Energy transfer in isotropic turbulence at low Reynolds numbers

Detailed measurements were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers generated by direct numerical simulation. It was observed that although the transfer resulted from triad interactions that were non-local in k space, the energy always transferred locally. The results are consistent with the notion of non-uniform advection of small weak eddies by larger and stronger ones, similar to transfer processes in the far dissipation range at high Reynolds numbers

Large eddy simulation of two-dimensional isotropic turbulence

Large eddy simulation (LES) of forced, homogeneous, isotropic, two-dimensional (2D) turbulence in the energy transfer subrange is the subject of this paper. A difficulty specific to this LES and its subgrid scale (SGS) representation is in that the energy source resides in high wave number modes excluded in simulations. Therefore, the SGS scheme in this case should assume the function of the energy source. In addition, the controversial requirements to ensure direct enstrophy transfer and inverse energy transfer make the conventional scheme of positive and dissipative eddy viscosity inapplicable to 2D turbulence. It is shown that these requirements can be reconciled by utilizing a two-parametric viscosity introduced by Kraichnan (1976) that accounts for the energy and enstrophy exchange between the resolved and subgrid scale modes in a way consistent with the dynamics of 2D turbulence; it is negative on large scales, positive on small scales and complies with the basic conservation laws for energy and enstrophy. Different implementations of the two-parametric viscosity for LES of 2D turbulence were considered. It was found that if kept constant, this viscosity results in unstable numerical scheme. Therefore, another scheme was advanced in which the two-parametric viscosity depends on the flow field. In addition, to extend simulations beyond the limits imposed by the finiteness of computational domain, a large scale drag was introduced. The resulting LES exhibited remarkable and fast convergence to the solution obtained in the preceding direct numerical simulations (DNS) by Chekhlov et al. (1994) while the flow parameters were in good agreement with their DNS counterparts. Also, good agreement with the Kolmogorov theory was found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary djnlx.tex fil

Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence

In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wavenumber shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimension, magnitude of triad interactions is large for nonlocal triads, and small for local triads. However, the shell-to-shell energy transfer rate is found to be local and forward. This result is due to the fact that the nonlocal triads occupy much less Fourier space volume than the local ones. The analytical results on three-dimensional shell-to-shell energy transfer match with their numerical counterparts. In two-dimensional turbulence, the energy transfer rates to the near-by shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.Comment: 10 pages, Revtex

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

On dynamically consistent eddy fluxes

Author Posting. © The Author, 2004. This is the author's version of the work. It is posted here by permission of Elsevier B. V. for personal use, not for redistribution. The definitive version was published in Dynamics of Atmospheres and Oceans 38 (2005): 123-146, doi:10.1016/j.dynatmoce.2004.11.003.The role of mesoscale oceanic eddies in driving the large-scale currents is studied in an eddy-resolving, double-gyre ocean model. The new diagnostic method is proposed, which is based on dynamical decomposition of the flow into the large-scale and eddy components. The method yields the time history of the eddy forcing, which can be used as additional, external forcing in the corresponding non-eddy-resolving model of the gyres. The main strength of this approach is in its dynamical consistency: the non-eddy-resolving solution driven by the eddy forcing history correctly approximates the original large-scale flow component. It is shown that statistical decompositions, which are based on space-time filtering diagnostics, are dynamically inconsistent. The diagnostics algorithm is formulated and tested, and the diagnosed eddies are analysed, both statistically and dynamically. It is argued that the main dynamic role of the eddies is to maintain the eastward-jet extension of the subtropical western boundary current (WBC). This is done largely by both the time–mean isopycnal-thickness flux and the relative-vorticity eddy flux fluctuations. The fluctuations drive large-scale flow through the nonlinear rectification mechanism. The relative-vorticity flux contributes mostly to the eastward jet meandering. Finally, eddy fluxes driven by both the eddies and the large-scale flow are found to be important. The latter is typically neglected in the analysis, but here it corresponds to important large-scale feedback on the eddies.Funding for this research was provided by NSF grant OCE 00–91836, by the Royal Society Fellowship, and by WHOI grants 27100056 and 52990035

Biophysical forcing of particle production and distribution during a spring bloom in the North Atlantic

Abstract: The beam attenuation serves as a proxy for particulate matter and is a key parameter in visibility algorithms for the aquatic environment. It is well known, however, that the beam attenuation is a function of the acceptance angle of the transmissometer used to measure it. Here we compare eight different transmissometers with four different acceptance angles using four different deployment strategies and sites, and find that their mean attenuation values differ markedly and in a consistent way with instrument acceptance angle: smaller acceptance angles provide higher beam attenuation values. This difference is due to variations in scattered light collected with different acceptance angles and is neither constant nor easy to parameterize. Variability (in space or time) in the ratios of beam attenuations measured by two different instruments correlates, in most cases, with the particle size parameter (as expected from Mie theory), but this correlation is often weak and can be the opposite of expectations based on particle size changes. We recommended careful consideration of acceptance angle in applications of beam transmission data especially when comparing data from different instruments

Biophysical forcing of particle production and distribution during a spring bloom in the North Atlantic

Abstract: The beam attenuation serves as a proxy for particulate matter and is a key parameter in visibility algorithms for the aquatic environment. It is well known, however, that the beam attenuation is a function of the acceptance angle of the transmissometer used to measure it. Here we compare eight different transmissometers with four different acceptance angles using four different deployment strategies and sites, and find that their mean attenuation values differ markedly and in a consistent way with instrument acceptance angle: smaller acceptance angles provide higher beam attenuation values. This difference is due to variations in scattered light collected with different acceptance angles and is neither constant nor easy to parameterize. Variability (in space or time) in the ratios of beam attenuations measured by two different instruments correlates, in most cases, with the particle size parameter (as expected from Mie theory), but this correlation is often weak and can be the opposite of expectations based on particle size changes. We recommended careful consideration of acceptance angle in applications of beam transmission data especially when comparing data from different instruments