Session AV: Geophysical Flows I

Hurricane Formation in Diabatic Ekman Turbulence

This study numerically examines the evolution of Diabatic Ekman Turbulence (DET) under various conditions. DET is quasi 2D turbulence that is modified by surface friction and parameterized cumulus convection. The self-organization of DET is here simulated in a 3-layer troposphere. In our primary model, winds over the ocean elevate the moist entropy of boundary layer air, whose convergence may then generate deep convection. After an incubation period, the influence of deep convection can supercede ideal 2D processes such as vortex merger. A strong cyclone-anticyclone asymmetry can develop, with relatively intense cyclones dominating the system. ``Hurricanes'' form at sufficiently high values of the sea-surface temperature (SST), the Coriolis parameter, and the surface-exchange coefficient for moist entropy~$C_E$. Increasing the momentum exchange coefficient $C_D$ shortens the incubation period, but decelerates the subsequent intensification of an emerging hurricane. Increasing $C_E$ or the SST accelerates all stages of hurricane genesis. As in more complex models, DET hurricanes can exhibit mesovortices and eyewall cycles. Moreover, their intensities increase with the SST and the ratio~$C_E/C_D$. In some regions of parameter space, low-level noise can evolve into a hurricane {\it or} a synoptic scale circulation. The effects of using different representations of cumulus convection or surface friction will be discussed. Supported by NSF-ATM-0750660.   

Velocity Fields of Jovian Dynamical Features using the Advection Corrected Correlation Image Velocimetry Method

We present the Advection Corrected Correlation Image Velocimetry (ACCIV) automated method for producing velocity fields from satellite and spacecraft image pairs of planetary atmospheres. The method combines a laboratory technique for tracking fluid motion, Correlation Image Velocimetry (CIV), with simulations of cloud advection to produce velocity fields with uncertainties as small as 3 ms$^{-1}$. On Jupiter, ACCIV has been most successful when applied to sets of images in which some image pairs are separated by short periods of time ($\sim $1 hour) and some image pairs are separated by longer periods ($\sim $10 hours). Given appropriate sets of images, ACCIV achieves unprecedented accuracy by combining the very large numbers of data points that automated techniques provide with the ability to track cloud features over long periods of time ($\sim $10-12 hours), previously only attainable by manual tracking methods. We present the application of ACCIV to the Great Red Spot, the Red Oval BA and several other dynamical features on Jupiter. We also present a velocity map of the entire Jovian cloud deck between 60\r{ } N and 60\r{ } S latitude produced from Cassini approach images from December 2000.   

Dynamics and Interactions of Jovian Vortices During the Last Year

Jupiter's atmosphere has been active during the last year with the Great, Little, and Oval Red Spots merging, almost merging, or repelling each other. These jovian storms are all anticyclonic vortices, with small Rossby numbers, embedded in an atmosphere with strong vertical stratification and horizontal shear. We use numerical and analytic models to compute and explain these vortex interactions. Many of the interactions are sensitive to equilibrium values of the ambient jovian atmosphere that are difficult to measure directly, such as the vertical shear and the vertical stratification. We show that the errors in the velocity measurements of the jovian vortices are sufficiently small, the equations are sufficiently well-conditioned, and the 3D models of the vortices sufficiently complex that the ``inverse problem'' can be solved and that we can determine many of the equilibrium values of the ambient jovian atmosphere.   

Zonal winds generated by tides

The fundamental role of tides in geo and astrophysics has been the subject of multiple studies for several centuries. Beyond the well known quasi periodic flows of ocean water on our shores, tides are also responsible for phenomena as varied as the intense volcanism on the Jovian satellite Io, or the synchronization of the Moon spin on its rotation around the Earth. We describe here a new phenomenon of zonal wind generation by tidal forcing. Following a recent theoretical and numerical analysis of Tilgner [1], we present the first experimental evidence that the nonlinear self-interaction of a tidally forced inertial mode can drive an intense axisymmetric flow in a rotating sphere. These results are relevant for zonal wind generation in planets and stars. [1] A. Tilgner, Zonal wind driven by inertial modes, {\it Phys. Rev. Lett.} {\bf 99}, 194501 (2007).   

Interaction of alternating oceanic zonal jets and wind-driven gyres

Recent evidence has unmasked the presence of alternating zonal jets superimposed on the larger scale midlatitude ocean circulation. Analogous jets are well-known from $\beta$-plane turbulence and are associated w ith a halting of the 2d inverse energy cascade by Rossby wave dispersion. Both the $\beta$-plane turbulence and the gyre scale dynamics are nonlinear and it seems reasonable to anticipate that the two will inter act. Some evidence for these interactions comes from observations: e.g., jets in the N. Atlantic are aligned at an angle to latitude circles, following a direction nearly parallel to the seaward extension of the Gulf Stream. In the North Pacific, both the jets and the Kuroshio extension are more nearly zonal. How jets interact with the wind-driven cirulation is considered in the quasi-geostrophic equations in a box ge ometry forced by i) a large scale wind, ii) a small scale stochastic forcing and iii) both. The first cas e is the classic midlatitude double gyre problem, the second has previously been used to model the jets an d the third allows us to consider interactions between the two. We focus primarily on the energetics.   

Kinematic dynamo of inertial waves

Inertial waves are natural oscillatory tridimensional perturbations in rapidly rotating flows. They can be driven to high amplitudes by an external oscillatory forcing such as precession, or by a parametric instability such as in the elliptical instability. Inertial waves were observed in a MHD-flow (Gans, 1971, JFM ; Kelley et al., 2008, GAFD) and could be responsable of dynamo action. For travelling waves, a constructive alpha-effect was identified (Moffatt, 1970, JFM), but it does not apply to confined inertial wave flows. Yet, recent numerical work demonstrated that precession driven MHD flows can sustain magnetic fields (Tilgner, 2005, POF; Wu \& Roberts, 2008, GAFD). This motivates us to study more precisely how inertial waves can exhibit dynamo action. Using a numerical code in cylindrical geometry, we find that standing inertial waves can generate a kinematic dynamo. We show that the dynamo-action results from a second order interaction of the diffusive eigenmodes of the magnetic field with the inertial wave. Scaling laws are obtained, which allows us to to apply the results to flows of geophysical interest.   

Spherical Couette flow in a three meter diameter system

Construction of the three-meter diameter spherical Couette experiment at the University of Maryland is complete. Prior to sodium experiments measurements have been performed using water as a test fluid. Pressure measurements are provided by three piezo-electric transducers mounted on the outer sphere inner surface at a colatitude of 23.6$^{\circ}$ and separated 90$^{\circ}$ azimuthally. In addition, a hot-film wall shear stress probe located near one of the pressure probes complements the measurements. Direct optical imaging of tracer particles in the fluid is also implemented. Preliminary analysis show evidence of inertial modes and non-linear interactions among them.   

A hydromagnetic spherical Couette experiment with a soft iron core

Understanding the geodynamo remains a central pursuit of Earth science. Increasingly powerful numerical simulations and the experimental generation of a magnetic field by a Von K\'{a}rm\'{a}n flow raise questions about the roles of turbulence and ferromagnetic materials. We present experimental studies of 110~L of conductive fluid (sodium) in a differentially rotating spherical Couette cell with Earth-like geometry. The inner boundary is ferromagnetic soft iron, which has large permittivity but small remembrance, and which was chosen in an attempt to better understand the results of Monchaux \textit{et.\ al} (2007). We measure magnetic induction via an array of Hall probes and project the data onto the vector spherical harmonics up to degree four, producing time series of Gauss coefficients. Varying the Ekman number, rotation rate ratio, and magnetic Reynolds number, we observe a variety of behaviors, including large induced fields, large resulting torques, intermittent broadband induction, Earth-like dipolar fields, and bistability.   

Dynamics of Pure Ice Streams and Surges

We examine a bottom sliding law that is capable of explaining pure ice streams and glacier surges within a simple model of ice flow over a homogeneous bed. The model resolves longitudinal stresses, and assumes a plug flow as supported by ice stream observations. The flow law is Newtonian and hence we neglect thermo-viscous and shear-thinning effects. The bottom sliding law is a multivalued relation between the bottom stress and the ice velocity, similar to that suggested by previous work (e.g. Fowler \& Johnson, 1996). The multivaluedness can be heuristically justified by variations in bed lubrication caused by changes in water formation rate and rearrangement of the drainage system. This sliding law accounts for two fundamental modes of flow, depending on the magnitude of the mass accumulation forcing: (i) a steady stream pattern, due to the coexistence of two stable velocities for a given bottom stress, the faster corresponds to an ice stream region and the slower to an inter-stream region. (ii) a relaxation oscillation mode (a surge).   

Wind-transport of barchan dunes in modulated gravity

Barchan dunes can be found in sand barren regions under steady wind conditions. They translate in the direction of the wind while their shape remains unchanged. They have a minimal length in the order of ten meters, which renders laboratory experiments almost impossible. The length scale is set by the details of the sand-wind interaction. Smaller dunes do not evolve into the typical barchan dune shape. Our experimental approach produces dramatically scaled down barchan dunes. The idea is to modulate gravity by vertical oscillation of the sand bed. We produce small dunes that travel in the turbulent boundary layer of an open windtunnel. Particle image velocimetry on the surface of moving dunes reveals the flux of creeping sand, while measurement of sand grains flying through the air quantifies the key mechanism that moves sand by wind: saltation. While the amount of sand flying with the flow does not vary strongly in an oscillation cycle, the sand creeping over the dune surface is only in motion when the effective gravity is smaller than g. Thus, modulation of gravity provides a unique view on sand transport in wind. Saltation is an activation process, and we demonstrate the importance of turbulence.