Abstract
In Part 1 (Wienkers, Thomas & Taylor, J. Fluid Mech., vol. 926, 2021, A6), we described the theory for linear growth and weakly nonlinear saturation of symmetric instability (SI) in the Eady model representing a broad frontal zone. There, we found that both the fraction of the balanced thermal wind mixed down by SI and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of SI we call ‘slantwise inertial instability’ by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in ‘slantwise convection.’ Here, we extend the theory from Part 1 using nonlinear numerical simulations to focus on the adjustment of the front following saturation of SI. We find that the details of adjustment and amplitude of the induced inertial oscillations depend on the front strength. While weak fronts develop narrow frontlets and excite small-amplitude vertically sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. The turbulent dissipation rate in these strong fronts is large, highly intermittent and intensifies during periods of weak stratification. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state, and in particular focus on the effect of varying the dimensionless front strength.
Highlights
Fronts, or regions with large horizontal density gradients, are common features of the ocean surface mixed layer
There, we considered the linear growth and weakly nonlinear saturation of symmetric instability (SI) in the idealised problem consisting of a broad frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance and bounded by flat no-stress horizontal surfaces
Considering the sharp density step formed at tf = 20.5 c ≈ 0.08 and so h ≈ 0.009. This inferred gravity current height does not seem to describe well the boundary features seen in the corresponding across-front slice at the bottom of the figure, suggesting that these are not gravity currents in the weakest front. In this two-part series, we explored how the equilibration of fronts by SI depends on the strength of the horizontal stratification, parameterised by Γ ≡ M2/f 2
Summary
Regions with large horizontal density gradients, are common features of the ocean surface mixed layer. We hypothesised that the fraction of the thermal wind mixed down by SI and the ensuing turbulence can be related to the amplitude of the subsequent inertial oscillations by using the theory of Tandon & Garrett (1994). We computed their parameter s, f ∂vs≡. The nonlinear consequences of these results from Part 1 – of the energy sources and thermal wind mixing rate, which were shown to strongly depend on Γ – are expected to influence the later evolution of the front beyond the initial saturation of SI. We further describe how these persistent SI modes can generate frontlets and bore-like gravity currents, and consider how this behaviour scales with front strength
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
