Comparing two formats of the MHD energy equation

[MasterD]

Is this the right format of the energy equation (equation 2.10)?

http://www-solar.mcs.st-and.ac.uk/~alan/sun_course/Chapter2/node3.html#energy

$$\frac{\rho^\gamma}{\gamma-1}\frac{D}{Dt}\left(\frac{p}{\rho^\gamma}\right)=-L$$

I know it in a different format:

$$\frac{dp}{dt}+\gamma p\nabla\cdot\mathbf{v}=-L$$

Where is the difference coming from?

 

[tiny-tim]

Hi MasterD!

Isn't your second equation the case for ρ = constant (and with D/Dt being the convective time derivative, ∂/∂t + v.∇)?

 

[MasterD]

Hi MasterD!

Isn't your second equation the case for ρ = constant (and with D/Dt being the convective time derivative, ∂/∂t + v.∇)?

Thanks for your reply Tim. $$\rho$$ is not constant, however.. D/Dt is indeed the convective time derivative.