- #1
Angelos K
- 48
- 0
Hi, there!
I'm trying to understand the derivation of (linearized) pertubation equations given in my lecture.
As usual the density and velocity fields are split into a homogeneous and an inhomogeneous part:
[tex]\rho(t,x) = \rho_0(t) + \delta \rho(x,t)[/tex]
[tex]\vec{v}(t,x) = \vec{v_0}(t) + \vec{\delta v}(x,t)[/tex]
Then (and that is what I don't understand) the claim is made that the background quantrities need to separately fullfill mass conservation. In other words:
[tex]\frac{\partial \rho_0}{\partial t} + \rho_0 \nabla * \vec{v_0} = 0[/tex]
Any idea where this comes from?
Many thanks in advance!
Angelos
I'm trying to understand the derivation of (linearized) pertubation equations given in my lecture.
As usual the density and velocity fields are split into a homogeneous and an inhomogeneous part:
[tex]\rho(t,x) = \rho_0(t) + \delta \rho(x,t)[/tex]
[tex]\vec{v}(t,x) = \vec{v_0}(t) + \vec{\delta v}(x,t)[/tex]
Then (and that is what I don't understand) the claim is made that the background quantrities need to separately fullfill mass conservation. In other words:
[tex]\frac{\partial \rho_0}{\partial t} + \rho_0 \nabla * \vec{v_0} = 0[/tex]
Any idea where this comes from?
Many thanks in advance!
Angelos