Dissipation scales and anomalous sinks in steady two-dimensional turbulence

In previous papers I have argued that the \emph{fusion rules hypothesis}, which was originally introduced by L'vov and Procaccia in the context of the problem of three-dimensional turbulence, can be used to gain a deeper insight in understanding the enstrophy cascade and inverse energy cascade of two-dimensional turbulence. In the present paper we show that the fusion rules hypothesis, combined with \emph{non-perturbative locality}, itself a consequence of the fusion rules hypothesis, dictates the location of the boundary separating the inertial range from the dissipation range. In so doing, the hypothesis that there may be an anomalous enstrophy sink at small scales and an anomalous energy sink at large scales emerges as a consequence of the fusion rules hypothesis. More broadly, we illustrate the significance of viewing inertial ranges as multi-dimensional regions where the fully unfused generalized structure functions of the velocity field are self-similar, by considering, in this paper, the simplified projection of such regions in a two-dimensional space, involving a small scale $r$ and a large scale $R$, which we call, in this paper, the $(r, R)$-plane. We see, for example, that the logarithmic correction in the enstrophy cascade, under standard molecular dissipation, plays an essential role in inflating the inertial range in the $(r, R)$ plane to ensure the possibility of local interactions. We have also seen that increasingly higher orders of hyperdiffusion at large scales or hypodiffusion at small scales make the predicted sink anomalies more resilient to possible violations of the fusion rules hypothesis.Comment: 22 pages, resubmitted to Phys. Rev.

Locality and stability of the cascades of two-dimensional turbulence

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L'vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of non-perturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade. For the enstrophy cascade, statistical stability requires large-scale dissipation and a vanishing downscale energy dissipation. A careful discussion of the subtle notion of locality is given at the end of the paper.Comment: v2: 23 pages; 4 figures; minor revisions; resubmitted to Phys. Rev.

Winterberg's conjectured breaking of the superluminal quantum correlations over large distances

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. Instead, we argue that Winterberg overestimated the intensity of the ZPF turbulent fluctuations. We calculate a very generous corrected lower bound for the transition distance which is consistent with current experiments.Comment: 7 pages, submitted to Int. J. Theor. Phy

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for Warwick Turbulence Symposium Workshop on Universal features in turbulence: from quantum to cosmological scales, 200

Sparse-Representation-Based Classification with Structure-Preserving Dimension Reduction

Sparse-representation-based classification (SRC), which classifies data based on the sparse reconstruction error, has been a new technique in pattern recognition. However, the computation cost for sparse coding is heavy in real applications. In this paper, various dimension reduction methods are studied in the context of SRC to improve classification accuracy as well as reduce computational cost. A feature extraction method, i.e., principal component analysis, and feature selection methods, i.e., Laplacian score and Pearson correlation coefficient, are applied to the data preparation step to preserve the structure of data in the lower-dimensional space. Classification performance of SRC with structure-preserving dimension reduction (SRC-SPDR) is compared to classical classifiers such as k-nearest neighbors and support vector machines. Experimental tests with the UCI and face data sets demonstrate that SRC-SPDR is effective with relatively low computation cost © 2014 Springer Science+Business Media New York

Horizontal transport, mixing and retention in a large, shallow estuary: Río de la Plata

© 2014, Springer Science+Business Media Dordrecht. We use field data and a high-resolution three-dimensional (3D) hydrodynamic numerical model to investigate the horizontal transport and dispersion characteristics in the upper reaches of the shallow Río de la Plata estuary, located between the Argentinean and Uruguayan coasts, with the objective of relating the mixing characteristics to the likelihood of algal bloom formation. The 3D hydrodynamic model was validated with an extensive field experiment including both, synoptic profiling and in situ data, and then used to quantify the geographic variability of the local residence time and rate of dispersion. We show that during a high inflow regime, the aquatic environment near the Uruguayan coast, stretching almost to the middle of the estuary, had short residence time and horizontal dispersion coefficient of around 77 (formula presented.), compared to the conditions along the Argentinean coastal regime where the residence time was much longer and the dispersion coefficient (40 (formula pr esented.)) much smaller, making the Argentinian coastal margin more susceptible for algae blooms

Toward Consistent Subgrid Momentum Closures in Ocean Models

State-of-the-art global ocean circulation models used in climate studies are only passing the edge of becoming “eddy-permitting” or barely eddy-resolving. Such models commonly suffer from overdissipation of mesoscale eddies by routinely used subgrid dissipation (viscosity) operators and a resulting depletion of energy in the large-scale structures which are crucial for draining available potential energy into kinetic energy. More broadly, subgrid momentum closures may lead to both overdissipation or pileup of eddy kinetic energy and enstrophy of the smallest resolvable scales. The aim of this chapter is twofold. First, it reviews the theory of two-dimensional and geostrophic turbulence. To a large part, this is textbook material with particular emphasis, however, on issues relevant to modeling the global ocean in the eddy- permitting regime. Second, we discuss several recent parameterizations of subgrid dynamics, including simplified backscatter schemes by Jansen and Held, stochastic superparameterizations by Grooms and Majda, and an empirical backscatter scheme by Mana and Zanna