  Layzer's approximation method for investigation of two fluid interface
structures associated with Rayleigh Taylor instability for arbitrary Atwood
number is extended with the inclusion of second harmonic mode leaving out the
zeroth harmonic one. The modification makes the fluid velocities vanish at
infinity and leads to avoidance of the need to make the unphysical assumption
of the existence of a time dependent source at infinity.
  The present analysis shows that for an initial interface perturbation with
curvature exceeding 1/(2sqrt{A}), where $A$ is the Atwood number there occurs
an almost free fall of the spike with continuously increasing sharpening as it
falls. The curvature at the tip of the spike also increases with Atwood number.
Certain initial condition may also result in occurrence of finite time
singularity as found in case of conformal mapping technique used earlier.
However bubble growth rate is not appreciably affected.
