Abstract
Turbulence in geophysical flows tends to organize itself so that the mean flow remains close to a stability boundary in parameter space. That characteristic suggests self-organized criticality (SOC), a statistical property that has been identified in a range of complex phenomena including earthquakes, forest fires and solar flares. This note explores the relationship between the properties of forced, sheared, stratified turbulence (as found in oceans, atmospheres and other geophysical fluids) and those of SOC. Self-organization to the critical state is demonstrated in a wide range of cases drawn mostly (but not entirely) from in situ observations of ocean turbulence. Turbulent events in the ocean also exhibit a second characteristic associated with SOC: their sizes follow a power-law distribution indicating self-similarity. These results suggest SOC as a new conceptual foundation for the study of geophysical turbulence, an explanation for the mixing efficiency of ocean turbulence and a potential for cross-fertilization with other areas of geophysics.
Highlights
The appearance of turbulence when Ri drops below 1/4 is not instantaneous; the instability grows exponentially at a rate which becomes positive when Ri < 1/4 and continues to increase as Ri decreases further. This lack of sharpness in the boundary between turbulence growth and decay might lead to a significant difference in behavior between forced, stratified shear flows and canonical models of SOC
We have seen that forced, stratified shear flows, such as are found in the oceans and atmosphere, resemble SOC by virtue of the instability that sets in at a critical value of the gradient Richardson number. (This contrasts with Kolmogorov’s isotropic turbulence, which does not fit the SOC paradigm because the flow is not attracted to a critical state)
We have seen that probability density functions of turbulent overturn sizes approximate a power law, a second defining characteristic of SOC
Summary
Turbulence acts in turn to diffuse the shear and to redirect Ri back toward the critical value. This critical Ri is analogous to the angle of repose in the sandpile example[7,8]. We will review an accumulation of evidence suggesting that the tendency to maintain Ri near 1/4 is a generic property of forced, stratified, parallel shear flows on geophysical scales, and that the SOC paradigm is relevant. (SOC) is a critical state of a nonlinear energy dissipation system that is slowly and continuously driven towards a critical value of a system-wide instability threshold, producing scale-free, fractal-diffusive, and intermittent avalanches with powerlaw-like size distributions.”. We close by discussing characteristics of geophysical turbulence whose relationship to SOC is less clear
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