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For layered systems, it is found that very low levels of heterogeneity leads

to an enhancement of the growth rate of the fingered zones, and that both harmonic and subharmonic resonances between the intrinsic scale of nonlinear fingering and those of the heterogeneity occur

Ref: Viscous fingering in periodically heterogeneous porous media. II.

Numerical simulations; 

A. De Wit and  G. M. Homsy

J. Chem. Phys. 107 (22), 8 December 1997

www.ulb.ac.be/sciences/nlpc/PDF/97.JCPII.pdf

Try this:

http://journals.cambridge.org/download.php?file=%2FFLM%2FFLM419%2FS0022112000001324a.pdf&code=8c01f3a15b53e8dbff41ae708a1ef5e1

I always assumed it was due to Rayleigh-Taylor  instability.  The same thing happens if you put heavy water on top of lighter oil.  Any acceleration will do this - it does not need to be gravity.

Dear Priyank,

You may find these references useful as well:

 The dynamics of mid-ocean ridge hydrothermal systems: Splitting plumes and fluctuating vent temperatures:  D Coumou, T Driesner, S Geiger, CA Heinrich… - Earth and Planetary …, 2006 - Elsevier  We present new, accurate numerical simulations of 2D models resembling hydrothermal  systems active in the high-permeability axial plane of mid-ocean ridges and show that fluid flow patterns are much more irregular and convection much more unstable than reported ...

Cited by 50 Related articles All 6 versions Cite Save

 Timescales of Thermal Fluctuations and of Vent Location Changes in Mid-Ocean Ridge Hydrothermal Systems From Numerical Modelling:  D Coumou, S Geiger, T Driesner… - AGU Fall Meeting …, 2005 - adsabs.harvard.edu ... Authors: Coumou, D.; Geiger, S.; Driesner, T.; Heinrich, CA. Affiliation: AA( ), AB( ), AC( ), AD( ). ... The high viscosity contrast between hot and cold fluids causes rising plumes to split (Taylor-Saffman fingering) making fluid flow patterns much more irregular. ...

Kind regards,

Steve

Thank you very much for such a valuable explanations/references.

Hi, your question is too general. In the context of Hele Shaw Cells the tip splitting  is a function of surface tension, this is a well known result.  Regards