  This paper is concerned with the propagation dynamics of time almost periodic
reaction-diffusion equations. Assuming the existence of a time almost periodic
traveling wave connecting two stable steady states, we focus especially on the
asymptotic behavior of average wave speeds in both rapidly oscillating and
slowly oscillating environments. We prove that, in the rapidly oscillating
case, the average speed converges to the constant wave speed of the homogenized
equation; while in the slowly oscillating case, it approximates the arithmetic
mean of the constant wave speeds for a family of equations with frozen
coefficients. In both cases, we provide estimates on the convergence rates
showing that, in comparison to the limiting speeds, the deviations of average
speeds for almost periodic traveling waves are at most linear in certain sense.
Furthermore, our explicit formulas for the limiting speeds indicate that
temporal variations have significant influences on wave propagation. Even in
periodic environments, it can alter the propagation direction of bistable
equations.
