Determining the Wavelength of Dendritic Sidebranches

We present a numerical method of determining the wavelength of dendritic sidebranches accompanying the needle crystal. Our method uses a linearization of the equations of interface evolution about the exact steady-state solution. We show that although the steady state is linearly stable, small perturbations will be selectively amplified, giving rise to observable branching. The sidebranches are stationary in the laboratory frame of reference and their wavelength scales as the tip radius for physical values of the dimensionless undercooling.