Assumptions to simplify the
problem
-A basic state of
static stability,namely that lighter fluid lies on the
top of heavier fluid, in order to
avoid Rayleigh-Taylor instability.
-Vertical scale large enough, namely there
woule be no upper or lower boundaries.
-Horizontal scale must be small enough
so that we can ignore rotation, namely L<<Rd, in Rd is
Rossby Number.
-Horizontal scale can not be too small
to ignore surface tension, namely L>d,d is the certain
value for a particular system. For example, for air-sea
system, d is about 7 nm.(For more details, see Kundu Sec
7.7)
-KHI and can be fully described and analyzed using
equations in two dimensions.(Squire’s theorem)
A simple illustrate
of K-H instability
http://www.brockmann-consult.de/CloudStructures/images/kelvin-helmholtz-instab/k-w-system.gif