Field theory of the inverse cascade in two-dimensional turbulence

A two-dimensional fluid, stirred at high wavenumbers and damped by both viscosity and linear friction, is modeled by a statistical field theory. The fluid's long-distance behavior is studied using renormalization-group (RG) methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732 (1977)]. With friction, which dissipates energy at low wavenumbers, one expects a stationary inverse energy cascade for strong enough stirring. While such developed turbulence is beyond the quantitative reach of perturbation theory, a combination of exact and perturbative results suggests a coherent picture of the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is derived from a generalized time-reversal symmetry and implies zero anomalous dimension for the velocity even when friction is present. Thus the Kolmogorov scaling of the inverse cascade cannot be explained by any RG fixed point. The beta function for the dimensionless coupling ghat is computed through two loops; the ghat^3 term is positive, as already known, but the ghat^5 term is negative. An ideal cascade requires a linear beta function for large ghat, consistent with a Pad\'e approximant to the Borel transform. The conjecture that the Kolmogorov spectrum arises from an RG flow through large ghat is compatible with other results, but the accurate k^{-5/3} scaling is not explained and the Kolmogorov constant is not estimated. The lack of scale invariance should produce intermittency in high-order structure functions, as observed in some but not all numerical simulations of the inverse cascade. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade--in agreement with simulations.Comment: 16 pages, 3 figures, REVTeX 4. Material added on energy flux, intermittency, and comparison with Burgers equatio

The Fidelity of Ocean Models With Explicit Eddies (Chapter 17)

Current practices within the oceanographic community have been reviewed with regard to the use of metrics to assess the realism of the upper-ocean circulation, ventilation processes diagnosed by time-evolving mixed layer depth and mode water formation, and eddy heat fluxes in large-scale fine resolution ocean model simulations. We have striven to understand the fidelity of these simulations in the context of their potential use in future fine-resolution coupled climate system studies. A variety of methodologies are used to assess the veracity of the numerical simulations. Sea surface height variability and the location of western boundary current paths from altimetry have been used routinely as basic indicators of fine-resolution model performance. Drifters and floats have also been used to provide pseudo-Eulerian measures of the mean and variability of surface and sub-surface flows, while statistical comparisons of observed and simulated means have been carried out using James tests. Probability density functions have been used to assess the Gaussian nature of the observed and simulated flows. Length and time scales have been calculated in both Eulerian and Lagrangian frameworks from altimetry and drifters, respectively. Concise measures of multiple model performance have been obtained from Taylor diagrams. The time-evolution of the mixed layer depth at monitoring stations has been compared with simulated time series. Finally, eddy heat fluxes are compared to climatological inferences

Closure of two dimensional turbulence: the role of pressure gradients

Inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be compatible with a recently proposed self-consistent Gaussian model. An analogous low order closure model for the longitudinal pressure gradient is proposed and its validity is numerically examined. In this case numerical evidence for the presence of higher order terms in the closure is found. The fundamental role of conditional statistics between longitudinal and transverse components is highlighted.Comment: 4 pages, 2 figures, in press on PR

Forcing-dependent dynamics and emergence of helicity in rotating turbulence

The effects of large-scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of direct numerical simulations, systematically varying the nature of the mechanical force in time. We find that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relative to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We demonstrate that the nature of the mechanical force in time and the emergence of helicity have direct implications for the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak turbulence

Basin scale assessment of gas hydrate dissociation in response to climate change

Paleooceanographic evidence has been used to postulate that methane from oceanic hydrates may have had a significant role in regulating climate. However, the behavior of contemporary oceanic methane hydrate deposits subjected to rapid temperature changes, like those now occurring in the arctic and those predicted under future climate change scenarios, has only recently been investigated. Field investigations have discovered substantial methane gas plumes exiting the seafloor along the Arctic Ocean margin, and the plumes appear at depths corresponding to the upper limit of a receding gas hydrate stability zone. It has been suggested that these plumes may be the first visible signs of the dissociation of shallow hydrate deposits due to ongoing climate change in the arctic. We simulate the release of methane from oceanic deposits, including the effects of fully-coupled heat transfer, fluid flow, hydrate dissociation, and other thermodynamic processes, for systems representative of segments of the Arctic Ocean margins. The modeling encompasses a range of shallow hydrate deposits from the landward limit of the hydrate stability zone down to water depths beyond the expected range of century-scale temperature changes. We impose temperature changes corresponding to predicted rates of climate change-related ocean warming and examine the possibility of hydrate dissociation and the release of methane. The assessment is performed at local-, regional-, and basin-scales. The simulation results are consistent with the hypothesis that dissociating shallow hydrates alone can result in significant methane fluxes at the seafloor. However, the methane release is likely to be confined to a narrow region of high dissociation susceptibility, defined by depth and temperature, and that any release will be continuous and controlled, rather than explosive. This modeling also establishes the first realistic bounds for methane release along the arctic continental shelf for potential hydrate dissociation scenarios, and ongoing work may help confirm whether climate change is already impacting the stability of the vast oceanic hydrate reservoir

Subtropical mode water variability in a climatologically forced model in the northwestern Pacific Ocean

Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 42 (2012): 126–140, doi:10.1175/2011JPO4513.1.A climatologically forced high-resolution model is used to examine variability of subtropical mode water (STMW) in the northwestern Pacific Ocean. Despite the use of annually repeating atmospheric forcing, significant interannual to decadal variability is evident in the volume, temperature, and age of STMW formed in the region. This long time-scale variability is intrinsic to the ocean. The formation and characteristics of STMW are comparable to those observed in nature. STMW is found to be cooler, denser, and shallower in the east than in the west, but time variations in these properties are generally correlated across the full water mass. Formation is found to occur south of the Kuroshio Extension, and after formation STMW is advected westward, as shown by the transport streamfunction. The ideal age and chlorofluorocarbon tracers are used to analyze the life cycle of STMW. Over the full model run, the average age of STMW is found to be 4.1 yr, but there is strong geographical variation in this, from an average age of 3.0 yr in the east to 4.9 yr in the west. This is further evidence that STMW is formed in the east and travels to the west. This is qualitatively confirmed through simulated dye experiments known as transit-time distributions. Changes in STMW formation are correlated with a large meander in the path of the Kuroshio south of Japan. In the model, the large meander inhibits STMW formation just south of Japan, but the export of water with low potential vorticity leads to formation of STMW in the east and an overall increase in volume. This is correlated with an increase in the outcrop area of STMW. Mixed layer depth, on the other hand, is found to be uncorrelated with the volume of STMW.E.M.D. acknowledges support of the Doherty Foundation and National Science Foundation (OCE-0849808). S.R.J was sponsored by the National Science Foundation (OCE-0849808). Participation of S.P. and F.B. was supported by the National Science Foundation by its sponsorship of the National Center for Atmospheric Research.2012-07-0

Eddy‐driven sediment transport in the Argentine Basin: Is the height of the Zapiola Rise hydrodynamically controlled?

In this study, we address the question whether eddy‐driven transports in the Argentine Basin can be held responsible for enhanced sediment accumulation over the Zapiola Rise, hence accounting for the existence and growth of this sediment drift. To address this question, we perform a 6 year simulation with a strongly eddying ocean model. We release two passive tracers, with settling velocities that are consistent with silt and clay size particles. Our experiments show contrasting behavior between the silt fraction and the lighter clay. Due to its larger settling velocity, the silt fraction reaches a quasisteady state within a few years, with abyssal sedimentation rates that match net input. In contrast, clay settles only slowly, and its distribution is heavily stratified, being transported mainly along isopycnals. Yet, both size classes display a significant and persistent concentration minimum over the Zapiola Rise. We show that the Zapiola Anticyclone, a strong eddy‐driven vortex that circulates around the Zapiola Rise, is a barrier to sediment transport, and hence prevents significant accumulation of sediments on the Rise. We conclude that sediment transport by the turbulent circulation in the Argentine Basin alone cannot account for the preferred sediment accumulation over the Rise. We speculate that resuspension is a critical process in the formation and maintenance of the Zapiola Rise

Vorticity statistics in the two-dimensional enstrophy cascade

We report the first extensive experimental observation of the two-dimensional enstrophy cascade, along with the determination of the high order vorticity statistics. The energy spectra we obtain are remarkably close to the Kraichnan Batchelor expectation. The distributions of the vorticity increments, in the inertial range, deviate only little from gaussianity and the corresponding structure functions exponents are indistinguishable from zero. It is thus shown that there is no sizeable small scale intermittency in the enstrophy cascade, in agreement with recent theoretical analyses.Comment: 5 pages, 7 Figure