ON THE ROLE OF SHEAR MIXING DURING TRANSIENT COASTAL UPWELLING

A two-dimensional two-layer model for wind-driven transient coastal up welling is formulated. The momentum equations include the turbulent dy namics and the time-dependent and nonlinear terms in both the cross- a nd along-shore directions. The continuity and heat equations allow mas s and heat turbulent transfer between both layers. The integral form o f the momentum, continuity and heat equations are closed using a two-r egime parameterization for the entrainment velocity. In the first regi me, corresponding to the early stages of upwelling, the interface quic kly raises due to Bur divergence near the coast. The entrainment veloc ity is small (0.1-1 m day(-1)), largely produced through KRAUS and TUR NER'S [(1967) Tellus, 19, 98-106] slow erosion of the thermocline. and it is estimated using NILLER and KRAUS' [(1977) In: Modelling and pre diction of the upper layers of the ocean, Pergamon Press, Oxford, pp.1 43-172] parameterization. When the bulk Richardson number (Ri) becomes close to its critical value then we switch to the second regime, duri ng which we calculate the entrainment velocity from the continuity equ ation under the condition that Ri remains near-critical, i.e. the equi valent of POLLARD et al. [(1973) Geophysical Fluid Dynamics, 4, 381-40 4] stability criterion for the upper ocean. The entrainment velocity q uickly becomes large (several m h-l), the interface deepens and strati fication is eroded. The existence of this regime is supported by obser vations of persistent near-critical gradient Richardson numbers (Ri(g) ) during coastal upwelling [JOHNSON (1981) In: Coastal upwelling, Amer ican Geophysical Union, Washington, DC., pp. 79-86; JOHNSON et al. (19 76) Journal of Physical Oceanography, 6, 556-574; KUNDU and BEARDSLEY, (1991) Journal of Geophysical Research, 96, 4855-4868]. Our model is applied to several initial temperature differences between the surface and bottom layers, with the upper layer depth and forcing parameters realistically chosen. The dynamically important mixing regime correspo nds to the second regime, with effective shear-induced mixing being pr oduced through a strong baroclinic coastal jet. A realistic front, for med between the well-mixed water near the coast and lighter offshore s urface water, propagates away from the coast. The offshore waters are characterized by the presence of inertial oscillations, overlying the Ekman flow. The inertial oscillations are too weak to produce any sign ificant mixing, but a comparison with DESZOEKE and RICHMAN'S [(1984) J ournal of Physical Oceanagraphy, 14, 364-377] semigeostrophic model (m odified to include the shear-mixing regime) shows that they are import ant enough to exert some control on the horizontal volume flux diverge nce near the coast. A relatively fast internal Poincare wave, propagat ing from the coast, has the effect of slowly dampening the inertial os cillations. The results are in good qualitative agreement with early o bservations by JOHNSON et al. (1976).