Consider two infinitely deep layers of fluids, with the upper layer having velocity
U1 > 0
and density Rho1, and the lower layer having velocity U2 > 0 and density Rho2. Waves with wavenumber k = g(U1 -U2)^-2 are generated on the interface by a mechanical device.
Initially at time t = 0, the system is stable, i.e. the wave amplitude is not growing.
Suppose the density of the upper layer is being increased very gradually with time t (measured in seconds), with
Rho1 = (0.5 + 10^-5 t)*Rho2; (1)
and Rho2 constant. At what t do the waves begin to grow exponentially due to the Kelvin-Helmholtz instability?
I don't know how to solve this, can someone help me?
Please help! 
Linear Mode
