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The stability of stratified flows at locations in the Clyde, Irish and CelticSeas on the UK Continental Shelf is examined. Flows are averaged over periodsof 12-30 min in each hour, corresponding to the times taken to obtain reliableestimates of the rate of dissipation of turbulent kinetic energy per unit mass,$\varepsilon$. The Taylor-Goldstein equation is solved to find the maximumgrowth rate of small disturbances to these averaged flows, and the criticalgradient Richardson number, $\textrm{Ri}_\textrm{c}$. The proportion ofunstable periods where the minimum gradient Richardson number,$\textrm{Ri}_{\textrm{min}}$, is less than $\textrm{Ri}_\textrm{c}$ is about35%. Cases are found in which $\textrm{Ri}_\textrm{c} <$ 0.25; 37% of the flowswith $\textrm{Ri}_{\textrm{min}}<$ 0.25 are stable, and$\textrm{Ri}_\textrm{c}<$ 0.24 in 68% of the periods where$\textrm{Ri}_{\textrm{min}}<$ 0.25. Marginal conditions with 0.8 $<$Ri$_{\textrm{min}}$$/$Ri$_\textrm{c}$ $<$ 1.2 occur in 30% of the periodsexamined. The mean dissipation rate at the level where the fastest growingdisturbance has its maximum amplitude is examined to assess whether theturbulence there is isotropic and how it relates to the Wave-Turbulenceboundary. It is concluded that there is a background level of dissipation thatis augmented by instability; instability of the averaged flow does not accountfor all the turbulence observed in mid-water. The effects of a horizontalseparation of the measurements of shear and buoyancy are considered. Theavailable data do not support the hypothesis that the turbulent flows observedon the UK shelf adjust rapidly to conditions that are close to being marginal,or that flows in a particular location and period of time in one sea havestability characteristics that are very similar to those in another.

On instability and mixing on the UK Continental Shelf