On instability and mixing on the UK Continental Shelf

TL;DR

This study investigates the stability and turbulence of stratified flows on the UK Continental Shelf, revealing that a significant portion of flows are marginally stable and turbulence is influenced by both instability and background dissipation.

Contribution

It provides a detailed analysis of flow stability, turbulence, and the relationship between Richardson numbers and turbulence in the UK shelf waters, using the Taylor-Goldstein equation and dissipation measurements.

Findings

Approximately 35% of unstable periods have Ri_min less than Ri_c.

A background level of dissipation exists beyond that caused by instability.

Flows do not rapidly adjust to marginal stability conditions.

Abstract

The stability of stratified flows at locations in the Clyde, Irish and Celtic Seas on the UK Continental Shelf is examined. Flows are averaged over periods of 12-30 min in each hour, corresponding to the times taken to obtain reliable estimates of the rate of dissipation of turbulent kinetic energy per unit mass, $\varepsilon$. The Taylor-Goldstein equation is solved to find the maximum growth rate of small disturbances to these averaged flows, and the critical gradient Richardson number, $\textrm{Ri}_\textrm{c}$. The proportion of unstable periods where the minimum gradient Richardson number, $\textrm{Ri}_{\textrm{min}}$, is less than $\textrm{Ri}_\textrm{c}$ is about 35%. Cases are found in which $\textrm{Ri}_\textrm{c} <$ 0.25; 37% of the flows with $\textrm{Ri}_{\textrm{min}}<$ 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 periods examined. The mean dissipation rate at the level where the fastest growing disturbance has its maximum amplitude is examined to assess whether the turbulence there is isotropic and how it relates to the Wave-Turbulence boundary. It is concluded that there is a background level of dissipation that is augmented by instability; instability of the averaged flow does not account for all the turbulence observed in mid-water. The effects of a horizontal separation of the measurements of shear and buoyancy are considered. The available data do not support the hypothesis that the turbulent flows observed on 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 have stability characteristics that are very similar to those in another.