Session FG: Geophysical Fluid Dynamics III

Lagrangian transport through an ocean front in the North-Western Mediterranean Sea

We analyze with the tools of lobe dynamics the velocity field from a numerical simulation of the surface circulation in the Northwestern Mediterranean Sea. We identify relevant hyperbolic trajectories and their manifolds, and show that the transport mechanism known as the ``turnstile,'' previously identified in abstract dynamical systems and simplified model flows, is also at work in this complex and rather realistic ocean flow. In addition nonlinear dynamics techniques are shown to be powerful enough to identify the key geometric structures in this part of the Mediterranean. In particular the North Balearic Front, the westernmost part of the transition zone between saltier and fresher waters in theWestern Mediterranean is interpreted in terms of the presence of a semipermanent ``Lagrangian barrier'' across which little transport occurs. Our construction also reveals the routes along which this transport happens.   

Dynamics of internal boluses across a shelf break

We present results of high-resolution two- and three-dimensional numerical simulations showing the interaction of nonlinear internal waves with a shelf break. The interaction of nonlinear incident waves with the shelf break results in the formation of upslope-surging vortex cores of dense fluid (referred to here as internal boluses) that propagate onto the shelf. We present results primarily focusing on understanding the dynamics of the interaction process with particular emphasis on the formation, structure and propagation of internal boluses onshelf.   

Turbulent mixing studies in an Oceanic Overflow Facility

We have built a facility (Oceanic Overflow Facility) allowing to study a gravity current along an inclined plate, flowing into a steady ambiant medium. At small values of the Richardson number, the shear dominates the stabilizing effect of the stratification and the flow at the interface of the current becomes unstable, resulting in a turbulent mixing. These currents occur in the oceanic thermohaline circulation and their mixing properties with the ambiant fluid have a strong influence on the dynamics of the overall circulation. Using PIV and PLIF to characterize respectively the velocity and density field, we study the statistical properties of the vertical mixing. Spatial spectra, as well as correlation functions and higher order moments are computed from the data, allowing to better characterize and parametrize the small scale turbulent mixing. This kind of parametrization can be a valuable input for ocean circulation models such as MICOM, HIM, POP or MIT General Circulation.   

Velocities and Temperatures of Jupiter's Great Red Spot and the New Red Oval and Implications for Global Climate Change

In 1998 - 2000 three jovian White Oval vortices near 34$^{o}$S merged and formed a new Oval. It turned from white to red in 2005. The reason for the color change is unknown but may signify a temperature change. Because the color changed one thermal time, or 7 years, after the mergers, it may indicate the global climate change that was predicted to occur after the mergers (based on the assumption that the chaotic mixing of heat due to the oscillatory motions of the White Ovals ceased after their mergers, so that latitudes near 34$^{o}$S became barriers to meridional heat transport.) We inferred vertical thermal structure from velocity measurements of the vortices (derived from cloud displacements). We report differences in aspect ratios, areas and peak velocities of the GRS and the Oval(s) from 1979, 2000, and 2006. We compare the areas of the clouds associated with the vortices with the areas enclosed by their outermost closed streamlines, and with the areas of the vortices' potential vorticity anomalies. We discuss the implications of our findings to Jovian climate.   

Extraction of Velocity Fields from Telescope Image Pairs of Jupiter's Great Red Spot, New Red Oval, and Zonal Jet Streams

We use a variety of new and old methods, including Coherence Image Velocimetry, image reconstruction, data assimilation of satellite imagery and animation, to extract Jovian velocity fields (and their uncertainties) from image pairs taken with the Hubble Space Telescope. Velocities are derived from cloud displacements in the image pairs. Our methods go far beyond the traditional technique of deriving a velocity vector by setting it equal to an image pair's cloud displacement vector divided by the time between images. The images in some pairs were taken as few as 12 minutes apart. To understand why new techniques are needed, we note that the characteristic velocities are $\sim $30ms$^{-1}$. Therefore, a cloud's displacement over 12 minutes is only 22km, which is less than half a pixel (and the spatial resolution in our observations was $\sim $5 pixels). To obtain sub-pixel resolution, it was necessary for us to use all of the data from all of the image pairs and to employ all of our techniques in an iterative manner. We outline how these methods work and how they can be applied to archived data sets of satellite imagery of the giant planets.   

Modeling and Data Assimilation of the Velocity of Jupiter's Great Red Spot and Red Oval

Data assimilation and modeling techniques are applied to new velocity fields of Jupiter's Great Red Spot (GRS) and Red Oval to determine quantities of physical interest such as the Rossby deformation radius (i.e., the vertical stratification) and the distribution of potential vorticity. One technique parameterizes the set of steady solutions to the shallow-water (SW) equations in terms of several unknowns, which include the deformation radius and the forcing from deeper layers. A genetic algorithm is used to determine the unknown parameter values such that a SW solution matches the input velocities to within the observational uncertainties. This typically results in a range of acceptable values for each parameter. However, only a subset of these values gives stable solutions, so that the range of acceptable parameter values is reduced. Models are also used to deduce the physics that makes the GRS ``hollow,'' i.e., have a minimum of potential vorticity in its interior.   

Numerical investigation of the dynamo bifurcation

The dynamo effect is the process by which the magnetic field of the Earth is generated. In the presence of a small initial magnetic field, convective motion in the fluid outer core produce currents and thus a magnetic field which can reinforce the initial field and sustain it against ohmic diffusion. There is also a feedback of the magnetic field on the flow which limits its growth. Our direct numerical approach consisted in solving the equations for the velocity field, the magnetic field and the temperature in a rapidly rotating spherical shell. We focused our study on the dynamo bifurcation. This dynamo bifurcation corresponds to the transition from a system with a decaying magnetic field to a system with a self-sustain magnetic field by an increase of the control parameter. Even though in this region of the parameter space the problem might appear more tractable, we observed a great variety of behaviors for the magnetic field, with for example metastable solutions or a magnetic field enhancing or limiting the convective motions. We also observed that the nature of the dynamo bifurcation can be strongly affected by a small change in the parameters.   

A Three-Dimensional Hydrodynamic Model for Delaware Bay Estuary

A numerical 3D model for the tidal portion of the Delaware Bay has been developed using the UnTRIM hydrodynamic kernel. The model extends from Trenton, NJ south past the inlet at Cape May, NJ and incorporates a large portion of the continental shelf (up to the 50 meter isobath) to capture the processes of the continental shelf and their relation and impact on the bay dynamics. Circulation patterns are successfully simulated by using a variable, harmonically decomposed, water level boundary condition of three diurnal (K$_{1}$, Q$_{1}$, O$_{1})$ and four semi-diurnal (K$_{2}$, S$_{2}$, N$_{2}$, M$_{2})$ components in both space and time. Various turbulence closure models are compared for use with the hydrodynamic model. Four of these models ($k-\varepsilon $, $k-\omega $, $k-kl$and $k-ge)$ have been implemented in the hydrodynamic code using Generic Length Scale (GLS) approach that mimics the models through its parameter combinations. Low order models show significant deviations from the measured salinity data. Among the two equation models, ($k-\varepsilon )$ approach appears to work the best even though it is difficult to discern general rules for the selection of an appropriate or the best model for other modeling domains.   

River width selection

The ancient problem of natural width selection in rivers has still remained open up to now. It is revisited, combining an experimental approach at laboratory scale, measurements on natural sand rivers and theory. We show that the scaling law of the width with the square root of flow rate, both obtained experimentally in controlled condition and in the field can be related to two mechanisms: \begin{itemize} \item the erosion threshold on the banks, \item the transverse diffusion of longitudinal momentum. \end{itemize} We show that a simple viscosity or an isotropic turbulent viscosity would lead to a different behavior. We recover quantitatively the shape of the bed, the velocity profile and the different scaling laws when the anisotropy of the Reynolds stress is taken into account. Our results open new perspectives about the parameters governing river morphology.