Derivation of Burgers' equation in sonic boom I am studyng Burgers equation.
In many resources is said that this equation arise in sonic boom model.
I' m look for derivation of this equation starting from Navier-Stokes or (Euler).
I know that Burgers appear in NS if you drop the pressure term, but in sonic boom you cannot do that (the pressure is there and it is also big) ?
Can someone explain me or recommend a good resource on this subject?
 A: You can start with the second Euler equation. For simplicity I use the 1 dimensional one, because astrophysical blast waves are often in good approximation spherical, so only the radial component matters.
$$\frac{\partial v}{\partial t} + v \frac{\partial v}{\partial x} + \frac{1}{\rho}\frac{\partial P}{\partial x} = 0$$
From your question I assume you know how to get there. Burgers equation now follows in the isothermal regime, where we use the isothermal equation of state:
$$P=\rho a²$$
with $a$ the sound speed. Now we are in the supersonic regime, i.e. $a\ll v$. Therefore, we can drop the pressure term as
$$|\frac{1}{\rho}\frac{\partial P}{\partial x}| = |\frac{a²}{\rho}\frac{\partial \rho}{\partial x}| \ll |v\frac{\partial v}{\partial x}|$$
(so, as an order of magnitude estimate the LHS is of order $a²$, whereas the RHS is of order $v²$, which is much bigger in the supersonic regime).
This leaves us with the Burgers equation:
$$\frac{\partial v}{\partial t} + v \frac{\partial v}{\partial x} = 0.$$
