Internal waves produced by a convective layer

Fluid impacts on the base of a stably stratified region of fluid cause internal-wave ripples whose spread is predominantly horizontal if the duration of the impacts is long compared with the natural period of the stratified fluid. The development of a single ripple in a slightly viscous fluid is calculated, first with a constant vertical gradient of potential density and then with a gradient varying linearly with height. The single-ripple results are used to find the intensity of the statistically steady wave motion generated by impacts which are randomly distributed in space and time. Above a critical height, dependent on the viscosity and stability of the fluid and on the time and length scales of the impacts, wave energy falls off as the −5/3 power of the height with a constant density gradient and as the −25/6 power with a linearly varying gradient. The predictions are compared with observations of temperature fluctuations in the stable region of an ice-water convection system and with observations of ‘clear-air turbulence’ over strato-cumulus cloud. Reasonable numerical agreement can be obtained with plausible values for the scales of the convective motion which provides the impacts.