By numerical and analytical study of the time-dependent Ginzburg-Landau equ
ation we show that vortex nucleation in superfluid He-3 by rapid thermal qu
ench in the presence of superflow is dominated by a transverse instability
of the moving normal-superfluid interface. Exact expressions for the instab
ility threshold as a function of supercurrent density and the front velocit
y are found.