Dynamics of advection-driven upwelling over a shelf break submarine canyon

The response over a submarine canyon to a several day upwelling event can be separated into three phases: an initial transient response; a later, much longer, steady advection-driven response; and a final relaxation phase. For the advection-driven phase over realistically steep, deep, and narrow canyons with near-uniform flow and stratification at rim depth, we have derived scale estimates for four key quantities. Observations from 5 real-world canyon studies and 3 laboratory studies are used to validate the scaling and estimate the scalar constant for each scale. Based on 4 geometric parameters of the canyon, the background stratification, the Coriolis parameter, and the incoming current, we can estimate (1) the depth of upwelling in the canyon to within 15 m, (2) the deep vorticity to within 15%, and (3) the presence/absence of a rim depth eddy can be determined. Based on laboratory data, (4) the total upwelling flux can also be estimated. The scaling analysis shows the importance of a Rossby number based on the radius of curvature of isobaths at the upstream mouth of the canyon. This Rossby number determines the ability of the flow to cross the canyon isobaths and generate the pressure gradient that drives upwelling in the canyon. Other important scales are a Rossby number based on the length of the canyon which measures the ability of the flow to lift isopycnals and a Burger number based on the width of the canyon that determines the likelihood of an eddy at rim depth. Generally, long canyons with sharply turning upstream isobaths, strong incoming flow, small Coriolis parameter, and weak stratification have the strongest upwelling response.