Seems like the stress power p can be written as p = Tij ∂vi /∂xj = ∂fi /∂xj ∂vi /∂xj = *T* ∇v
right? Taken from the book Continuum Mechanics by Lai et al 4.12.7. Maybe someone can be so pedagogic as to write it down in its components? This is a key to understand vortex flow. The value of p is negative in the cases of Schauberger flow which has been reported as having "negative" viscosity. Maybe p = Tij,j vi = ∂fi /∂xj /∂xj vi = *********** = ∂**2**f**i **/∂x**j**2 **v**i** * They seem algebraically equivalent but the latter is intuitively more correct. ** David David Jonsson, Sweden, phone callto:+46703000370 On Tue, Jun 2, 2009 at 7:16 PM, David Jonsson <[email protected]>wrote: > Hi again > > Has this really not been performed? > > The question is if p can be written in a combined form. > > *p *= ⋅ + f⋅v > > *p *= power per volume or area provided to the fluid > > = torque on the fluid, the stress tensor elements T12-T21 > > = ∇×v* *= vorticity, infinitesimal rotation in the fluid > > f* *= the volumetric force on the fluid > > v* = *the speed of the fluid (in Euler description) > > David > > David Jonsson, Sweden, phone callto:+46703000370 > > On Mon, May 18, 2009 at 2:27 PM, David Jonsson < > [email protected]> wrote: > >> HI >> >> Is there a way to write >> >> p=torque*vorticity >> and >> p=force*(linear)speed >> >> in a combined way? Seems like it could be done with a tensor? >> >> David >> >> David Jonsson, Sweden, phone callto:+46703000370 >> >> >
