Characteristics of a front formed by cooling of the sea surface and inflow of the fresh water

Two numerical studies (Endoh, 1977;Harashimaet al., 1978) have been proposed on a front formed by a coupling effect of cooling of the sea surface and inflow of the fresh water in a vertical two-dimensional plane without the rotation of the earth. It is, however, not easy to interpret their numerical results. A simple interpretation will be proposed by an analytical study in this paper.It is found that local convection due to the density inversion, which is expressed by the convective adjustment of the vertical diffusion coefficient in the actual numerical calculations, plays an important role on the front formation.The characteristics of the front is also clarified in the case of steady state. Namely, simple functional dependences are obtained of the position and the width of the front, the horizontal and the vertical velocities and the distribution of the buoyancy and the salinity in the neighborhood of the front on the horizontal coordinate, the cooling rate, the eddy coefficients of diffusion and viscosity, the water depth and the vertically averaged horizontal fluxes of buoyancy and salinity.