Cross-front Velocity Research Articles

The submesoscale, the finescale and their interaction at a mixed layer front

The spindown of a geostrophically balanced density front in an upper-ocean mixed layer is simulated with a large eddy simulation (LES) model that resolves O(1000) m down to O(1) m scale. Our goal is to examine the interaction between the submesoscale and the turbulent finescale, and another related goal is to use the turbulence-resolving simulation to better characterize vertical transport, frontogenesis and dissipative processes. The flow passes through symmetric and baroclinic instabilities, spawns vortex filaments of O (100) m thickness as well as larger eddies with cross-front velocity as large as the along-front velocity, and develops turbulence that is spatially localized and organized. A O(100) m physical-space filter is applied to the simulated flow so that the coherent submesoscale is separated from the finescale in a decomposition that preserves the spatial organization of the flow unlike the typical practice of a split into a frontal average and a fluctuation that obscures the coherent submesoscale. The energy spectrum exhibits a change of slope at O(100) m with an approximately −5/3 slope over a subrange of the finescale. Analysis of the submesoscale vertical velocity (as large as 5mm/s) in the upper layer of the front reveals that downwelling is limited to the thin vortex filaments and the junction of the submesoscale eddies with these filaments while upwelling occurs over spatially extensive regions in the eddies. Conditional averaging shows that heavier (lighter) fluid is preferentially downwelled (upwelled) by these coherent submesoscale structures leading to an overall buoyancy flux that is restratifying. The submesoscale is unbalanced with local Rossby number as large as 5. The kinetic energy (KE) transport equations are evaluated separately for the submesoscale and the finescale to understand energy pathways in this problem. The buoyancy flux (associated with coherent motions) transfers the potential energy of the front and acts as the primary source of submesoscale KE which is then transported across the front with a fraction transferred to the finescale. The transfer, limited to thin regions of O(100) m horizontal width, is accomplished by primarily horizontal strain in the upper 10 m and by vertical shear in the rest of the 50-m deep mixed layer. Frontogenetic mechanisms are diagnosed through analysis of the transport equation for squared buoyancy gradient. Horizontal strain is the primary frontogenetic term that is especially strong in the near-surface layer. The frontogenesis is counteracted primarily by horizontal diffusion in the top 10 m while, further below, the balance is with the horizontal gradient of vertical velocity.

Vertical slice modelling of nonlinear Eady waves using a compatible finite element method

A vertical slice model is developed for the Euler–Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady–Boussinesq model). The model is a solution of the full three-dimensional equations with no variation normal to the slice, which is an idealised problem used to study the formation and subsequent evolution of weather fronts. A compatible finite element method is used to discretise the governing equations. To extend the Charney–Phillips grid staggering in the compatible finite element framework, we use the same node locations for buoyancy as the vertical part of velocity and apply a transport scheme for a partially continuous finite element space. For the time discretisation, we solve the semi-implicit equations together with an explicit strong-stability-preserving Runge–Kutta scheme to all of the advection terms. The model reproduces several quasi-periodic lifecycles of fronts despite the presence of strong discontinuities. An asymptotic limit analysis based on the semi-geostrophic theory shows that the model solutions are converging to a solution in cross-front geostrophic balance. The results are consistent with the previous results using finite difference methods, indicating that the compatible finite element method is performing as well as finite difference methods for this test problem. We observe dissipation of kinetic energy of the cross-front velocity in the model due to the lack of resolution at the fronts, even though the energy loss is not likely to account for the large gap on the strength of the fronts between the model result and the semi-geostrophic limit solution.

Density and flow structure in the Clyde Sea front

A well-defined front in temperature and salinity separates the stratified Clyde Sea water from the vertically well mixed water of the North Channel. The detailed structure of the front was observed in autumn 1990 by a combination of, repeated crossings of the front using a ship-borne ADCP and a towed undulating CTD system, and the deployment of a fixed mooring system with temperature, salinity and velocity sensors for a period of 12 days. The results show that the front was situated on the Great Plateau near a contour of log 10( H/ U 3 2)=2.7∼3.7 where H is the water depth and U 2 the amplitude of M 2 tidal velocity. The temperature structure in the Clyde Sea was inverted and the Clyde Sea surface temperature was lower than that of the vertically well mixed water in the North Channel. Since the salinity gradient was stronger than the temperature gradient with fresher water on the surface, the density structure was predominantly controlled by salinity. There were indications of warm and saline bottom water upwelling on the mixed side of the front during spring tides. This upwelling disappeared and the salinity and temperature structure at the front was more diffuse during the neap tide period. A jet-like along-front residual current was observed flowing to the northwest in the surface layer with a counter flow to the southeast in the bottom layer. The vertical difference in velocity was about 9 cm s −1 and was approximately consistent with the shear determined from the thermal wind relation. Both cross- and along-front components of the current observed at the mooring station varied in response to the advection of the front, although both components had large variations with periods of less than one day and several days. The front was advected past the mooring system by a mean flow from the North Channel to the inner basin, while oscillating 3–5 km back and forth with the tidal currents. From the velocity at a current meter mooring and CTD data, the front was estimated to have moved up to 20 km during the observational period and the cross frontal velocity was inferred to be 3–4 cm s −1.

On the Efficiency of Baroclinic Eddy Heat Transport across Narrow Fronts*

A simple theory is developed that relates the amplitude of eddy heat (or density) flux across a narrow front to the basic frontal parameters. By assuming that heat is transported primarily by baroclinic eddy pairs, an analytical expression for the cross-front eddy heat flux is derived as u9r9 5 ceVmDr, where u9 and r9 are deviations from the temporal or spatial mean cross-front velocity and density, Dr is the density change across the front, Vm is a scale for the alongfront velocity (which may be interpreted as the maximum alongfront velocity for a front with density change Dr over a horizontal scale of the deformation radius, assuming a deep level of no motion), and ce is an efficiency constant. Similar expressions for the eddy heat flux have been proposed previously, based on scaling or energetics arguments, but neither an a priori estimate for the value of the efficiency constant ce nor a clear dynamical understanding of what determines its value has been forthcoming. The theory presented here provides a dynamically based means of estimating the efficiency constant, which may be approximately interpreted as the ratio of the speed at which eddies propagate away from the front to the alongfront velocity, resulting in ce 0.045. Eddy-resolving numerical models are used to test this theoretical estimate for both unforced and forced frontal problems. For a wide range of parameters the cross-frontal heat transport is carried primarily by heton-like eddy pairs with values of ce between 0.02 and 0.04, in general agreement with the theory. These values of ce are also consistent with numerous previously published laboratory and numerical studies.

A Numerical Model of the Fluid Motion at a Density Front in the Presence of Background Turbulence

Abstract The effects of background turbulence on gravity currents produced by lock exchange are investigated using a numerical model with the aim of understanding the fluid motions associated with coastal fronts. It is shown that, at high turbulence intensities, the mutual intrusion of gravity currents is inhibited and the horizontal mass transport is dominated by the turbulent diffusion. The propagation of the front, the horizontal density flux, and the potential energy anomaly are calculated and are compared with available experimental data. The model is extended to include the effects of background rotation. It is found that, in the presence of background turbulence, the geostrophic equilibrium cannot be achieved, and the cross-frontal velocity persists indefinitely. The effects of rotation on the fluid motions were found to be impaired by the background turbulence.

Balanced and Unbalanced Upper-Level Frontogenesis

The dynamics of frontogenesis at upper levels are investigated using a hierarchy of three numerical models. They are, in order of decreasing sophistication, the anelastic (AN), the geostrophic momentum (GM), and the quasi-geostrophic (QG) approximations to the full equations of motion. Each model is two-dimensional and assumes the same basic-state, which incorporates the frontogenetical mechanisms of confluence and horizontal shear. The dependence of the numerical solutions on the initial vertical shear of the cross-front component of the geostrophic wind, λ, and its associated along-front temperature gradient is examined in detail. For the values of λ chosen, the along-front temperature gradient is either zero (λ = 0) or such that cold air is advected along the upper front (λ < 0). Intercomparison of the broad-scale structure of the upper-level jet–fronts as described by the AN and GM models shows close agreement. For zero or weak shears (λ = 0 s−1 or λ = −2 × 10−3 s−1), the solutions are essentially identical. Vertical shear in the cross-front geostrophic wind serves to increase the amplitude of the cross-front circulation and displace the subsiding branch toward the warmer air. In the cases of weak or zero shear, the dominant mechanism for generating vertical vorticity at upper levels is the stretching of preexisting vertical vorticity, whereas for stronger shear (λ = −5.741 × 10−3 s−1) the key process becomes the tilting of horizontal vorticity into the vertical by differential vertical motion. In contrast, the QG model exhibits marked differences with its AN and GM counterparts, which become even more pronounced as |λ| is increased. These differences are related largely to the neglect of vortex tilting in generating vertical vorticity in the OG model. The GM and QG models assume cross-front thermal wind balance at all time. A posteriors examination of the numerical solutions shows this to be an excellent approximation when the vertical shear in the cross-front geostrophic wind is weak. For strong vertical shear of the cross-front geostrophic wind, the unbalanced along-front ageostrophic wind is proportional to the vertical advection of the cross-front velocity. Diagnoses of these simulations reveal thermal wind balance to be less well satisfied. It is shown that in contrast to the GM and QG models, wherein the along-front ageostrophic velocity is passive and thus cannot contribute to the evolution of the jet–front system, the unbalanced along-front flow contributes significantly to the dynamics as described by the AN model.

Frontogenesis in Mixed Layers

Abstract A unified theory of frontogenesis in mixed layers is proposed. Analytical solutions of the nonlinear mass and density balances in a mixed layer are found in the Lagrangian frame for a wide class of entrainment parameterizations. These solutions show mixed-layer depth and density to be functions of particle position and separation, where mixing is represented by an integral over time following a particle. Thus, given a knowledge of only the crossfront velocity field, the likelihood of frontal formation can be predicted. Both surface convergence, and divergence in conjunction with vertical mixing can be frontogenetic. Three different types of fronts, distinguished by their associated crossfront velocity fields, are discussed. Large-scale fronts, such as the subtropical front, are described by a convergent surface flow acting upon an initial horizontal density gradient. The powerful divergence caused by an offshore Ekman flow forced to zero at a coast causes upwelling fronts. The divergence associat...

Large-Scale Response of the Pacific Ocean Subarctic Front to Momentum Transfer: A Numerical Study

A numerical four-layer hydrodynamical model is implemented to investigate the role the atmosphere exerts on the dynamics of the subarctic front. While the effect of the westerly winds causes a southward shift of the front, the effect of a negative curl shows convergence at the front. This convergence strongly favors frontogenesis. The salient features at the wake of a strong cyclone can be summarized as follows: (i) upwelling of 20 m of the four interfaces occurs; (ii) the water remains upwelled for several weeks; (iii) the e-folding time scale of the vertical oscillations induced by the storm's passage is of the order of 10 days; (iv) a region of relative maximum convergence is observed in the lower layers below a region of relative maximum upwelling in the upper layer, and (v) the along- and cross-front velocity fields are in quadrature in time, with the cross-front velocity lagging the along-front velocity. With the exception of the cyclone case, it is established that the effects of the atmospheric wind forcing are confined to the upper layer. These results are supported by oceanic observations. Finally, it is also proved that the response of the front to the atmospheric momentum transfer is not sensitive to the initial form of the subarctic front.