### Abstract:

Analytical and idealized-numerical models were used to understand the physical processes that govern the seasonal variation and fate of the freshwater in the Alaska Coastal Current (ACC). The ACC is forced by freshwater inflow and by mean easterly winds that cause downwelling over the shelf. Two-dimensional modeling using a line-source buoyant inflow gives the coastal current depth <math> <f> H=<fr><nu>3<sup>2/3</sup></nu><de>2</de></fr><fen lp="par"><fr><nu> f<sup>2</sup>Q<sup>2</sup></nu><de>g<sup>'</sup></de></fr> <rp post="par"></fen>t<sup>2/3</sup></f> </math> and coastal current width <math> <f> Y<inf>2D</inf>=3<sup>1/3</sup><fen lp="par"><fr><nu>g<sup>' </sup>Q</nu><de>f<sup>2</sup></de></fr><rp post="par"></fen><sup> 1/3</sup>t<sup>1/3</sup></f> </math>, where f is the Coriolis frequency, g ' is reduced gravity, Q is inflow rate and t is time since inflow began. Addition of downwelling wind-stress causes a steep coastal current front that intersects the bottom and is either convecting, stable and steady, or stable and oscillatory depending on <math> <f> <fr><nu>D</nu><de><g>d</g><inf>*</inf></de></fr></f> </math> and <math> <f> <fr><nu>b<inf>y</inf></nu><de>f<sup>2</sup></de></fr></f> </math>, where D is bottom depth, delta* is an Ekman depth and by is the cross-shelf buoyancy gradient. Three-dimensional modeling of a half-line source initially develops two-dimensionally but becomes three-dimensional from a balance between coastal influx of buoyancy and its downstream transport. This balance results in a coastal current depth limit <math> <f> H<inf><rf>max</rf></inf>=<fen lp="par"><fr><nu>2Qf</nu><de>g<sup> '</sup></de></fr><rp post="par"></fen><sup>1/2</sup>x<sup> 1/2</sup></f> </math>, where x is along-shelf distance. This limit is unchanged under downwelling wind-stress and is reached on time scales of less than 1 month for the ACC. The half-line source coastal current width develops as <math> <f> Y<inf>2D</inf></f> </math> away from the beginning of the line source. Imposition of a downwelling wind-stress tau results in an approximate balance among wind-stress and along- and cross-shelf momentum advection so that the current width is reduced to <math> <f> Y<inf>wind</inf>≈L<inf>D</inf><fen lp="par"><fr><nu>Qf</nu> <de><g>t</g>/<g>r</g><inf>0</inf></de></fr><rp post="par"></fen><sup> 1/2</sup></f> </math>, where LD is the Rossby radius of deformation. Waves and eddying motions eventually grow in the half-line source coastal current with wavelengths proportional to the coastal current width and with a downstream phase speed slower than the maximum current speed. These features cause an offshore flux of buoyant water, a broader coastal current and accumulation of buoyancy on the shelf. Increasing downwelling wind stress reduces the effects of the instabilities. Although buoyancy accumulates on the shelf during most model runs, there is little accumulation under maximum winter downwelling wind-stress. This suggests that freshwater accumulates on the shelf from spring through fall, but is then transported downstream during winter.