J. Fluid Mecli. zyxwvutsrq (1995), zyxwvutsrq 001. zyxwvutsrqp 304, pp. 27-46 Copyright zyxwvutsrq 0 1995 Cambridge University Press zyxwvu 27 Onset of stratification in a mixed layer subjected to a stabilizing buoyancy flux By Y. NOH' AND H. J. S. FERNANDO2 Department of Astronomy and Atmospheric Sciences, Yonsei University, Seoul 120-749, Korea z * Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, (Received 10 June 1994 and in revised form 10 July 1995) The formation of a thermocline in a water column, in which shear-free turbulence is generated both at the surface and bottom, and a stabilizing buoyancy flux is imposed at the surface, is studied using a laboratory experiment and a numerical model with the aim of understanding the formation of a tidal front in coastal seas. The results show that the formation of a thermocline, which always occurs in the absence of bottom mixing, is inhibited and the water column maintains a vertically mixed state, when bottom mixing becomes sufficiently strong. It is found from both experimental and numerical results that the criterion for the formation of a thermocline is determined by the balance between the rate of work that is necessary to maintain a mixed state against the formation of stratification by the buoyancy flux and the turbulent kinetic energy flux from the bottom supplied to the depth of thermocline formation. The depth of the thermocline, when it is formed, is found to decrease with bottom mixing. AZ 85287-6106, USA 1. Introduction In coastal regions of the ocean where a relatively shallow shelf occupies large areas, the turbulence generated by the tidal friction causes the formation of a sharp boundary between the well-mixed shelf water and the stratified water of the contiguous deep ocean. To predict the position of such fronts, Simpson & Hunter (1974) proposed a criterion based on the parameter B*, which determines whether the water column is well-mixed or stratified. The parameter /3* was obtained by considering the balance between the potential energy increase of the well-mixed state against the stratified state induced by buoyancy flux and the turbulent kinetic energy generation by the tidal friction at the bottom. This gives where Q is the buoyancy flux at the surface, H is the height of the water column and z U, is the amplitude of the tidal velocity. When B* is small in shallow water (p* < lo5, Simpson, Allen & Morris 1978), the sea water maintains a well-mixed state with relatively uniform vertical density distribution, and the heat supplied to the surface is effectively transferred to the bottom. On the other hand, as /3* becomes larger with the increase of the water depth, a thermocline appears, which prohibits vertical heat transfer, thus making the temperature at the sea surface much higher than for the well- mixed state. The boundary between the well-mixed and stratified waters appears as a tidal front at the sea surface. There have been numerous studies on tidal front formation (Fearnhead 1975 ; Simpson et al. 1978; Pingree & Griffiths 1978; Bye 1990). All the previous models, 'lowever, are based on the global balance between the input of kinetic energy from the B* = HQIu:, (1-1)