Vorticity Averages

Abstract

Recent studies of turbulent fluid motions have drawn attention to the transfer of vorticity. There have been some attempts to study turbulence by plane models, but these have been criticized justly for failing to reveal the true nature of a phenomenon which depends essentially on threedimensional convection. I have thought it worthwhile to eschew current conjectures regarding turbulence, turning in preference to the method of a master of the theory of vortices and applying it to the discovery of certain average properties of the continuous rotational motion of any medium whatever. This memoir therefore makes no attempt to deal with the problem of turbulence, but it is possible that the theorems presented here, being exact consequences of the kinematical equations, may nevertheless enjoy a certain relevance.