next up previous
Next: Conductive Heating Up: Fluid Instabilities Previous: Rayleigh-Taylor Instability

Kelvin-Helmholtz Instability

: The Kelvin-Helmholtz (KH) instability results from velocity shears between two media. These media need not even be of different densities. Any time there is a non-zero curvature, the flow of one fluid around another will lead to a slight centrifugal force which in turn leads to a change in pressure thereby amplifying the ripple. The most familiar example of this is wind blowing over calm water. Tiny dimples in the smooth surface will quickly be amplified to small waves and finally to frothing white-caps.

As with RT instability, any sort of surface tension will hinder KH instabilities. If there is some restoring force Tg, the instability will arise if

\begin{displaymath}\Delta v^2 \ge \frac{2(\rho_1 +\rho_2 )}{\rho_1 \rho_2 }[T_g(\rho_2 -\rho_1 )]^{1/2}.\end{displaymath}

For water waves, surface tension stabilizes the interface until the wind reaches v > 650 cm s-1 (12.5 knots). For astrophysical applications, magnetic field tension supplies a stabilizing force. The stability requirement is

\begin{displaymath}\Delta v \leq 2 v_A = \frac{2B}{(\mu_o \rho)^{1/2}}.\end{displaymath}

In the evolved stages of KH instability, cyclonic 'cat-eye' structures are formed. When combined with RT instabilities, KH tends to form 'mushroom caps' on the end of RT fingers. Since the growth rate of these fingers is proportional to their cross section, KH tends to slow down finger growth.


next up previous
Next: Conductive Heating Up: Fluid Instabilities Previous: Rayleigh-Taylor Instability
Charles Danforth
1999-03-24