Energetics of a naturally occurring shear instability

Abstract

Using observations of an energetic shear instability (Seim and Gregg, 1994), we examine the energy budget of the mixing event by comparing microstructure measurements of the dissipation rates of turbulent kinetic energy ε and turbulent potential energy χpe with changes in fine‐scale velocity and density. Two sets of observations are used. The first set sampled the shear instability early in its evolution, when overturns occurred in strong stratification. The second set of observations found the same water vertically homogenized by turbulent mixing. In a frame of reference moving with the billows we solve a set of time‐dependent energy equations to estimate the buoyancy flux Jb, turbulent production P, and strength of nonlocal forcing in the mean kinetic and mean potential energy budgets. The turbulent energy equations are approximately steady when evaluated for several buoyancy periods, simplifying to local balances. We find Jb ≈ χpe/2 ≈ −5.5×10−7 W kg−1 and P ≈ ε − Jb ≈ 2.4×10−6 W kg−1 to within a factor of 2. The decrease in mean kinetic energy is approximately locally balanced by P, but unlike the kinetic energy, only 25% of the increase in mean potential energy is explained by Jb. This implies no net radiation of energy into the surrounding stratified fluid, but the large uncertainties in Jb and P make this result tenuous. We find the flux Richardson, Rƒ = Jb/P ≈ 0.22±0.1; that is, one quarter of the turbulent energy released by the instability goes toward increasing the mean potential energy of the water column. The billows generated an average momentum flux of 0.22 Pa for more than an hour, and peak values exceeded 1.5 Pa. The average value is comparable to maximum momentum flux values in boundary layers over ice and under ice.