We have formulated 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 easily 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, with lv scaled in a way that is 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 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, ũ. Our study highlights the need to consider the length scale and its estimation in environmental flows.
Motivated by observations of fine scale vertical shear and its contribution to mixing in the tropical ocean, we have explored the impact of vertical resolution in an ocean model on sea surface temperature in the tropical Pacific Ocean. We have conducted two model experiments that differ in the vertical discretization only, with the grid spacing in one being significantly smaller than the other in the upper ocean. We find that the difference SST between the high and low vertical resolution experiments is positive in the equatorial cold tongue and negative along the South American coast, thus reducing the commonly seen cool and warm biases in the two regions, respectively. The change in the structure of the vertical diffusivity is identified as the primary cause in reducing the biases. In the central equatorial Pacific, the change in the vertical diffusivity from low to high vertical resolution in the upper pycnocline results in a positive temperature difference that propagates eastward as an equatorial Kelvin wave, rising to the sea surface in the central and eastern regions to increase the sea surface temperature there. In the far eastern equatorial Pacific, the change in the vertical diffusivity in the lower pycnocline produces a negative temperature difference that propagates poleward as coastal Kelvin waves along the west coast of the American continent, outcropping along the South American coast to reduce the sea surface temperature there. The high vertical resolution experiment captures much of the small-scale vertical velocity shear and resolves the fine details of the stratification in the upper ocean. Our analysis suggests that the shear-generated turbulence is the primary contributor to the change in the vertical diffusivity in the central region whereas stratification is the dominant factor in the far eastern region.
Major lessons learnt are the importance of relatively small vertical scale flow features in producing turbulent mixing in the equatorial thermocline, the importance of the vertical distribution of that mixing and its impact on ocean surface temperatures which in turn affects ocean/atmosphere interactions. We have established the need to determine the spatial and temporal variability of mixing together with the factors controlling the finescale structures in the flow. The TPOS process studies need to take this into account.
Jia Y., K.J. Richards and H. Annamalai (2021). The impact of vertical resolution in reducing biases in sea surface temperature in a tropical Pacific Ocean model. Ocean Modelling, 157, 101722.
Richards K.J., A. Natarov and G.S. Carter (2021). Scaling of shear-generated turbulence: the equatorial thermocline, a case study. Under review with J. Geophys. Res.