Scaling of Shear‐Generated Turbulence: The Equatorial Thermocline, a Case Study
2021
Richards, K. J. | Natarov, A. | Carter, G. S.
We formulate an expression for the turbulent kinetic energy dissipation rate, ϵ, associated with shear‐generated turbulence in terms of quantities in the ocean or atmosphere that, depending on the situation, may be measurable or resolved in models. The expression depends on the turbulent vertical length scale, ℓᵥ, the inverse time scale N, and the Richardson number Ri = N²/S², where S is the vertical shear, with ℓᵥ scaled in a way consistent with theories and observations of stratified turbulence. Unlike previous studies, the focus is not so much on the functional form of Ri, but the vertical variation of the length scale ℓᵥ. Using data from two ∼7‐day time series in the western equatorial Pacific, the scaling is compared with the observed ϵ. The scaling works well with the estimated ϵ capturing the differences in amplitude and vertical distribution of the observed ϵ between the two times series. Much of those differences are attributable to changes in the vertical distribution of the length scale ℓᵥ, and in particular the associated turbulent velocity scale, uₜ. We relate uₜ to a measure of the fine‐scale variations in velocity, u∼. Our study highlights the need to consider the length scale and its estimation in environmental flows. The implications for the vertical variation of the associated turbulent diffusivity are discussed.
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