Exact Solutions of Wind-Driven Coastal Upwelling and Downwelling over Sloping Topography

Abstract

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping topographies. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer and no along-slope dependence of the variables; however, dependence in the cross-slope and vertical directions is retained. Density and the along-slope component of momentum are advected by the cross-slope velocity, with thermal wind balance maintained at all times. The time-dependent initial value problem is solved with constant initial stratification and no initial along-slope flow. Previously, this model has been used to study upwelling over flat-bottomed ocean, but the novel features in this work are the study of exact solutions for a family of sloping topographic profiles, for both upwelling and downwelling. The exact solutions are compared to numerical solutions from a primitive equation ocean model configured in a similar twodimensional geometry. The exact solutions predict that deep undercurrents will develop only over steep topographic slopes and the cross-slope flow in the deep frictionless interior will be increasingly surface intensified as the topographic slope increases.

Dynamics of the summer shelf circulation and transient upwelling off Ningaloo Reef, Western Australia

“…The vertical structure of the cross‐shelf transport during wind‐driven coastal upwelling should depend on the Burger number ( B = αN / f ) [ Lentz and Chapman , ], where α is the shelf slope and N is the buoyancy frequency. Lentz and Chapman [] proposed that when B > 2, the subsurface onshore transport of water required to balance the near‐surface offshore flow is being sourced from the interior of the water column with little contribution from the frictional‐influenced bottom boundary layer [ Choboter et al ., ]. A comparison of some typical parameter values at upwelling sites along North and South America is shown in Table ; while stratification values off the Ningaloo coast in summer are not too different from typical values at other sites, the Ningaloo continental shelf is uniquely characterized by its steep shelf slope (~1/50; up to 3 times steeper than the other sites).…”

The effect of changes in surface winds and ocean stratification on coastal upwelling and sea surface temperatures in the Pliocene

“…There have been many studies of upwelling systems using idealized, sometimes analytic, models that illustrate the main factors participating in the upwelling dynamics [e.g., Pedlosky , , ; Allen , , ; Lentz and Chapman , ; Choboter et al , , ; Samelson and de Szoeke , ]. However, none of the analytic models have been able to represent the nonlinearities in a continuously‐stratified configuration in a way that is fully consistent with observations.…”

How the Source Depth of Coastal Upwelling Relates to Stratification and Wind

“…As a result, several other factors that affect upwelling are neglected. To start, we ignore bottom topography, which impacts the source depth through altering the cross‐shore velocity and its depth structure (Choboter et al., 2011; Jacox & Edwards, 2011, 2012; Lentz & Chapman, 2004). Here, we focus on upwelling just from the interior and not coming upslope through the bottom boundary layer.…”