2 results
Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence
- ANNALISA BRACCO, JAMES C. MCWILLIAMS
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- Journal:
- Journal of Fluid Mechanics / Volume 646 / 10 March 2010
- Published online by Cambridge University Press:
- 08 March 2010, pp. 517-526
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- Article
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Turbulent solutions of the two-dimensional Navier–Stokes equations are a paradigm for the chaotic space–time patterns and equilibrium distributions of turbulent geophysical and astrophysical ‘thin’ flows on large horizontal scales. Here we investigate how homogeneous, stationary two-dimensional turbulence varies with the Reynolds number (Re) in stationary solutions with large-scale, random forcing and viscous diffusion, also including hypoviscous diffusion to limit the inverse energy cascade. This survey is made over the computationally feasible range in Re ≫ 1, approximately between 1.5 × 103 and 5.6 × 106. For increasing Re, we witness the emergence of vorticity fine structure within the filaments and vortex cores. The energy spectrum shape approaches the forward-enstrophy inertial-range form k−3 at large Re, and the velocity structure function is independent of Re. All other statistical measures investigated in this study exhibit power-law scaling with Re, including energy, enstrophy, dissipation rates and the vorticity structure function. The scaling exponents depend on the forcing properties through their influences on large-scale coherent structures, whose particular distributions are non-universal. A striking result is the Re independence of the intermittency measures of the flow, in contrast with the known behaviour for three-dimensional homogeneous turbulence of asymptotically increasing intermittency. This is a consequence of the control of the tails of the distribution functions by large-scale coherent vortices. Our analysis allows extrapolation towards the asymptotic limit of Re → ∞, fundamental to geophysical and astrophysical regimes and their large-scale simulation models where turbulent transport and dissipation must be parameterized.
4 - Particle motion in a sea of eddies
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- By Claudia Pasquero, ESS University of California, Irvine, California, USA, Annalisa Bracco, Physical Oceanography Dept., Woods Hole Oceanographic Institute, Woods Hole, Massachusetts, USA, Antonello Provenzale, ISAC-CNR, Torino, CIMA, Savona, Italy, Jeffrey B. Weiss, PAOS University of Colorado, Boulder, Colorado, USA
- Edited by Annalisa Griffa, University of Miami, A. D. Kirwan, Jr., University of Delaware, Arthur J. Mariano, University of Miami, Tamay Özgökmen, University of Miami, H. Thomas Rossby, University of Rhode Island
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- Book:
- Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics
- Published online:
- 07 September 2009
- Print publication:
- 10 May 2007, pp 89-118
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Summary
Abstract
As more high-resolution observations become available, our view of ocean mesoscale turbulence more closely becomes that of a “sea of eddies.” The presence of the coherent vortices significantly affects the dynamics and the statistical properties of mesoscale flows, with important consequences on tracer dispersion and ocean stirring and mixing processes. Here we review some of the properties of particle transport in vortex-dominated flows, concentrating on the statistical properties induced by the presence of an ensemble of vortices. We discuss a possible parameterization of particle dispersion in vortex-dominated flows, adopting the view that ocean mesoscale turbulence is a two-component fluid which includes intense, localized vortical structures with non-local effects immersed in a Kolmogorovian, low-energy turbulent background which has mostly local effects. Finally, we report on some recent results regarding the role of coherent mesoscale eddies in marine ecosystem functioning, which is related to the effects that vortices have on nutrient supply.
Introduction
The ocean transports heat, salt, momentum and vorticity, nutrients and pollutants, and many other material and dynamical quantities across its vast spaces. Some of these transport processes are at the heart of the mechanisms of climate variability and of marine ecosystem functioning. In addition, a large portion of the available data on ocean dynamics are in the form of float and drifter trajectories. These provide a Lagrangian view of the ocean circulation which is not always easy to disentangle.