(226b) Current Controversy Surrounding the Basic Equations of Hydrodynamics. A Review

Four contextually and physically different fluid velocities appear in the basic pre-constitutive equations of hydrodynamics and transport phenomena.  These are: (i) the mass velocity appearing in the continuity equation; (ii) the momentum velocity appearing in  the inertia term of the linear momentum equation; and, in the energy equation: (iii) the kinetic energy velocity, together with (iv) the velocity multiplying the pressure tensor such that their product is proportional to the rate at which thermodynamic work is being done. These four velocities are implicitly assumed in the literature to be physically synonymous, as attested to by the fact that all four are denoted by a common symbol, typically  “v”, when formulating the basic mass, momentum and energy transport equations Questions have recently arisen regarding the assumed equality of these velocities, with several groups of researchers (including the author) arguing against equality. The talk will review the background underlying the issue, while advancing plausible quantitative arguments against equality in circumstances where the fluid is compressible.  It will be shown that the consequences of inequality are important for compressible fluids, especially for rarefied gases.