Wind-driven circulation in a shelf valley. Part II : Dynamics of the along-valley velocity and transport

Abstract

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 I, 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 0(1) Rossby number. A major difference between the two regimes is the along-shelf length scales of the along-valley flows L. In the upwelling regime Ls, depends on the valley width W, and the wavelength lambda(1w) of the coastal-trapped lee wave arrested by the along-shelf flow U-s. In the downwelling regime L depends on the inertial length scale U-s|'f and W-c. The along-valley velocity scale in the upwelling regime, given by

V-u approximate to root pi H-c/H-s integral W-c lambda(1w)/2 pi L-x (1+L-x(2)/L-c(2))(-1) e(-(pi Wc)/(lambda 1w),)

is based on potential vorticity (PV) conservation and lee-wave dynamics (Hs and H, are the shelf and valley depth scales, respectively, and fis the Coriolis parameter). The velocity scale in the downwelling regime, given by

|v(d)| approximate to (H-s/H-s)[1 + (L-x(2)/L-x(2))](-1) fL,

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.