The ratio between the 2D nonlinear timescale, t_nl = 1/(k_⊥u_t), and the 3D vortex stretching timescale, t_3D ∼ 1/(k_⊥u_r), where k_⊥ are modes on the surface of the contact discontinuity, u_t is the turbulent component of the velocity in the transverse plane to the surface, and u_r is the radial velocity (a compressible mode), penetrating through the unstable layer (discussed in Section 4.1). Each line represents a different population of SNRs, binned by the radius of the contact discontinuity, R_c (∼age). The ±1 is indicated with the black dashed lines. For t_nl/t_3D > 1, the modes generated on the surface shed into the surrounding medium through vortex stretching. For t_nl/t_3D < 1, the modes are confined to interact (and potentially cascade) on the surface. Old SNRs may become confined owing to the decaying u_r, whereas young SNRs can efficiently radiate the turbulence that develops at the contact discontinuity.