Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session HN: Geophysical Flows II |
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Chair: Alexander Gluhovsky, Purdue University Room: Hilton Chicago PDR 2 |
Monday, November 21, 2005 1:20PM - 1:33PM |
HN.00001: A Mechanism for the Formation of Jets and Vortices in Rotating Flows Leslie Smith, Youngsuk Lee Numerical simulations of `reduced models' including only near-resonant triad interactions are compared to full simulations of 3D rotating flow and 2D beta-plane flow forced randomly at small scales. In 3D rotating flow at moderate Rossby numbers, Smith and Lee (2005) showed that near resonances capture the important characteristics of the full simulations: efficient energy transfer to large scales, the formation of vortical columns, and symmetry breaking in favor of cyclones. Neither non-resonances nor near-2D interactions reproduce those features. On the beta-plane at moderate Rhines numbers, near resonances are responsible for the formation of large-scale zonal flows. As in full simulations with linear damping, they lead to symmetry breaking in the meridional derivative of the zonally averaged vorticity. The flow generated by near resonances is shown to be marginally stable according to the Rayleigh-Kuo theorem. [Preview Abstract] |
Monday, November 21, 2005 1:33PM - 1:46PM |
HN.00002: Two-particle dispersion in stably stratified and rotating turbulence Lukas Liechtenstein, Fabien S. Godeferd, Claude Cambon Geophysical flows are always subjected to stratification due to density gradients, and to the earth's rotation. Although the role of turbulence in mixing is still not clearly understood, it is of prime importance in geophysical flows. A good understanding of the physical mechanisms underlying the evolution of two particle dispersion is important for modelling turbulent diffusion. We study a simplified case which nevertheless captures the most important physical mechanisms in geophysical flows in the Boussinesq system of equations with the Brunt-Vaisala frequency N a parameter for the stratification and f, the Coriolis parameter. We generate and compare two particle dispersion from direct numerical simulation (DNS) and kinematic simulation (KS) for different ratios of rotation to stratification. KS only involves linear dynamics in the evolution of the velocity field and exhibits no coherent vortices, while DNS is a fully nonlinear simulation exhbiting typical coherent structures for rotating and stratified turbulence. The absence of nonlinearities and coherent structures only weakly influences single particle dispersion. However, two particle dispersion is widely affected by nonlinearities in the velocity field evolution. We characterize two particle dispersion for rotating and stratified turbulence compared to isotropic turbulence. Furthermore, we isolate features, which appear or disappear depending on the nonlinearity in the flow. [Preview Abstract] |
Monday, November 21, 2005 1:46PM - 1:59PM |
HN.00003: The Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence Beth Wingate, Susan Kurien, Leslie Smitih A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The K\'arm\'an-Howarth type of equation is derived for the dynamics of the two-point correlation function. Combinations of the Rossby, Froude, Prandtl and Reynolds numbers are used to investigate various limiting cases of the dynamics. Regimes in which one might expect a potential vorticity inertial range are identified. In the cases of large Rossby and Froude numbers and quasi-geostrophic dynamics, a result analogous to the Kolmogorov 4/5-law for the third-order velocity structure function is derived for the third-order mixed correlation between potential vorticity and velocity. [Preview Abstract] |
Monday, November 21, 2005 1:59PM - 2:12PM |
HN.00004: Non-Boussinesq and finite depth effects in surface quasi-geostrophic dynamics Richard Scott Surface quasi-geostrophic (SQG) dynamics describes the slow vortical motion of rotating, stratified fluid under the assumption that interior gradients of potential vorticity (the active scalar) vanish; it has applications in atmospheric and oceanic dynamics and provides a simple setting for the study of finite-time singularity formation. This talk will discuss two variants of standard SQG dynamics. First, we consider non-Boussinesq effects, relevant to the large-scale atmospheric situation, retaining the compressibility of the background density profile; this renders the large-scale dynamics spectrally nonlocal, with a character resembling two-dimensional barotropic vortex dynamics, while having little effect at small scales. Second, motivated by the observed jump in static stability at the tropopause, we consider the effect of blurring the distribution of surface scalar over a finite depth; this introduces a length scale below which the dynamics again becomes spectrally nonlocal and similar in character to two-dimensional barotropic vortex dynamics. In each case we consider shear instability and equilibrium energy spectra as particular examples. [Preview Abstract] |
Monday, November 21, 2005 2:12PM - 2:25PM |
HN.00005: Entrainment rates in rotating gravity currents Mathew Wells, John Wettlaufer Many marginal seas produce dense water in shallow shelf regions that are drained by gravity currents. The action of rotation, dissipation and local stratification results in a trajectory of the current at an angle to the maximum slope. The velocity of such currents scales like $U \sim g' tan(S)/f$, where $f$ is the Coriolis parameter, $g'$ the reduced gravity and $S$ the slope (Nof, 1983). In non-rotating laboratory experiments, Ellison and Turner (1959) found an entrainment ratio like $E \sim Fr$, where the Froude number is $Fr = U /\sqrt{g' h}$ and $h$ is the current thickness. Substution of the Nof velocity in the definition of the Froude number predicts that $E \sim 1/f \times \sqrt{g'/h} $, for constant $S$. We have been able to verify this new prediction in a series of rotating laboratory experiments. Both the density of the incoming fluid and the rotation rate were varied. The entrainment ratio $E$ decreased inversely with increasing Coriolis parameter $f$, and increased as the square root of the initial density anomaly $g'$; as would be expected if the flow velocity is set by a geostrophic balance. Our experiments also find to the same entrainment ratio as the Ellison and Turner (1959) experiments for the same Froude numbers. [Preview Abstract] |
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