On the role of shear mixing during transient coastal upwelling

Abstract

A two-dimensional two-layer model for wind-driven transient coastal upwelling is formulated. Toe momentum equations include the turbulent dynamics and the time-dependent and nonlinear terms in both the cross- and along-shore directions. The continuity and heat equations allow mass and heat turbulent transfer between both layers. Toe integral form of the momentum, continuity and heat equations are closed using a two-regime parameterization for the entrainment velocity. In the first regime, corresponding to the early stages of upwelling, the interface quickly raises due to flux divergence near the coast. Toe entrainment velocity is small (0.1-1 m day-1), largely produced through KRAus and TURNER's [(1967) Tellus, 19, 98--106] slow erosion of the thermocline, and it is estimated using NnLER and KRAus' [(1977) In: Modelling and prediction of the upper layers of the ocean, Pergamon Press, Oxford, pp.143-172] parameteriza­ tion. When the bulk Richardson number (Ri) becomes close to íts critica! value then we switch to the second regime, during which we calculate the entrainment velocity from the continuity equation under the condition that Ri remains near-critical, i.e. the equivalent of PoLLARD et al. [(1973) Geophysical Fluid Dynamics, 4, 381-404] stability criterion for the upper ocean. Toe entrainment velocity quickly becomes large (severa! m h-1), the interface deepens and stratifi­cation is eroded. Toe existence of this regime is supported by observations of persistent near­critical gradient Richardson numbers (Rig) during coastal upwelling [JoHNSON (1981) In: Coastal upwelling, American Geophysical Union, Washington, DC., pp. 79-86; JoHNSON et al. (1976) Journal of Physical Oceanography, 6, 556-574; KuNDU and BEARDSLEY, (1991) Joumal of Geophysical Research, 96, 4855-4868]. Our model is applied to severa! initial temperature differences between the surface and bottom layers, with the upper !ayer depth and forcing parameters realistically chosen. The dynamically important mixing regime corresponds to the second regime, with effective shear-induced mixing being produced through a strong baroclinic coastal jet. A realistic front, formed between the well­mixed water near the coast and lighter offshore surface water, propaga tes away from the coast. Toe offshore waters are characterized by the presence of inertial oscillations, overlying the Ekman flow. The inertial oscillations are too weak to produce any significant mixing, but a comparison with DESzoEKE and RicHMAN's [(1984) Journal of Physical Oceanography, 14, 364-377) semigeos­trophic model (modified to include the shear-mixing regime) shows that they are important enough to exert sorne control on the horizontal volume flux divergence near the coast. A relatively fast interna! Poincare wave, propagating from the coast, has the effect of slowly dampening the inertial oscillations. The results are in good qualitative agreement with early observations by JoHNSON et al. (1976).