Hello Friends there,

I am in Germany and doing my study works, by my work on the instabilities of the separating flows, I encounter the so called Kelvin-Helmholz Instability.

who can explain to me what exactly does this kind of Instability mean?

Thanks alot in advance!!!

Anan

THe Kelvin-Helmhotlz instability is also know as the shearing instability and is due mainly to the shear (difference in velocity) between two layers of flows.

Assume you have a layer of fluid flowing at a velocity v0 and next to it a layer of fluid flowing (parallel to the first one) at a velocity say -v0 (you can always find a moving frame of reference in which the two flows have this particular configuration of velocities; and it is easier to understand this way). And assume for simplicity that we are in two dimensions, so that the surface of separation between the two flowing layers is actually a line, and assume that initially this line is straight. Now if you perturb this line, so that now it looks locally like a sine wave of small amplitude, then you have actually a 'bump' of the +v0 layer into the region of the -v0 layer and vice versa (the opposite). So the 'bump' of +v0 is pushed 'backwards by the -v0 layer, this makes the nice (initial) sine wave tun into a wave with sharp edges that emplifies. This is similar to the wind blowing on the surface of the water, forming a wave pattern that eventually folds onto itself (and brake down, splashing, because of gravity). The KH instability leads first to a wavy pattern of the surface of separation of the two flows, then it can lead to nice vortices of the flows entering each other in the direction normal to the surface of separation.

You can also try the following experiment:

take a cup and its saucer. Pour some coffee (about 2/3 of the cup) in the cup and put the cup on its saucer (the best is to have a cup shaped a little like a V, rather than a mug). Let the coffee rest. Then very carefully and slowly pour some milk in the coffee, if possible from the edge of the cup to avoid strong mixing and turbulence). Again let the milk settle. Now using your finger pointed downwards turn the cup around (on the saucer) by pushing gently the ear of the cup. Try to make a regular one turn/sec or faster. Continue turning untill you see the milk creating an outer ring in the black coffee. When you see a nice and broad ring then stop turning! The outer edge of the cup will start to slow down the outer ring of milk and the shear between the milk ring and the inner coffee will create a Kelvin-Helmholtz instability. As soon as you stop turning vortex-like shapes of milk and coffee will appear for a while (they are beautifull!) untill some turbulence will take place and mixe the milke with the coffee. Then of course drink the coffee! I hope you will have a nice time.

Patrick

Dear Patrick,

thank you so much for explain me the KH instability in such a clear way!

I bet you have also clear idea on the socalled "secondary instability", with respect to the primary instability.

let's say, if a 2-D vortex roll twist to become Lamda-formed structures, it should be due to the primary instability;

if later the Lamda-formed structures burst into a chaos-like turbulece, then it was due to "secondary instability", right?

any logical relations between the "primary" and "secondary" instabilities?

thanks a lot in advance!!!

Anan