  We report results obtained from the study of 12 thermonuclear X-ray bursts in
6 AstroSat observations of a neutron star X-ray binary and well-known X-ray
burster, 4U 1636$-$536. Burst oscillations at $\sim$581 Hz are observed with
4$-$5$\sigma$ confidence in three of these X-ray bursts. The rising phase burst
oscillations show a decreasing trend of the fractional rms amplitude at
3$\sigma$ confidence,by far the strongest evidence of thermonuclear flame
spreading observed with AstroSat. During the initial 0.25 second of the rise a
very high value (34.0$\pm$6.7%) is observed. The concave shape of the
fractional amplitude profile provides a strong evidence of latitude-dependent
flame speeds, possibly due to the effects of the Coriolis force. We observe
decay phase oscillations with amplitudes comparable to that observed during the
rising phase, plausibly due to the combined effect of both surface modes as
well as the cooling wake. The Doppler shifts due to the rapid rotation of the
neutron star might cause hard pulses to precede the soft pulses, resulting in a
soft lag. The distance to the source estimated using the PRE bursts is
consistent with the known value of $\sim$6 kpc.

High Energy Astrophysical Phenomena