This is an interesting question, and I think that an instability can occur depending on the velocity difference U1-U2. The condition for the onset of the instability could be derived by rotating the direction of g and following the criterion (4.0) in 

https://www.rsmas.miami.edu/users/isavelyev/GFD-2/KH-I.pdf

I think that some statement about that can be found in the book of Kundu. A recent article stated in the introduction the reference for inclined direction of gravity:

http://elie.korea.ac.kr/~cfdkim/papers/2DMultiKHI.pdf

Let us know if you find some relevant reference

Hello,

Thanks for reply. Will look at references you provided. 

Perhaps the quickest/'cheap' analogue of this is to consider the KH instabilities seen in Jupiter's atmosphere (e.g. around the great red spot or between bands). 

References to this abound; one can search on the internet and find several (e.g. even at https://en.wikipedia.org/wiki/Hydrodynamic_stability !)

Dear Dewakar

K-H instabilities are primarily caused by frictional effects between two fluids or gas and fluid growing with a velocity difference. The direction of gravity force acting relative to such  fluid motion is of secondary importance.

I suggest the We (Weber) number calculated with the local velocity difference of the two fluid streams as a dimensionless criterion for the appearance of the K-H instabilities.

Regards

Erich

I'd conditionally endorse/agree with Erich's suggestion: 

• the Weber number is the ratio of inertia to surface-tension (or TKE to sfc.energy); 
• thus you'd want to state whether they are actually different fluids and there is a surface tension, or else you'd have to define an analogue to it...

good luck though :)

@Erich @Mark

Thanks for kind reply. As you have mentioned that direction of gravity is of secondary importance but won't the effect change if direction is parallel as compared to being normal. In definition of weber number, the effect of inertia is only accounted through velocity and there is no accounting of acceleration ( external like gravity  here).

In such scenario, does it also imply that conditions (for K-H) will be same in zero gravity ?

Thanks

I just recommend you a book on fluid instability by Dr. Chandrasekhar's. I am confident you will find all the answers related to instability