# Shocks

Shocks by definition are discontinuities in the fluid properties (e.g. density, velocity, pressure). A schematic image is shown in Fig.1, where we can clearly identify the discontinuity as a “shock jump”. The values of the fluid properties change abruptly at that interface. Pressure, energy and density have values $P_2$, $u_2$ and $\rho_2$ respectively to the left of the shock, while to the right the values are $P_1$, $u_1$ and $\rho_1$

This kind of discontinuities can not be solved by the Euler equation because spatial derivatives are not defined at that point. To overcome this problem, we define the Rankine-Hugoniot jump conditions.

## Rankine-Hugoniot jump conditions

The Rankine-Hugoniot jump conditions describe the behavior of shock in the interface between two medium with different properties. (see Fig. 1) The Rankine-Hugoniot jump conditions are given by three equations

$\rho_1 u_1 = \rho_2 u_2$
$\rho_1 u_1^2 + p_1 = \rho_2 u_2^2 + p_2$
$e_1 + \frac{1}{2} u_1^2 + p_1/\rho_1 = e_2 + \frac{1}{2} u_2^2 + p_2/\rho_2$

which are nothing more than conservation of mass, momentum and energy respectively.

## Shocks in the Interstellar Medium

Schocks are a common phenomenon in the insterstellar medium (ISM). Among the sources that produce shocks we can find:

• Novae and Supernovae: Explosions expelling material that produce shocks in the surrounding medium.
• Outflows: Different types of outflows can create shocks when interacting with the surrounding material. Among them we can find stellar winds, jets, galactic fountains and AGN feedback. An example are Herbig-Haro (HH) objects, which is basically jets emanating from Young Stellar Objects (YSOs) and producing “bow shocks” in the surrounding medium.
• Turbulence: Turbulence is defined as the transport of energy between different scales of the system. For example it is believed that an injection of energy at larger scales of the system can produce shocks in a smaller scales due to turbulent transport of energy.

Below there is an example of a supernova explosion simulation, where we can clearly distinguished the development of forward and reverse shocks. For comparison you can check images of Kepler’s supernova remnant and Cassiopeia A (you can find a really interesting 3D view of Cassiopeia in Pierre’s module).

For comparison we also add a video of a Sedov explosion run in pyro2:

If you are interested on how magnetic fields can influences shocks, you should visit Philip’s module.