Fyris Alpha - 3D KH Test

3D Kelvin–Helmholtz Test

This test consists of a dense central layer moving with respect to a lower density layer above and below the dense layer. Using periodiuc boundaries on all sides, a steady state can be established. Noise is added to the dense layer velocity field at the 1% level to seed the Kelvin-Helmholtz instability (KH instability). Note, the parameters here are identical to the 2D version of this problem, excepting only the presence of the third z-axis.

There is not an analysitcal solution, but the growth of the y-component of the kinetic energy grows in essentially the same fashon as the test performed by the Athena code: (URL). There is a brief settling period, followed by exponential growth and finally saturation. The three resolutions excite increasing maximum wave number modes, and the higher wave number modes grow more quickly than the lower wave number modes, as expected.

Initial Conditions:

Adiabatic index: Gamma = 1.4
Three Layers
- Upper, 0.25 < y < 0.50, Density, d = 1.0, Pressure, P = 2.5, Velocity, v_x0 = -0.5
- Middle, -0.25 < y < 0.25, Density, d = 2.0, Pressure, P = 2.5, Velocity, v_x0 = +0.5
- Lower, -0.50 < y < -0.25, Density, d = 1.0, Pressure, P = 2.5, Velocity, v_x0 = -0.5, same as upper
Pressure is set to P = 2.5 everywhere
Middle layer, velocity components v_x and v_y are modified with white noise, amplitude 0.01 peak to peak, ie +/- 0.005
- v_x = v_x0 + 0.01*(ran(1.0)-0.5), where ran(1.0) returns uniform random number 0.0 <= n < 1.0
- v_y = 0.01*(ran(1.0)-0.5)

Grid:

128 x 128x128, 256x256x256, 512x512x512 cells.
Domain: -0.5 < x < 0.5, -0.5 < y < 0.5, -0.5 < z < 0.5, (0.0, 0.0 in the centre of a unit square)
All boundaries are periodic.