User:Loren36/kelvin
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[edit] Theory
The dispersion relation for the Kelvin-Helmholtz instability can be derived by assuming that the fluids are incompressible flow and irrotational such that the fluid velocities u1 and u2 may be defined by a scaler potential φ1 and φ2 corresponding to the top and bottom fluid respectively, such that:
Using Reynolds decomposition, the scaler potential is decomposed into an ensemble of time varying perturbations superimposed upon a time independent mean state:
- φi(x,y,z,t) = Φi + φi'(x,y,z,t)
The interface between the two fluids ζ is described in a similar manner, such that
