Continental Shelf Baroclinic Instability. Part II: Oscillating Wind Forcing

Abstract

Continental shelf baroclinic instability energized by fluctuating alongshore winds is treated using idealized primitive equation numerical model experiments. A spatially uniform alongshore wind, sinusoidal in time, alternately drives upwelling and downwelling and so creates highly variable, but slowly increasing, available potential energy. For all of the 30 model runs, conducted with a wide range of parameters (varying Coriolis parameter, initial stratification, bottom friction, forcing period, wind strength, and bottom slope), a baroclinic instability and subsequent eddy field develop. Model results and scalings show that the eddy kinetic energy increases with wind amplitude, forcing period, stratification, and bottom slope. The dominant alongshore length scale of the eddy field is essentially an internal Rossby radius of deformation. The resulting depthaveraged alongshore flow field is dominated by the large-scale, periodic wind forcing, while the cross-shelf flow field is dominated by the eddy variability. The result is that correlation length scales for alongshore flow are far greater than those for cross-shelf velocity. This scale discrepancy is qualitatively consistent with midshelf observations by Kundu and Allen, among others.

Cross-Shelf Exchange

“…These mask weaker, largerscale interior cross-shelf flows. The smaller scale features are evidently related to baroclinic instability of the wind-driven alongshore flow Brink and Seo, 2015) which is surely active in many upwelling regions (Barth, 1989 a, b;Barth, 1994;Durski and Allen, 2005) and perhaps much more widely. The underlying observational issues boil down to observing a weak cross-shelf net flow in a noisy, complex setting.…”

Rectified flow in a stratified coastal ocean

“…In some cases, for example involving an adverse steady wind stress τ 0 (e.g., runs 36 or 38), a mean alongshore flow pattern will vanish (e.g., when τ 0 > 0, there may not be a negative v S ), in which case, the missing positive or negative extreme is denoted by a blank in Table 1. The magnitude of Castelao et al (2010)'s rectified cross-shelf flow is identified with ψ S and the positive alongshore current rectification identified by Brink and Seo (2016) is identified with v Max . Occasionally, the bottom boundary layer <ψ> minimum merges with the nearshore minimum, but this is usually not the case.…”

“…Coastal oceanographers are familiar with the idea that fluctuating currents, such as tides, can generate mean alongshore and cross-shelf flow (e.g., Huthnance 1973;Loder 1980;Garrett and Loder 1981;Brink 2010). That these flows arise is not surprising because the bottom slope provides a strong and ubiquitous "topographic beta" that effectively provides a preferred alongshore direction (in the sense of long topographic Rossby wave propagation) for any steady barotropic flow.…”

“…More recently, Brink and Seo (2016) used idealized numerical models to show that fluctuating alongshore wind stresses can drive a positive (i.e., opposite to the sense of long topographic wave propagation) mean alongshore flow in a two-or three-dimensional stratified coastal ocean. In addition, Kuebel-Cervantes, Allen, and Samelson (2004) did a similar two-dimensional model run and obtained a similar mean flow, although this was not emphasized due to their concentration on Lagrangian flow patterns.…”

Some considerations about coastal ocean observing systems

“…It seems likely (Brink 1987) that this spatial scale discrepancy is associated with different aspects of the flow field dominating: wind driving for alongshore flow, and small-scale eddies for cross-shelf flows outside the surface or bottom boundary layers. This eddy scale would presumably be around the internal Rossby radius of deformation, or around 5 km over midlatitude shelves (K. H. Brink and H. Seo, 2016). If indeed the crossshelf flow is dominated by different, smaller-scale physics than what drives the alongshore flow, the measurement and prediction problem, at least from a deterministic standpoint, becomes very difficult.…”