In this paper we consider the steady water wave problem for waves that possess a merely Lr−integrable vorticity, with r ∈ (1,∞) being arbitrary. We rst establish the equivalence of the three formulations the velocity formulation, the stream function formulation, and the height function formulation in the setting of strong solutions, regardless of the value of r. Based upon this result and using...

Physics of Fluids 11(1999), 875-879. In this paper, we discuss zonally periodic steady quasigeostrophic waves in a β−plane channel, by using variational methods. A class of steady quasigeostrophic waves are determined by the potential vorticity field profile, g(·), which is a function of the stream function. We show that zonally periodic steady quasigeostrophic waves exist when the bottom topog...

This work reports evidence for the existence of coherent structures in steady-state shear-flow driven plasmas in the Large Plasma Device W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 1991 facility at UCLA. The measurements are performed with the vorticity probe VP , a probe that directly measures the plasma vorticity associated with the E B shear flow by means of a method that is both simpler...