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

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

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

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

Mesoscale perturbations control inter-ocean exchange south of Africa

The quantification of inter-ocean leakage from the South Indian to the South Atlantic Ocean is an important measure for the role of the Agulhas system in the global thermohaline circulation. To explore the specific role of mesoscale variability (such as Agulhas rings and Mozambique eddies) in this process a high-resolution model (based on NEMO-ORCA) for the Agulhas region has been set up. It is nested into a global coarse-resolution model. The high-resolution nest captures all salient features of the greater Agulhas region, including the upstream perturbations of the Agulhas Current and Natal Pulses along the African coast. A comparison of the inter-ocean exchange in the high-resolution nest with its coarse resolution counterpart reveals that the latter significantly over-estimates the amount of water flowing into the Atlantic Ocean, demonstrating the need to explicitly simulate the mesoscale features. A sensitivity experiment that excludes the upstream perturbations revealed no difference in the amount of inter-ocean exchange. However, the realistic representation of Agulhas rings and their drift path into the South Atlantic depends on the simulation of those upstream perturbations

Variability and coherence of the Agulhas Undercurrent in a High-resolution Ocean General Circulation Model

The Agulhas Current system has been analyzed in a nested high-resolution ocean model and compared to observations. The model shows good performance in the western boundary current structure and the transports off the South African coast. This includes the simulation of the northward-flowing Agulhas Undercurrent. It is demonstrated that fluctuations of the Agulhas Current and Undercurrent around 50–70 days are due to Natal pulses and Mozambique eddies propagating downstream. A sensitivity experiment that excludes those upstream perturbations significantly reduces the variability as well as the mean transport of the undercurrent. Although the model simulates undercurrents in the Mozambique Channel and east of Madagascar, there is no direct connection between those and the Agulhas Undercurrent. Virtual float releases demonstrate that topography is effectively blocking the flow toward the north

Sea level variability in the Arctic Ocean from AOMIP models

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): C04S08, doi:10.1029/2006JC003916.Monthly sea levels from five Arctic Ocean Model Intercomparison Project (AOMIP) models are analyzed and validated against observations in the Arctic Ocean. The AOMIP models are able to simulate variability of sea level reasonably well, but several improvements are needed to reduce model errors. It is suggested that the models will improve if their domains have a minimum depth less than 10 m. It is also recommended to take into account forcing associated with atmospheric loading, fast ice, and volume water fluxes representing Bering Strait inflow and river runoff. Several aspects of sea level variability in the Arctic Ocean are investigated based on updated observed sea level time series. The observed rate of sea level rise corrected for the glacial isostatic adjustment at 9 stations in the Kara, Laptev, and East Siberian seas for 1954–2006 is estimated as 0.250 cm/yr. There is a well pronounced decadal variability in the observed sea level time series. The 5-year running mean sea level signal correlates well with the annual Arctic Oscillation (AO) index and the sea level atmospheric pressure (SLP) at coastal stations and the North Pole. For 1954–2000 all model results reflect this correlation very well, indicating that the long-term model forcing and model reaction to the forcing are correct. Consistent with the influences of AO-driven processes, the sea level in the Arctic Ocean dropped significantly after 1990 and increased after the circulation regime changed from cyclonic to anticyclonic in 1997. In contrast, from 2000 to 2006 the sea level rose despite the stabilization of the AO index at its lowest values after 2000.This research is supported by the National Science Foundation Office of Polar Programs (under cooperative agreements OPP- 0002239 and OPP- 0327664) with the International Arctic Research Center, University of Alaska Fairbanks, and by the Climate Change Prediction Program of the Department of Energy’s Office of Biological and Environmental Research. The development of the UW model is also supported by NASA grants NNG04GB03G and NNG04GH52G and NSF grants OPP-0240916 and OPP-0229429

The DOE E3SM Coupled Model Version 1: Overview and Evaluation at Standard Resolution

This work documents the first version of the U.S. Department of Energy (DOE) new Energy Exascale Earth System Model (E3SMv1). We focus on the standard resolution of the fully coupled physical model designed to address DOE mission-relevant water cycle questions. Its components include atmosphere and land (110-km grid spacing), ocean and sea ice (60 km in the midlatitudes and 30 km at the equator and poles), and river transport (55 km) models. This base configuration will also serve as a foundation for additional configurations exploring higher horizontal resolution as well as augmented capabilities in the form of biogeochemistry and cryosphere configurations. The performance of E3SMv1 is evaluated by means of a standard set of Coupled Model Intercomparison Project Phase 6 (CMIP6) Diagnosis, Evaluation, and Characterization of Klima simulations consisting of a long preindustrial control, historical simulations (ensembles of fully coupled and prescribed SSTs) as well as idealized CO2 forcing simulations. The model performs well overall with biases typical of other CMIP-class models, although the simulated Atlantic Meridional Overturning Circulation is weaker than many CMIP-class models. While the E3SMv1 historical ensemble captures the bulk of the observed warming between preindustrial (1850) and present day, the trajectory of the warming diverges from observations in the second half of the twentieth century with a period of delayed warming followed by an excessive warming trend. Using a two-layer energy balance model, we attribute this divergence to the model’s strong aerosol-related effective radiative forcing (ERFari+aci = -1.65 W/m2) and high equilibrium climate sensitivity (ECS = 5.3 K).Plain Language SummaryThe U.S. Department of Energy funded the development of a new state-of-the-art Earth system model for research and applications relevant to its mission. The Energy Exascale Earth System Model version 1 (E3SMv1) consists of five interacting components for the global atmosphere, land surface, ocean, sea ice, and rivers. Three of these components (ocean, sea ice, and river) are new and have not been coupled into an Earth system model previously. The atmosphere and land surface components were created by extending existing components part of the Community Earth System Model, Version 1. E3SMv1’s capabilities are demonstrated by performing a set of standardized simulation experiments described by the Coupled Model Intercomparison Project Phase 6 (CMIP6) Diagnosis, Evaluation, and Characterization of Klima protocol at standard horizontal spatial resolution of approximately 1° latitude and longitude. The model reproduces global and regional climate features well compared to observations. Simulated warming between 1850 and 2015 matches observations, but the model is too cold by about 0.5 °C between 1960 and 1990 and later warms at a rate greater than observed. A thermodynamic analysis of the model’s response to greenhouse gas and aerosol radiative affects may explain the reasons for the discrepancy.Key PointsThis work documents E3SMv1, the first version of the U.S. DOE Energy Exascale Earth System ModelThe performance of E3SMv1 is documented with a set of standard CMIP6 DECK and historical simulations comprising nearly 3,000 yearsE3SMv1 has a high equilibrium climate sensitivity (5.3 K) and strong aerosol-related effective radiative forcing (-1.65 W/m2)Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151288/1/jame20860_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151288/2/jame20860.pd

Irreversibility of the two-dimensional enstrophy cascade

We study the time irreversibility of the direct cascade in two-dimensional turbulence by looking at the time derivative of the square vorticity along Lagrangian trajectories, a quantity called metenstrophy. By means of extensive direct numerical simulations we measure the time irreversibility from the asymmetry of the probability density function of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what is found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what is observed for the energy cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility