Simulate the evolution of an axisymmetric cylindrical jet in cylindrical coordinates. Use an external Mach number of 20 and initial pressure equilibrium with the uniform environment in two dimensions. Use a resolution of 10 cells per beam radius. Perform a second Simulation with 20 cells per beam radius. In your report:
a) Show 4 sufficiently different snapshots of the logarithmic density distribution for each simulation.
b) On a characteristic density distribution, explain where bow shock, cocoon, Mach disc and contact surface are located.
c) Point out the location of Kelvin-Helmholtz instabilities and contact surfaces.
d) Estimate the shear velocity at the contact surface, calculate the growth rate for the Kelvin-Helmholtz instability analytically and compare to your simulation.
e) Do you expect Rayleigh-Taylor instabilities anywhere?
f) Measure the propagation speed of the leading bow shock on the jet axis by comparing its position in the 4 snapshots you made and explain its magnitude.
g) Does the velocity of the bow shock change with resolution?
h) Find the backflow and explain the magnitude of the backflow velocity at different locations.
i) Describe the differences between the low and the high-resolution simulation. Check if the Rankine-Hugoniot jump conditions are satisfied in the respective simulations