2D KelvinHelmholtz 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 KelvinHelmholtz instability (KH instability).
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: see the details here. There is a brief settling period, followed by exponential growth and finally saturation. The three resolutions excite increasing maximum wavenumber modes, and the higher wavenumebr modes grow more quickly than the lower wavnumber 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 128, 256x256, 512x512 cells.
 Domain: 0.5 < x < 0.5, 0.5 < y < 0.5, (0.0, 0.0 in the centre of a unit square)
 All boundaries are periodic.
Algorithm settings
 CFL number: 0.8
 Striping correction on, artificial viscosity parameter: alpha = 0.001
 DivV threshold: 1.0, Scale: 1.0
 Flattening: minimum 0.0, maximum 1.0
Ending condition
 Time, t = 5.0
Results
Yaxis kinetic energy 0.5*d*v_y^2
QuickTime movies
t = 0.0  5.0, 100 frames, one each for 512x512, 256x256 and 128x128 cell grids
128 x 128 cells
256 x 256 cells
512 x 512 cells