A simpler velocity quasi-potential PDE in fluid mechanics, MHD included

Abstract

This work studies and clarifies some local physical phenomena in fluid mechanics (and MHD), in the form of an intrinsic analytic study, regarding the PDEs of the velocity potential and
(especially) 2-D “quasi-potential†(their simpler and special forms), over the virtual “isentropic†or 3-D (V,Ω) surfaces and along the “isentropic & isotachic†space curves, written for any potential and even rotational flow of an inviscid compressible fluid for both steady and unsteady motions. Using the advantages offered by the special virtual surfaces and space curves here introduced and a smart intrinsic coordinate system, a simpler PDE in only two variables, and more, a Laplace’s PDE (for any rotational pseudo-flow), was obtained, instead of the general PDE in three variables. So far, this equation was known for potential flows only. Extensions to rotational flows of a viscous compressible fluid and in MHD were given.