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  • 1
    Electronic Resource
    Electronic Resource
    Temporal scaling behavior of decaying two-dimensional turbulence (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 608-621 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Decaying two-dimensional turbulence is characterized by the emergence of coherent vortices, which subsequently dominate the evolution. The temporal scaling behavior of the flow is analyzed using a scaling theory, a long-time integration of the fluid equations, and a dissipative, modified point-vortex model that represents the turbulence as a system of interacting coherent structures. Good agreement is found in the behavior of average vortex properties, low-order moments of the flow fields, and the form of self-similar evolution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858647
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  • 2
    Electronic Resource
    Electronic Resource
    Anisotropic geophysical vortices (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 4 (1994), S. 305-311 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A survey is made of many types of coherent vortices in the Earth's ocean and atmosphere. These vortices often occur with strong, environmentally induced anisotropy in their velocity and vorticity fields. We propose a definition of the essential characteristics of coherent vortices and formulate hypotheses concerning their dynamical role in complex, anisotropic fluid motions. Finally, we analyze numerical solutions both for uniformly rotating, stably stratified three-dimensional flow and for two-dimensional flow for the phenomena of enstrophy cascade and dissipation, intermittency, isotropy in the appropriate coordinate frame, coherent vortex emergence, vortex population dynamics, and approach to a nonturbulent end state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166010
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  • 3
    Electronic Resource
    Electronic Resource
    Nonergodicity of point vortices (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 835-844 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The motion of N point vortices in a two-dimensional fluid is a Hamiltonian dynamical system with a 2N-dimensional phase space. The equations of motion for point vortices in a two-dimensional square doubly periodic domain are derived from those for an open domain. The Hamiltonian has three known constants of the motion and is thus believed to be nonintegrable for four or more vortices. Trajectories are numerically integrated from several initial conditions containing six vortices with varying total energy. Ergodicity on the surface defined by the constants of the motion is directly tested by comparing time-average and ensemble-average vortex pair statistics. It is found that the dynamics is not ergodic. There is evidence that the nonergodicity is not due to a gross fragmentation of phase space as might result from a broken symmetry. Vortex pair statistics are also used to test the randomness of the chaotic motion. It is found that the time-averaged statistics of the vortices are clearly distinct from those of independent random walkers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858014
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  • 4
    Electronic Resource
    Electronic Resource
    A demonstration of the suppression of turbulent cascades by coherent vortices in two-dimensional turbulence (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 547-552 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The role of coherent vortices in suppressing the rates of cascade (i.e., spectrum evolution through scale transfer and dissipation) is demonstrated in numerical solutions of decaying two-dimensional turbulence at high Reynolds number. The demonstration is made by comparing the evolution of a primary solution that has well-developed vortices with other solutions that initially have equivalent wavenumber spectra but lack vortices because of an imposed phase scrambling. The solutions without vortices have substantially greater cascade rates. Furthermore, when the primary solution is compared with other solutions whose initial conditions are constructed only from isolated, axisymmetric vortices, their spectrum evolution is qualitatively similar. This demonstrates the control of cascade rates by coherent vortices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857755
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  • 5
    Electronic Resource
    Electronic Resource
    Weakly decaying turbulence in an equivalent-barotropic fluid (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 938-950 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical solutions are analyzed for the evolution of turbulent flow in an equivalent-barotropic fluid (i.e., a shallow water layer in the limit of strong rotation) from random, narrow-band initial conditions with small viscosity. Particular attention is given to the regime of small deformation radius: the solutions are weakly dissipative of both energy and potential enstrophy; after a brief initial interval of broadening in wave number, the shapes of the energy and potential enstrophy spectra are nearly invariant in time but their centroids move toward larger scales, and coherent vortex structures spontaneously develop with a preferred shape of axisymmetric potential vorticity monopoles. An asymptotic model is derived for small deformation radius, and its behavior exhibits the essential features of the equivalent-barotropic model. Solutions are analyzed for increasing deformation radii, ranging from small to infinite (i.e., nondivergent, two-dimensional flow). In this sequence, both the dynamical evolution rates (e.g., dissipation) and the degree of non-Gaussianity (intermittency) increase substantially. In particular, the spatial sparseness of the coherent vortices increases with deformation radius.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857970
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  • 6
    Electronic Resource
    Electronic Resource
    Coherent structures and dynamics in a neutrally stratified planetary boundary layer flow (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 2626-2639 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Coherent structures and the dynamics of a neutrally stratified planetary boundary layer flow are studied through a large eddy simulation, which includes surface roughness, Coriolis force, and a capping inversion. Quadrant analysis and flow visualization show that low-speed negative momentum flux (ejection) is the dominant feature throughout most of the boundary layer. The initiation of vortical structures is observed to be associated with vorticity sheets and pressure maxima, which are formed dynamically when low-speed negative momentum flux collides with either high-speed negative momentum flux (sweep) or the mean flow. Four dimensional conditional averages are used to study the statistical behavior of ejections and sweeps. The shape, strength, lifetime, and origin of the conditionally sampled structures at three different heights are discussed. Near the surface, sweeps are observed to induce ejections when colliding with the surface. The evolution of sweep-induced ejections near the wall is discussed. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869048
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  • 7
    Electronic Resource
    Electronic Resource
    Fluctuation growth and instability associated with a singularity of the balance equations (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 2587-2596 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Large-scale flows in the atmosphere and ocean are usually in a state of approximate momentum balance, the simplest form of which is geostrophy. Furthermore, balanced models have often been shown to be quite accurate in this regime, with the quasigeostrophic equations the simplest such model and the balance equations a more accurate one, even though such models exclude the rapidly oscillatory, unbalanced dynamics of acoustic, gravitational, and inertial oscillations. However, this behavior is not universal, and here we investigate the fluid dynamics on one of the margins of this regime. We solve for linearized, inviscid fluctuations about a horizontal shear flow with spatially uniform vorticity and strain rate in a rotating, stratified, incompressible fluid, without making any balanced approximations. In both parallel and elliptical shear flows, we find that a significant increase occurs in the growth of unbalanced fluctuations near the violation of a necessary condition for the time integrability of the balance equations. This condition is that the absolute vertical vorticity everywhere exceeds the modulus of the horizontal strain rate. Thus, we seemingly have found a new boundary to the regime of large-scale dynamics, with its approximate gradient-wind balance, anisotropic velocity field, and mostly "slow-manifold" evolutionary behavior. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869772
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  • 8
    Electronic Resource
    Electronic Resource
    The breakdown of large-scale flows in rotating, stratified fluids (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 3178-3184 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Flows under the influences of environmental rotation and stable density stratification often exhibit an approximate force balance and a consequently slow rate of evolution at large Reynolds number. Such flows are typically anisotropic in their velocity field. This regime is relevant to large-scale motions in the Earth's atmosphere and ocean, as well as many other planetary and astrophysical systems. The Balance Equations are usually an accurate approximate model for this regime. However, they have solvability limits associated with a change of type in their time-integration operator. In this paper we derive these limiting conditions for the conservative Balance Equations in isentropic coordinates, show that the least familiar of these conditions coincides with loss of convexity of the streamfunction for horizontal velocity in the inertial reference frame, and identify these conditions with the general conditions for symmetric loss of stability for circular and parallel flows as well as for the three-dimensional loss of stability for elliptical flows. We then conjecture that the identified limits of balance coincide generally with the boundary between the distinctive nonlinear dynamical behaviors (i.e., their turbulent cascade and dissipation rates) associated with the large- and small-scale regimes in geophysical and astrophysical flows. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869844
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  • 9
    Electronic Resource
    Electronic Resource
    Multigrid solution of stably stratified flows: The quasigeostrophic equations (1996)
    Springer
    Journal of scientific computing 11 (1996), S. 47-69 
    Details
    ISSN: 1573-7691
    Keywords: Multigrid ; quasigeostrophic equations ; geophysical turbulence ; parallel computation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Two approaches are investigated to the multigrid solution of the quasi-geostrophic equations—a fundamental nonlinear system of partial differential equations that models large-scale planetary flows. One approach employs standard coarsening with pointwise SOR and the other line relaxation with partial coarsening. The latter solver is implemented in turbulent-flow simulations on the CRAY C-90 supercomputer. This solver is robust with respect to anisotropy of the operator due to stratification, and it efficiently exploits the vectorization and parallelization capabilities of the machine. The approach taken is applicable to more complex related systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02088949
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  • 10
    Electronic Resource
    Electronic Resource
    A grid nesting method for large-eddy simulation of planetary boundary-layer flows (1996)
    Springer
    Boundary layer meteorology 80 (1996), S. 167-202 
    Details
    ISSN: 1573-1472
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models. Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00119016
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