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Submesoscale Processes and Dynamics Leif N JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/, Submesoscale processes and dynamics Leif N. Thomas Woods Hole Oceanographic Institution, Woods Hole, Massachusetts Amit Tandon Physics Department and SMAST, University of Massachusetts, Dartmouth, North Dartmouth, Massachusetts Amala Mahadevan Department of Earth Sciences, Boston University, Boston, Massachusetts Abstract. Increased spatial resolution in recent observations and modeling has revealed a richness of structure and processes on lateral scales of a kilometer in the upper ocean. Processes at this scale, termed submesoscale, are distinguished by order one Rossby and Richardson numbers; their dynamics are distinct from those of the largely quasi-geostrophic mesoscale, as well as fully three-dimensional, small-scale, processes. Submesoscale pro- cesses make an important contribution to the vertical flux of mass, buoyancy, and trac- ers in the upper ocean. They flux potential vorticity through the mixed layer, enhance communication between the pycnocline and surface, and play a crucial role in changing the upper-ocean stratification and mixed-layer structure on a time scale of days. In this review, we present a synthesis of upper-ocean submesoscale processes, arising in the presence of lateral buoyancy gradients. We describe their generation through fron- togenesis, unforced instabilities, and forced motions due to buoyancy loss or down-front winds. Using the semi-geostrophic (SG) framework, we present physical arguments to help interpret several key aspects of submesoscale flows. These include the development of narrow elongated regions with O(1) Rossby and Richardson numbers through fron- togenesis, intense vertical velocities with a downward bias at these sites, and secondary circulations that redistribute buoyancy to stratify the mixed layer. We review some of the first parameterizations for submesoscale processes that attempt to capture their con- tribution to, firstly, vertical buoyancy fluxes and restratification by mixed layer insta- bilities and, secondly, the exchange of potential vorticity between the wind- and buoyancy- forced surface, mixed layer, and pycnocline. Submesoscale processes are emerging as vi- tal for the transport of biogeochemical properties, for generating spatial heterogeneity that is critical for biogeochemical processes and mixing, and for the transfer of energy from the meso to small scales. Several studies are in progress to model, measure, ana- lyze, understand, and parameterize these motions. 1. Introduction submeso (∼1 km) scales, that lie intermediate to meso- and small-scale three-dimensional motions, are less understood The dynamics of O(1) Rossby number, submesoscale pro- and only more recently brought to light through observa- cesses at O(1km) in the upper ocean plays an important tional, modeling and analytical studies. The submesoscale, role in the vertical flux of mass, buoyancy, and tracers in characterized by O(1) Rossby number dynamics, is not de- the upper ocean. In addition, they are thought to be in- scribed appropriately by the traditional quasi-geostrophic strumental in transferring energy and properties from the theory that applies to mesoscales. It is not fully three- largely adiabatic mesoscale (∼10–100km) flow field, to a dimensional and nonhydrostatic, either, but is inevitably scale where mixing can occur. The breakdown of geostrophic crucial to bridging the, meso and smaller, scales through balance in this regime leads to the development of secondary processes and dynamics that we are just beginning to under- ageostrophic circulations with relatively large vertical ve- stand. The objective of this article is to review and synthe- locities compared to those associated with the mesoscale. size the understanding of submesoscales put forth through recent diverse studies. Hence they are vital to the exchange of properties between Our discussion will focus on the upper ocean, where sub- the surface mixed layer and thermocline. mesoscale processes are particularly dominant due to the The oceanic mesoscale flow field, characterized by a hor- presence of lateral density gradients, vertical shear, weak izontal length scale of 10–100 km, has been studied exten- stratification, a surface boundary that is conducive to fron- sively for its dynamics and its contribution to the lateral togenesis. and a relatively small Rossby radius based on the transport of heat, momentum and tracers via eddies. Simi- mixed layer depth. This is not to say that submesoscales larly, three-dimensional processes at small length scales less are solely an upper ocean phenomenon. In the ocean in- than a kilometer (0.1–100 m) have been investigated for their terior and abyss there exists a commonly observed class of contribution to mixing and energy dissipation. However, vortical motions with length scales less than the mesoscale, termed submesoscale coherent vortices (SCVs). A thorough review on the observations and dynamics of SCVs can be found in McWilliams [1985]. Copyright 2007 by the American Geophysical Union. The motivation to study submesoscales comes from sev- 0148-0227/07/$9.00 eral factors. Since the geometrical aspect (depth to length) 1 X - 2 THOMAS ET AL.: SUBMESOSCALE PROCESSES AND DYNAMICS ratio, and Rossby number Ro, associated with meso and transects. We are at an exciting juncture because we are larger scale flow are 1, and the Richardson number Ri now able to achieve the required resolution in models and 1, the associated vertical velocities are 10−3 − 10−4 orders observations to capture this scale. The results from high res- of magnitude smaller than the horizontal velocities, which olution numerical modeling and analytical studies, several of −1 are typically 0.1m-s . However, localized submesoscale which are discussed in this review, suggest that both forced regions develop in which Ro and Ri are O(1). At these and unforced instabilities drive submesoscale processes. sites, submesoscale dynamics generate vertical velocities of −3 −1 −1 We begin Section 2 by defining submesoscales and de- O(10 ms ) or ∼100m-day that are typically an order of scribing phenomena with which they are associated. Fur- magnitude larger than those associated with the mesoscale, ther, we examine mechanisms that generate submesoscales and play an important role in the vertical transport and in the upper ocean. In Section 3, we present a mathematical mixing of properties in the upper ocean. The intense ver- framework for understanding the secondary circulation asso- tical velocities in the surface and mixed layer may commu- ciated with fronts, where submesoscales are found to occur. nicate with the mesoscale up- and down-welling associated with the geostrophic frontal meander scale. Thus, subme- This is used to provide a dynamical explanation for sev- soscale processes are instrumental in transferring properties eral key features of submesoscale phenomena. In Section 4, and tracers, vertically, between the surface ocean and the we discuss the implications of submesoscales, which include interior. They enhance, for example, nutrient supply and mixed layer restratification, vertical transport and biogeo- the exchange of dissolved gases with the atmosphere. chemical fluxes, and potential vorticity fluxes. Finally, we A large part of the ocean’s kinetic energy resides at meso provide a discussion of outstanding questions and possible and larger scales. At these scales, oceanic flow is largely two- connections to other areas. dimensional and in a state of hydrostatic and geostrophic balance from which it is difficult to extract energy. A ma- jor conundrum [McWilliams et al., 2001; McWilliams, 2003] 2. Phenomenology therefore, is how energy is transferred from the meso scale 2.1. What are submesoscales? to the small scale at which it can be dissipated through three-dimensional processes. The strong ageostrophic flow An active flow field in the upper ocean generates local- at submesoscales can extract energy from the balanced state ized regions, typically along filaments or outcropping isopy- and transfer it to smaller scales. The quasi two-dimensional cnals, within which the relative vertical vorticity ζ equals mesoscale flow field is characterized by kinetic energy spec- or exceeds the planetary vorticity f. The dynamics within tra with a slope of -3. Three-dimensional numerical simu- these regions differs from mesoscale dynamics characterized lations at progressively finer resolutions show that resolving by small Rossby number (Ro 1). We thus define subme- submesoscale processes leads to flattening the kinetic energy soscale flows based on dynamics, as those where the Rossby spectra slope to -2 [Capet et al., 2007a] and a transfer of en- number, defined by Ro = ζ/f, is O(1). ergy to larger, as well as smaller scales [Boccaletti et al., Since ζ ∼ U/L and Ro = U/fL, the length scale for 2007]. submesoscales, L = U/f. The horizontal velocity scale Yet another factor associated with submesoscale instabil- U can be defined further assuming thermal wind balance, ities, is the flux of potential vorticity to and from the sur- U ∼ byH/f, where buoyancy b ≡ −gρ/ρ0, y is the direction face to interior ocean and the change in stratification of the of lateral buoyancy gradient, ρ is the density anomaly from mixed layer. Submesoscale instabilities in the mixed layer the mean density ρ , and H, the mixed layer depth, is the are shown to hasten restratification and buoyancy transport 0 vertical extent over which velocity and lateral density gradi- several fold, as compared to what can be
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