Guillaume Lapeyre

Upper Ocean Turbulence from High-Resolution 3D Simulations

Abstract The authors examine the turbulent properties of a baroclinically unstable oceanic flow using primitive equation (PE) simulations with high resolution (in both horizontal and vertical directions). Resulting dynamics in the surface layers involve large Rossby numbers and significant vortical asymmetries. Furthermore, the ageostrophic divergent motions associated with small-scale surface frontogenesis are shown to significantly alter the nonlinear transfers of kinetic energy and consequently the time evolution of the surface dynamics. Such impact of the ageostrophic motions explains the emergence of the significant cyclone–anticyclone asymmetry and of a strong restratification in the upper layers, which are not allowed by the quasigeostrophic (QG) or surface quasigeostrophic (SQG) theory. However, despite this strong ageostrophic character, some of the main surface properties are surprisingly still close to the surface quasigeostrophic equilibrium. They include a noticeable shallow (≈k−2) velocity s...

Dynamics of the Upper Oceanic Layers in Terms of Surface Quasigeostrophy Theory

In this study, the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity. First, it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and submesoscale anomalies in the ocean interior are strongly correlated to the surface density anomalies. Then, using the invertibility of potential vorticity, the dynamics are decomposed in terms of a solution forced by the three-dimensional (3D) potential vorticity and a solution forced by the surface boundary condition in density. It is found that, in the upper oceanic layers, the balanced flow induced only by potential vorticity is strongly anticorrelated with that induced only by the surface density with a dominance of the latter. The major consequence is that the 3D balanced motions can be determined from only the surface density and the characteristics of the basin-scale stratification by solving an elliptic equation. These properties allow for the possibility to reconstruct the 3D balanced velocity field of the upper layers from just the knowledge of the surface density by using a simpler model, that is, an “effective” surface quasigeostrophic model. All these results are validated through the examination of a primitive equation simulation reproducing the dynamics of the Antarctic Circumpolar Current.

Oceanic Restratification Forced by Surface Frontogenesis

Potential vorticity (PV) conservation implies a strong constraint on the time evolution of the mean density at a given depth. The authors show that, on an f plane and in the absence of sources and sinks of PV, it only depends on two terms, namely, the time evolution of the product between density anomaly and relative vorticity and the vertical PV flux. This primitive equation result, which applies at any depth, suggests that the ageostrophic dynamics induced by baroclinic eddies strongly affect the mean oceanic stratification profile. This result is illustrated for two simple initial-value simulations of a baroclinic, balanced jet. For initial situations propitious to surface frontogenesis, the simulations show a restratification over the whole water column characterized by the amplification in time of the Brunt–Vaisala frequency in the upper oceanic layers. In the absence of surface frontogenesis, such as when the jet is initialized at the middepth of the water column, the restratification is much weaker and slower. Because both simulations have similar kinetic energy and growth rate of baroclinic instability, the results clearly reveal that the restratification is driven by surface frontogenesis in the first case and by vertical PV flux in the interior in the second case. The authors also point out that the dynamics of the interior PV is tightly related to the surface dynamics because of total mass conservation.

Three‐dimensional reconstruction of oceanic mesoscale currents from surface information

The ability to reconstruct the three-dimensional (3D) dynamics of the ocean by an effective version of Surface Quasi-Geostrophy (eSQG) is examined. Using the fact that surface density plays an analogous role as interior potential vorticity (PV), the eSQG method consists in inverting the QG PV generated by sea-surface density only. We also make the extra assumption that sea-surface temperature (SST) anomalies fully represent surface density anomalies. This approach requires a single snapshot of SST and the setup of two parameters: the mean Brunt-Vaisala frequency and a parameter that determines the energy level at the ocean surface. The validity of this approach is tested using an Ocean General Circulation Model simulation representing the North Atlantic in winter. It is shown that the method is quite successful in reconstructing the velocity field at the ocean surface for mesoscales (between 30 and 300 km). The eSQG framework can also be applied to reconstruct subsurface fields using surface information. Results show that the reconstruction of velocities and vorticity from surface fields is reasonably good for the upper 500 m and that the success of the method mainly depends on the quality of the SST as a proxy of the density anomaly at the base of the mixed layer. This situation happens after a mixed-layer deepening period. Therefore the ideal situation for the application of this method would be after strong wind events.

Potential use of microwave sea surface temperatures for the estimation of ocean currents

In this paper, we examine the emerging potential offered by satellite microwave radiometer SST measurements to complement altimeter data to quantitatively derive surface ocean currents. The proposed methodology does not follow standard sequential temporal analysis but follows the application of the Surface Quasi-Geostrophic (SQG) theory. Accordingly, under favourable environmental conditions, the implementation for this methodology is simple and robust, and most importantly, solely requires a single SST image. For the present demonstration, altimetric measurements are used to infer a necessary adjustment to match the kinetic energy level for length scales smaller than 300 km. This helps to derive a regional effective Brunt-Vaisala frequency to produce SQG surface current estimates. As demonstrated, the results are very encouraging and strongly invite to consider the systematic use of satellite microwave radiometer measurements.

Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence

This paper investigates the dynamics of tracer gradient for a two-dimensional flow. More precisely, the alignment of the tracer gradient vector with the eigenvectors of the strain-rate tensor is studied theoretically and numerically. We show that the basic mechanism of the gradient dynamics is the competition between the effects due to strain and an effective rotation due to both the vorticity and to the rotation of the principal axes of the strain-rate tensor. A nondimensional criterion is derived to partition the flow into different regimes: In the strain dominated regions, the tracer gradient vector aligns with a direction different from the strain axes and the gradient magnitude grows exponentially in time. In the strain-effective rotation compensated regions, the tracer gradient vector aligns with the bisector of the strain axes and its growth is only algebraic in time. In the effective rotation dominated regions, the tracer gradient vector is rotating but is often close to the bisector of the strain...

Impact of the small-scale elongated filaments on the oceanic vertical pump.

Oceanic mesoscale eddies (with a diameter of 50-100 km) are known to be associated with significant vertical tracer fluxes in the upper few hundred meters. In particular, they are important for the biogeochemical system, accounting for 20-30% of the vertical nutrient transport. However, estimates of the global tracer fluxes neglect the role played by thin elongated filaments (with a width of 5-10 km). These sub-mesoscale structures are produced by eddy interactions and ubiquitous in regions between eddies. We use a Surface Quasi-Geostrophic model to quantify their impact on the net vertical tracer flux into the surface layers. We show that eddy interactions are an important source of tracer injection because they lead to the production of filaments and to large vertical velocities within these structures. This is attributed to the frontogenetic dynamics induced by the horizontal stirring processes. When taking into account this process for the global statistics of tracer injection, the tracer flux associated with the filaments is as significant as that associated with the eddies. This outcome points out the necessity to explicitly include the filamentation process in global ocean model studies.

Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence

This paper discusses the application of Lyapunov theory in chaotic systems to the dynamics of tracer gradients in two-dimensional flows. The Lyapunov theory indicates that more attention should be given to the Lyapunov vector orientation. Moreover, the properties of Lyapunov vectors and exponents are explained in light of recent results on tracer gradients dynamics. Differences between the different Lyapunov vectors can be interpreted in terms of competition between the effects of effective rotation and strain. Also, the differences between backward and forward vectors give information on the local reversibility of the tracer gradient dynamics. A numerical simulation of two-dimensional turbulence serves to highlight these points and the spatial distribution of finite time Lyapunov exponents is also discussed in relation to stirring properties. (c) 2002 American Institute of Physics.

Surface kinetic energy transfer in surface quasi-geostrophic flows

The relevance of surface quasi-geostrophic dynamics (SQG) to the upper ocean and the atmospheric tropopause has been recently demonstrated in a wide range of conditions. Within this context, the properties of SQG in terms of kinetic energy (KE) transfers at the surface are revisited and further explored. Two well-known and important properties of SQG characterize the surface dynamics: (i) the identity between surface velocity and density spectra (when appropriately scaled) and (ii) the existence of a forward cascade for surface density variance. Here we show numerically and analytically that (i) and (ii) do not imply a forward cascade of surface KE (through the advection term in the KE budget). On the contrary, advection by the geostrophic flow primarily induces an inverse cascade of surface KE on a large range of scales. This spectral flux is locally compensated by a KE source that is related to surface frontogenesis. The subsequent spectral budget resembles those exhibited by more complex systems (primitive equations or Boussinesq models) and observations, which strengthens the relevance of SQG for the description of ocean/atmosphere dynamics near vertical boundaries. The main weakness of SQG however is in the small-scale range (scales smaller than 20–30 km in the ocean) where it poorly represents the forward KE cascade observed in non-QG numerical simulations.

Tracking coherent structures in a regional ocean model with wavelet analysis: Application to Cape Basin eddies

[1] This study is mainly aimed at proposing objective tools for the identification and tracking of three-dimensional eddy structures. It is conducted with a high-resolution numerical model of the ocean region around South Africa, and emphasis is put on Cape Basin anticyclones and cyclones thought to be actively implicated in the Indian-Atlantic interocean exchange. We settle on wavelet analysis for the decomposition and processing of successive maps of relative vorticity for a simulation run with 1/10 degrees resolution. The identification of three- dimensional coherent structures comes with the calculation of eddy trajectories and the time evolution of eddy properties. Instantaneous mass transport and momentum of eddies are calculated from the knowledge of instantaneous drift velocities, volumes, and diameters. The success of the regional model and of the analysis technique is assessed through comparisons with equivalent observations.