Kelvin-Helmholtz Instability

Velocity Shear

Differential speed between adjacent streams drives the exponential growth of perturbations along the contact surface. Shear magnitude dictates whether initial disturbances damp out through viscous dissipation or amplify into rolling vortices. Viscosity acts as a stabilizing force that suppresses short-wavelength ripples, leaving only longer perturbations to grow when the velocity difference surpasses a specific threshold.

Density Stratification

Gravitational forces counteract velocity shear by attempting to keep lighter fluid above denser fluid in stable layers. Buoyancy forces suppress vertical displacement, requiring the kinetic energy of the faster stream to overcome potential energy barriers before billows can form. Density gradients determine the Richardson number, a dimensionless parameter that measures the relative stability of stratified shear flows against overturning.

Vortex Breakdown

Rotational rollers eventually stretch beyond their linear stability limits and degenerate into complex turbulent structures that disperse kinetic energy throughout the fluid. Energy cascades from large billow scales down to viscous dissipation scales where friction converts mechanical motion into thermal energy. Momentum exchange accelerates drastically across the boundary once this chaotic mixing phase is established.