Variational principle of Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides a fast
and accurate way for speed calculations.
A variational principle based computation is carried out
on a large ensemble of KPP random speeds through spatial, mean zero,
stationary, Gaussian random shear flows inside two dimensional channel domains.
In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speed
obeys the quadratic law. In the large rms amplitude regime, the enhancement follows the linear law.
An asymptotic ensemble averaged speed formula
is derived and agrees well with the numerics. Related theoretical results are presented
with a brief outline of the ideas in the proofs.
The ensemble averaged speed is found to increase sublinearly with enlarging
channel widths, while the speed variance decreases.
Direct simulations in the small rms regime
suggest quadratic speed enhancement law for non-KPP nonlinearities.