Nonlinear Models of Coastal Upwelling and Coastal Jets in Continuously Stratified Seas

Abstract

Abstract Nonlinear models of continuously stratified seas are developed for vertical sections to study the mechanism of generation of coastal upwelling and coastal jets in two different kinds of sea. One is bounded by two vertical coasts without elevation of the sea surface but with flat bottom, so-called the finite (or closed) sea, whereas the other is a semi-infinite sea bounded by only one vertical coast with elvation of the sea surface and with flat or inclined bottom. Constant wind stress in the first case and constant wind stress or negative wind stress curl in the second case are abruptly imposed. The key procedure for the mathematical analysis is to calculate the horizontal pressure gradient firstly by a special treatment. In the first case it is shown that the width of baroclinic jets depends upon (os)1/2 and the distribution of isopycnic lines indicates warm and cold regions. Relative importance of each term in the equilibrium among forces is determined. Distribution of the stream function in vertical section reveals the upper and bottom Ekman layers. Two coastal jets are found with different longshore velocities. The distribution of density anomalies displays the horizontal diffusion adjustment. An unstable case appears depending on the surface boundary condition. In the second case, the vertical velocity will be stronger in the sea less stratified, with an inclined bottom and with a negative wind stress curl. The horizontal offshore velocity increases its strength in a sea with inclined bottom and with negative wind stress curl. The vertical circulation pattern reveals the upwelling only. The distribution of density shows the isopycnic lines lifted upward near the shores. Obviously, the range of the sea surface elevation is larger near the shore than far from the shore. The jet is narrower than the Rossby radius of deformation. The coastal jet does not evolve when the coefficient of horizontal turbulence increases to a certain limiting value.