TL;DR: In this paper, the formation of strong and potentially singular fronts in a two-dimensional quasigeostrophic active scalar is studied through the symbiotic interaction of mathematical theory and numerical experiments.
Abstract: The formation of strong and potentially singular fronts in a two-dimensional quasigeostrophic active scalar is studied through the symbiotic interaction of mathematical theory and numerical experiments. This active scalar represents the temperature evolving on the two dimensional boundary of a rapidly rotating half space with small Rossby and Ekman numbers and constant potential vorticity. The possibility of frontogenesis within this approximation is an important issue in the context of geophysical flows. A striking mathematical and physical analogy is developed between the structure and formation of singular solutions of this quasi-geostrophic active scalar in two dimensions and the potential formation of finite time singular solutions for the 3-D Euler equations. Detailed mathematical criteria are developed as diagnostics for self-consistent numerical calculations indicating strong front formation. These self-consistent numerical calculations demonstrate the necessity of nontrivial topology involving hyperbolic saddle points in the level sets of the active scalar in order to have singular behaviour; this numerical evidence is strongly supported by mathematical theorems which utilize the nonlinear structure of specific singular integrals in special geometric configurations to demonstrate the important role of nontrivial topology in the formation of singular solutions.
TL;DR: In this article, an analytic approach is made to a frontogenesis model based on the classic horizontal deformation field, which is solved exactly for a Boussinesq, uniform potential vorticity fluid.
Abstract: The approximation of geostrophic balance across a front is studied. Making this approximation, an analytic approach is made to a frontogenesis model based on the classic horizontal deformation field. Kelvin's circulation theorem suggests the introduction of a new independent variable in the cross-front direction. The problem is solved exactly for a Boussinesq, uniform potential vorticity fluid. Non-Boussinesq, non-uniform potential vorticity, latent heat, and surface friction effects are all studied. Using a two-region fluid we model the effects of confluence near the tropopause. A similar approach is made to the appearance of fronts in the finite-amplitude development of the simplest Eady wave; this is also solved analytically. Based on the surface fronts produced by these models, we give a general model of a strong surface front. There is a tendency to form discontinuities in a finite time.
TL;DR: In this paper, the evolution of main fronts between 0° and 150°E was analyzed to investigate the main fronts in the central South Atlantic, where the central south Atlantic is featured by the Subtropical Frontal Zone (STFZ), bordered by the North and South Subtropicals Fronts (NSTF and SSTF, respectively), and by the Polar Frontal Zones (PFZ), with the Subantarctic and Polar Fronts(SAF and PF, respectively).
Abstract: All available meridional sections have been analyzed to investigate the evolution of main fronts between 0° and 150°E. The central South Atlantic is featured by the Subtropical Frontal Zone (STFZ), bordered by the North and South Subtropical Fronts (NSTF and SSTF, respectively), and by the Polar Frontal Zone (PFZ), bordered by the Subantarctic and Polar Fronts (SAF and PF, respectively). This structure becomes more complex in the African sector as the Agulhas Retroflection and the bottom topography force a more convoluted pattern. The Retroflection and associated Agulhas Front (AF) press the SSTF from 38° to 42°–43°S. Strong interactions of the AF, SSTF, and SAF with topography shift the fronts but do not obliterate them. The AF can be traced reliably up to 52°E, sometimes up to 75°E. The SAF is deflected from 45° to 43°S by the Mid-Ocean Ridge and converges with the SSTF north of the Prince Edward Islands to form a combined SSTF/SAF. This front intensifies east of 50°–52°E as a result of the confluence with the AF, and between 52° and 65°E a triple AF/SSTF/SAF (“the Crozet Front”) is observed. The PF continues along 49° and 50°S between the Crozet Plateau and the Ob-Lena (Conrad) Rise, passing north of Kerguelen, nearly joining the triple Crozet Front. Downstream of the Kerguelen-Amsterdam Passage, the canonical structure is being restored (SSTF, SAF, PF); however, the front parameters in the Australian sector are different from the African sector, largely because of strong air-sea interaction and cross-frontal exchanges in the Crozet-Kerguelen region. The SSTF, squeezed between the AF and SAF, loses characteristics to both. The SSTF/SAF interaction results in the Australian SAF being warmer and saltier downstream, while the SSTF becomes shallower and weaker. The Australian STF derives its characteristics mostly from the AF, thus bringing the modified Agulhas waters to the Pacific Ocean. The newly defined North Subtropical Front (NSTF) was distinguished in the Indian Ocean between 31° and 38°S. The front marks the southern boundary of the subtropical salty, warm water pool of the central South Indian Ocean. The NSTF location is coincident with the position of the wind convergence between westerlies and easterlies, suggesting the possible wind-driven frontogenesis.
TL;DR: In this paper, a submesoscale transition in the eddy variability as the horizontal grid scale is reduced to O(1) km is described in terms of the emergent flow structure and the associated time-averaged eddy fluxes.
Abstract: In computational simulations of an idealized subtropical eastern boundary upwelling current system, similar to the California Current, a submesoscale transition occurs in the eddy variability as the horizontal grid scale is reduced to O(1) km. This first paper (in a series of three) describes the transition in terms of the emergent flow structure and the associated time-averaged eddy fluxes. In addition to the mesoscale eddies that arise from a primary instability of the alongshore, wind-driven currents, significant energy is transferred into submesoscale fronts and vortices in the upper ocean. The submesoscale arises through surface frontogenesis growing off upwelled cold filaments that are pulled offshore and strained in between the mesoscale eddy centers. In turn, some submesoscale fronts become unstable and develop submesoscale meanders and fragment into roll-up vortices. Associated with this phenomenon are a large vertical vorticity and Rossby number, a large vertical velocity, relatively flat horizontal spectra (contrary to the prevailing view of mesoscale dynamics), a large vertical buoyancy flux acting to restratify the upper ocean, a submesoscale energy conversion from potential to kinetic, a significant spatial and temporal intermittency in the upper ocean, and material exchanges between the surface boundary layer and pycnocline. Comparison with available observations indicates that submesoscale fronts and instabilities occur widely in the upper ocean, with characteristics similar to the simulations.
TL;DR: In this article, the authors focused on the structural characteristics of fronts and their associated jet streams near the tropopause, and on the diagnosis of the frontogenetic processes and secondary circulations governing their life cycles.
Abstract: The advent of kite and balloon-borne meteorograph soundings during the early 1900s and the subsequent deployment of regional rawinsonde networks provided the observational basis for the study of the spatial and temporal evolution of fronts, jet streams and the tropopause. During the mid-century years (1935–1965), researchers focused on the structural characteristics of fronts and their associated jet streams near the tropopause, and on the diagnosis of the frontogenetic processes and secondary circulations governing their life cycles. The pioneering observational study by J. Bjerknes and E. Palm n (1937) showed fronts to be transitional zones of finite width (~100 km) and depth (~1 km), rather than near zero-order discontinuities extending from the surface to the tropopause. Newton (1954) presented the most comprehensive diagnosis of all components of upper-level frontogenesis during this period, and Sawyer (1956) and Eliassen (1962) derived the diagnostic theory for geostrophically forced secondary circulations about fronts based on the semigeostrophic equations, which was later expanded to the temporal dimension by Hoskins (1971) and Hoskins and Bretherton (1972).