Vertically integrated models of bottom mixed layer growth in the ocean

Jin, You-Huang (1991) Vertically integrated models of bottom mixed layer growth in the ocean. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

A new vertically integrated model is developed for the growth of bottom mixed layers. Unlike the usual slab models this model retains the vertical variation of mean speed with height, which appears as a parameter in the energy balance. The mixed layer growth problem is solved analytically for a horizontal flat bottom and numerically for a sloping flat bottom. A relaxation problem, the decay of motion in the bottom mixed layer after the geostrophic flow in the interior ceases, is also solved analytically and numerically. Finally solutions including thermal wind effects on bottom mixed layer growth are obtained for both a horizontal flat bottom and a sloping flat bottom. -- For the horizontal flat bottom case, an algebraic formula for mixed layer thickness is obtained for arbitrary values of the Brunt-Vaisala frequency and Coriolis parameter. The results show that the vertical variation of speed must be taken into account when the ratio of the Brunt-Vaisala frequency to the Coriolis parameter is less than or of order unity, and that the formula is consistent with that obtained by Weatherly and Martin (1978). Formulae for dependence of friction velocity and veering angle on stratification are also obtained. -- For a sloping bottom at the initial stage of bottom boundary layer growth the vertically integrated model produces results very similar to those obtained by Weatherly and Martin (1978) using the Mellor and Yamada Level II turbulent closure model. The main effect of bottom slope is to produce upwelling or downwelling within the bottom boundary layer. After the initial period of boundary layer development the vertically integrated buoyancy force can grow to reach a balance with the vertically integrated driving pressure gradient so that the Ekman transport is extinguished and the layer becomes arrested. The length of the initial period greatly depends on the sign of bottom slope. -- The effects of thermal wind are shown to be important. For a horizontal flat bottom if the vertical shear in the interior is positive the mixed layer grows indefinitely. If the vertical shear is negative the thickness reaches a constant value or decreases with time. For a sloping flat bottom the thermal wind is important when the isopycnal slope is comparable to or much greater than the bottom slope. The results are in agreement with the observations made by Weatherly and Van Leer (1977) on the western Florida Continental Shelf.

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