  We study the asymptotics of front speeds of the reaction-diffusion equations
with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity and zero mean stationary
ergodic Gaussian shear advection on the entire plane. By exploiting connections
of KPP front speeds with the almost sure Lyapunov exponents of the parabolic
Anderson problem, and with the homogenized Hamiltonians of Hamilton-Jacobi
equations, we show that front speeds enhancement is quadratic in the small root
mean square (rms) amplitudes of white in time zero mean Gaussian shears, and it
grows at the order of the large rms amplitudes. However, front speeds diverge
logarithmically if the shears are time independent zero mean stationary ergodic
Gaussian fields.
