INVISCID 2-DIMENSIONAL VORTEX DYNAMICS AND A SOLITON EXPANSION OF THESINH-POISSON EQUATION

The dynamics of inviscid. steady, two dimensional flows is examined fo r the case of a hyperbolic sine functional relation between the vortic ity and the stream function. The 2-soliton solution of the sinh-Poisso n equation with complex wavenumbers will reproduce the Mallier-Maslowe pattern, a row of counter-rotating vortices. A special 4-soliton solu tion is derived and the corresponding flow configuration is studied. B y choosing special wavenumbers complex flows bounded by two rigid wall s can result. A conjecture regarding the number of recirculation regio ns and the wavenumber of the soliton expansion is offered. The validit y of the new solution is verified independently by direct differentiat ion with a computer algebra software. The circulation and the vorticit y of these novel flow patterns are finite and are expressed in terms o f well defined intervals. The questions of the linear stability and th e nonlinear evolution of a finite amplitude disturbance of these stead y vortices are left for future studies. (C) 1998 American Institute of Physics.