Wind-Driven Circulation in a Shelf Valley. Part II: Dynamics of the Along-Valley Velocity and Transport.

The dynamics controlling the along-valley (cross-shelf) flow in idealized shallow shelf valleys with small to moderate Burger Number are investigated, and analytical scales of the along-valley flows are derived. This paper follows Part 1 which shows that along-shelf winds in the opposite direction to coastal-trapped wave propagation (upwelling regime) force a strong up-valley flow caused by the formation of a lee wave. In contrast, along-shelf winds in the other direction (downwelling regime) do not generate a lee wave and consequently force a relatively weak net down-valley flow. The valley flows in both regimes are cyclostrophic with order-one Rossby number. A major difference between the two regimes is the along-shelf length scales of the alongvalley flows, Lx. In the upwelling regime Lx depends on the valley width, Wc, and the wavelength (iw) of the coastal-trapped lee wave arrested by the along-shelf flow, Us. In the downwelling regime Lx depends on the inertial length scale, \Us\lf, and Wc. The alongvalley velocity scale in the upwelling regime, given by VN ≈ √ π Hc/H3 fWcλlw/2πLx(1+L2x/L2c)-1e-(πWMc)(λlw), is based on potential vorticity (PV) conservation and lee-wave dynamics (Hs and Hc are the shelf and valley depth scales, respectively, and fis Coriolis). The velocity scale in the downwelling regime, given by |Vc|≈(Hc|Hs)[1+L2x|L2c]-1fLx is based on PV conservation. The velocity scales are validated by the numerical sensitivity simulations and can be Useful for observational studies of along-valley transports. The work provides a framework for investigating cross-shelf transport induced by irregular shelf bathymetry and calls for future studies of this type under realistic environmental conditions and over a broader parameter space. [ABSTRACT FROM AUTHOR]