Scale Evolution of Finite-Amplitude Instabilities on a Coastal Upwelling Front

Abstract

Nonlinear model simulations of a coastal upwelling system show frontal instabilities that initiate at short alongshore scales but rapidly evolve to longer wavelengths. Several factors associated with the nonstationarity of this basic state contribute to the progression in scale. A portion of the system evolution is associated with the external forcing. Another portion is associated with the alteration of the alongshore mean flow resulting from wave growth. Direct interactions between the finite-amplitude disturbances also promote emergence of new scales. The relative role of each of these mechanisms is isolated through tangent linear simulations about basic states that approximate the nonlinear system to differing degrees. The basic states include an alongshore uniform time-evolving upwelling solution, the alongshore average of a three-dimensionally evolving upwelling solution, and the full three-dimensional nonlinear solution. Disturbance growth about a frozen-field upwelling state is also examined. Perturbation experiments are performed for persistent and relaxed wind forcing. Although the frontal disturbances in the nonlinear model exhibit a progression to larger scale over the full range of forcing scenarios considered, the mechanisms most responsible for the process differ between wind-forced and unforced cases. Under relaxed wind conditions, the perturbation growth experiments indicate that the scale evolution over the first four days is reflected in the way linear disturbances respond to the adjustment of an alongshore uniform upwelling front to wind cessation. The continued increase in scale between days 4 and 7 is related to the linear disturbance evolution on the alongshore average of a flow state that has been altered by wave-mean flow interaction. Past day 7, the observed scale change is not captured in the linear growth experiments and evidently results largely from nonlinear wave-wave interaction processes. Under sustained upwelling winds, the linear growth experiments fail to describe even the earliest scale change in the nonlinear solutions, indicating that nonlinear wave-wave effects are significant from very near the start of the simulations.

The Influence of a Submarine Canyon on the Circulation and Cross-Shore Exchanges around an Upwelling Front

“…Initial conditions in temperature and salinity are set horizontally uniform and taken from the average profiles from all spring-summer glider observations off Oregon during the period 2006-14. Thus, our density and stratification conditions are similar to previous studies of coastal upwelling instabilities off Oregon (Durski and Allen 2005).…”

“…Vertical mixing follows the Mellor-Yamada level 2.5 closure scheme (Mellor and Yamada 1982); the background vertical viscosity and diffusivity are 1 3 10 25 and 5 3 10 26 m 2 s 21 , respectively. Bottom stress is calculated with a quadratic drag law using a bottom roughness of 2 3 10 22 m. ROMS has been used in several studies of flow over topography, including submarine canyons (e.g., She and Klinck 2000;Dinniman and Klinck 2002;Rennie et al 2009;Chen et al 2014;Connolly and Hickey 2014) and banks (e.g., Kim et al 2009;Whitney and Allen 2009a,b), and in studies of frontal instabilities (e.g., Durski and Allen 2005;Capet et al 2008;Brink 2016a).…”

“…The lateral density gradients around the front sustain the development and evolution of a geostrophically balanced upwelling jet that flows downstream with core velocities ;0.5 m s 21 (e.g., O'Brien and Hurlburt 1972;Kosro et al 1997;Castelao and Barth 2007). This process is also characterized by low (high) sea level nearshore (offshore) (e.g., Whitney and Allen 2009a), and the formation of prominent frontal instabilities in the form of filaments around the front (Flament et al 1985; Washburn and Armi 1988;Barth 1989;Durski and Allen 2005;Troupin et al 2012).…”

“…Cross-shelf exchanges can be significantly enhanced not only by the presence of a major bathymetric barrier as a submarine canyon (Allen and Durrieu de Madron 2009), but also due to the high vorticity field created by frontal instabilities (Durski and Allen 2005;Wang and Jordi 2011). Although shelf-slope exchanges have been widely studied and reviewed (e.g., Houghton et al 1988;Huthnance 1995;Dinniman and Klinck 2004;Brink 2016a), there is scarce information on the combined effect and/or the interaction between surface frontal instabilities and a submarine canyon.…”

Generation of the Cape Ghir upwelling filament: A numerical study

“…Nevertheless, the role of high-frequency wind variations cannot be discarded: off the Oregon coast, experiments with temporally variable winds (Durski and Allen, 2005), with relaxed and sustained winds (Durski et al, 2007) or with a timeperiodic winds (Durski et al, 2008) underlined their role in the creation of alongshore-scale instabilities and large-scale disturbances in the upwelling front. Experiments with more realistic winds will be performed in a future work.…”