Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 883-904, doi:10.1175/JPO-D-17-0084.1.
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.
Both WGZ and SJL were supported
by the National Science Foundation (NSF)
through Grant OCE 1154575.WGZis also supported by
the NSF Grant OCE 1634965 and SJL by NSF Grant
Woods Hole Open Access Server