Strongly shocked cylindrically convergent implosions were conducted on
the OMEGA laser. The directly driven targets consist of a low-density foam
core and an embedded aluminum shell covered by an epoxy ablator. The outer
surface of the aluminum shell has imposed single-mode perturbations with
wave numbers k = 0.25, 0.7, 1.05, and 2.5 (rad/μm) and
initial amplitudes η0 /λ = 0.04, 0.11, 0.33, and
0.4. In our convergent geometry, perturbation growth without evidence of
saturation, for η/λ as large as 4.5 is observed for
k < 1. For k > 1 growth rate scaling with
wavenumber breaks down and transition to turbulence is suggested.