The Probability Distribution of the Thorpe Displacement within Overturns in Juan de Fuca Strait

Abstract

Vertical mixing in the ocean can sometimes be quantified by measurements of the Thorpe overturning scale, LT. In regions of weak mixing and weak density gradients such measurements may be limited by slow sensor response times (or sampling rates) and/or by lack of resolution and noise in the density measurements. On the other hand, the Thorpe scale can be written as LT = (?∞0 L2P1(L) dL)1/2, where P1(L) is the probability of the Thorpe displacement, L. Data from Juan de Fuca Strait, British Columbia, show that, even though the probability of a small Thorpe displacement is much greater than that of a large Thorpe displacement, it is the large and more easily resolved values of L that dominate the Thorpe scale. It is found to be possible to determine LT down to a scale of 0.4 m with a conventional conductivity?temperature?depth instrument. This corresponds to values of K? ? 10?4 m2 s?1 in summertime if LT ≈ (?/N3)1/2, as is confirmed using velocity and temperature microstructure data. Here P1(L) is a convolution of the probability distribution of overturn height, P2(H), with the probability distribution of the fractional displacement within each overturn, P3(L/H). Data show that P2(H) is dominated by small overturns, consistent with previous work on the thickness of turbulence patches. Finally, the distribution of P3(L/H) is examined and compared with the prediction of a very simple kinematic model. The data show a pattern similar to that predicted by the model, though with more small L/H and fewer medium to large L/H than in the model.