary layer.
 Publication:

USSR Report Earth Sciences JPRS UES
 Pub Date:
 July 1984
 Bibcode:
 1984RpESc.......81G
 Keywords:

 ClebschGordan Coefficients;
 Hamiltonian Functions;
 Hydrodynamic Equations;
 Oscillating Flow;
 Planetary Waves;
 Shear Flow;
 Atmospheric Boundary Layer;
 Canonical Forms;
 Flow Velocity;
 Nonlinear Evolution Equations;
 Fluid Mechanics and Heat Transfer