Bach Lien Hua

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...

Do Altimeter Wavenumber Spectra Agree with the Interior or Surface Quasigeostrophic Theory

In high-eddy-energy regions, it is generally assumed that sea level wavenumber spectra compare well with quasigeostrophic (QG) turbulence models and that spectral slopes are close to the expected k−5 law. This issue is revisited here. Sea level wavenumber spectra in the Gulf Stream, Kuroshio, and Agulhas regions are estimated using the most recent altimeter datasets [the Ocean Topography Experiment (TOPEX)/Poseidon, Jason-1, the Environmental Satellite (Envisat), and the Geosat Follow-On]. The authors show that spectral slopes in the mesoscale band are significantly different from a k−5 law, in disagreement with the QG turbulence theory. However, they very closely follow a k−11/3 slope, which indicates that the surface quasigeostrophic theory (SQG) is a much better dynamical framework than the QG turbulence theory to describe the ocean surface dynamics. Because of the specific properties of the SQG theory, these results offer new perspectives for the analysis and interpretation of satellite data.

An exact criterion for the stirring properties of nearly two-dimensional turbulence

Abstract An exact criterion can be found for partitioning the fluid into regions with different dynamical properties, from both the points of view of particle dispersion and tracer gradient evolution. This criterion differs markedly, both in its magnitude and spatial scales, from the Okubo-Weiss criterion which depends upon the differential geometry of the streamfunction field and coincides with the eigenvalues of the velocity gradient tensor. The new criterion corresponds to the eigenvalues of the acceleration gradient tensor, whose spatial distribution depends instead upon the topology of the pressure field. This result holds for all flows for which a continuous momentum equation can be prescribed. We provide numerical evidence for the quantitative importance of the time change of the strain-rate components in the dispersion problem in freely decaying two-dimensional turbulence.

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.

Inertial nonlinear equilibration of equatorial flows

We explore the nature of inertial equilibration of equatorial flows in the presence of mean meridional and vertical shears of the basic state, with oceanic applications in mind. The study is motivated by the observational evidence that the subthermocline equatorial mean circulation displays nearly zero Ertel potential vorticity away from the equator, when taking into account the non-traditional horizontal component of the Earth rotation. This observed state precisely verifies the marginal condition for inertial instability: a linear analysis for the equatorial β-plane confirms that the usual condition of instability, namely that Ertel potential vorticity should be of opposite sign to the vertical Coriolis parameter, remains valid even when the traditional approximation is relaxed. Analytical linear normal modes reveal that a meridional shear of the basic state leads to a vertical stacking of equatorially-trapped zonal flows of alternate signs, with a new centre of symmetry located at the dynamical equator. A vertical shear of the basic state causes a meridional stacking of extra-equatorial zonal flows. In an inviscid framework, a two-dimensional formulation is ill-posed and we resort to non-hydrostatic viscous simulations to determine the nonlinear normal forms of the system. The influence of a small-scale eddy diffusivity and a large-scale Rayleigh damping on the equilibrated vertical scale is determined numerically. The nonlinear equilibration occurs through a steady-state bifurcation from a basic state without jets to another steady state with secondary jets of alternate signs. The final state corresponds to eastward jets located on the geographic equator, while westward jets are located near the dynamical equator. These results are consistent with in situ observations of equatorial deep jets. The analogy between the equatorial meridional shear flow and the cylindrical Couette–Taylor flow with an axial density stratification is detailed. There is a strong similarity in the general symmetries and nonlinear normal forms of the two problems. Similarly to the homogeneous Couette–Taylor flow, the gap width between the two cylinders is important for determining the axial scale of the secondary flow through the Reynolds number. For the equatorial problem, an upper bound for the height scale of inertial jets is such that the corresponding equatorial radius of deformation times √2 fits between the geographic and dynamic equators. One of our main conclusions is that the raison d ’ etre of the observed region of zero Ertel potential vorticity is to facilitate angular momentum exchanges between the two hemispheres and inertial deep jets are the byproducts of this angular momentum mixing.

Three-dimensional stirring of thermohaline fronts

This study investigates the stirring of the thermohaline anomalies in a fully turbulent quasi-geostrophic stratified flow. Temperature and salinity fields are permanently forced at large scales and are related to density by a linear equation of state. We show, using some inherent properties of quasi-geostrophic turbulence, that the 3-D ageostrophic circulation is the key dynamical characteristic that governs the strength and the spatial distribution of small-scale thermohaline fronts that are strongly density compensated. The numerical simulations well illustrate the formation by the mesoscale eddy field of sharp thermohaline fronts that are mainly located in the saddle regions and around the eddy cores and have a weak signature on the density field. One important aspect revealed by the numerical results is that the thermohaline anomalies experience not only a direct horizontal cascade but also a significant vertical cascade. One consequence of this 3-D cascade is that the ultimate mixing of the thermohaline anomalies will not be necessarily maximum at the depth where the large-scale temperature and salinity anomalies are maximum. Some analytical arguments allow us to identify some of the mechanisms that drive this 3-D cascade.

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.

On the Catalytic Role of High Baroclinic Modes in Eddy-driven Large-Scale Circulations

Abstract This paper investigates the tridimensional consistency of the resolution of eddy scales in simulating large-scale flows. The generation of classical wind-forced, eddy-driven double-gyre circulation is investigated with a multilayered quasi-geostrophic model. Six-layers on the vertical have been chosen to assure the convergence of the baroclinic instability. Emphasis is on the resolution of the high baroclinic modes and its effects on the dynamics of the midlatitude jet. Several eddy-resolving experiments, identical except for the horizontal resolution, which can be low (20 km) or high (10 km), are compared. In every experiment, the scales associated with the first and second baroclinic modes are well resolved, but those associated with the third and higher baroclinic modes are so only in 10-km experiments For a better illustration of the importance of the high vertical modes, three-layer experiments having configurations equivalent to that of the six-layer experiments have been conducted. Note th...

Lagrangian accelerations in geostrophic turbulence

A distinctive property of Lagrangian accelerations in geostrophic turbulence is that they are governed by the large and intermediate scales of the flow, both in time and space, so that the inertial part of the dynamics plays a much larger role than in three-dimensional turbulence where viscous effects are stronger. For the case of geostrophic turbulence on a β-plane, three terms contribute to the Lagrangian accelerations: the ageostrophic pressure gradient which often is the largest term, a meridional acceleration due to the β-effect, and an acceleration due to horizontally divergent ageostrophic motions. Both their spectral characteristics and patterns in physical space are studied in this paper. In particular the total accelerations field has an inertial spectrum slope which is identical to the geostrophic velocity field inertial slope. The accelerations gradient tensor is shown to govern the topology of quasi-geostrophic stirring and transport properties. Its positive eigenvalues locate accurately the position of extrema of potential vorticity gradients. The three-dimensional distribution of tracer gradients is such that the vertical distribution is entirely constrained by the horizontal one, while the reverse is not true. We make explicit analytically their dependence on the three-dimensional accelerations gradient.

Lagrangian Velocity Spectra at 700 m in the Western North Atlantic

Abstract Pending an appropriate scaling of each trajectory by its Lagrangian integral timescale TL, there exists a generic shape of the Lagrangian frequency spectrum for the trajectories of the 700-m dataset in western North Atlantic, which are stationary on the timescale of 200 days. The generic spectral shape contains a plateau at the lowest frequencies extending up to ν0∼(30TL)−1, a power-law behavior with an intermediate spectral slope α = 0.25 between ν0 and ν1∼(3∼4TL)−1, and a steeper slope n ≥ 3 at larger frequencies. Such a steep slope at large frequencies implies that most of Lagrangian dispersion can be ascribed to low and intermediate frequency motions. The variance of the Lagrangian acceleration computed from such a spectrum is finite, indicating continuous particle accelerations and supporting a truly Lagrangian behavior of the 700-m floats. The existence of an intermediate power-law behavior in the spectrum can be linked with the trapping of some trajectories by persistent energetic structur...