Bottom-trapped currents as statistical equilibrium states above topographic anomalies

Oceanic geostrophic turbulence is mostly forced at the surface, yet strong bottom-trapped flows are commonly observed along topographic anomalies. Here we consider the case of a freely evolving, initially surface-intensified velocity field above a topographic bump, and show that the self-organization into a bottom-trapped current can result from its turbulent dynamics. Using equilibrium statistical mechanics, we explain this phenomenon as the most probable outcome of turbulent stirring. We compute explicitly a class of solutions characterized by a linear relation between potential vorticity and streamfunction, and predict when the bottom intensification is expected. Using direct numerical simulations, we provide an illustration of this phenomenon that agrees qualitatively with theory, although the ergodicity hypothesis is not strictly fulfilled

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

Towards the Use of POP in a Global Coupled Navy Prediction System

LONG-TERM GOALS: Development of a global high resolution coupled atmosphere/ocean/ice model that assimilates data providing initial conditions from which forecasts are performed. Additionally, very high-resolution regional air/ocean coupled models will be nested into the global system at key strategic locations.Award Number: N0001401WR2015

The ACPI Project, Element 1: Initializing a Coupled Climate Model from Observed Conditions

A problem for climate change studies with coupled ocean-atmosphere models has been how to incorporate observed initial conditions into the ocean, which holds most of the ‘memory’ of anthropogenic forcing effects. The first difficulty is the lack of comprehensive three-dimensional observations of the current ocean temperature (T) and salinity (S) fields to initialize to. The second problem is that directly imposing observed T and S fields into the model results in rapid drift back to the model climatology, with the corresponding loss of the observed information. Anthropogenic forcing scenarios therefore typically initialize future runs by starting with pre-industrial conditions. However, if the future climate depends on the details of the present climate, then initializing the model to observations may provide more accurate forecasts. Also, this ∼130 yr spin up imposes substantial overhead if only a few decades of predictions are desired. A new technique to address these problems is presented. In lieu of observed T and S, assimilated ocean data were used. To reduce model drift, an anomaly coupling scheme was devised. This consists of letting the model’s climatological (pre-industrial) oceanic and atmospheric heat contents and transports balance each other, while adding on the (much smaller) changes in heat content since the pre-industrial era as anomalies. The result is model drift of no more than 0.2 K over 50 years, significantly smaller than the forced response of 1.0 K. An ensemble of runs with these assimilated initial conditions is then compared to a set spun up from pre-industrial conditions. No systematic differences were found, i.e., the model simulation of the ocean temperature structure in the late 1990s is statistically indistinguishable from the assimilated observations. However, a model with a worse representation of the late 20th century climate might show significant differences if initialized in this way.This work was supported by the Department of Energy under grant DE-FG03– 98ER62505

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

Turbulent small-scale dynamo action in solar surface simulations

We demonstrate that a magneto-convection simulation incorporating essential physical processes governing solar surface convection exhibits turbulent small-scale dynamo action. By presenting a derivation of the energy balance equation and transfer functions for compressible magnetohydrodynamics (MHD), we quantify the source of magnetic energy on a scale-by-scale basis. We rule out the two alternative mechanisms for the generation of small-scale magnetic field in the simulations: the tangling of magnetic field lines associated with the turbulent cascade and Alfvenization of small-scale velocity fluctuations ("turbulent induction"). Instead, we find the dominant source of small-scale magnetic energy is stretching by inertial-range fluid motions of small-scale magnetic field lines against the magnetic tension force to produce (against Ohmic dissipation) more small-scale magnetic field. The scales involved become smaller with increasing Reynolds number, which identifies the dynamo as a small-scale turbulent dynamo.Comment: accepted by Ap

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

Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations

A parameterization for the restratification by finite-amplitude, submesoscale, mixed layer eddies, formulated as an overturning streamfunction, has been recently proposed to approximate eddy fluxes of density and other tracers. Here, the technicalities of implementing the parameterization in the coarse-resolution ocean component of global climate models are made explicit, and the primary impacts on model solutions of implementing the parameterization are discussed. Three global ocean general circulation models including this parameterization are contrasted with control simulations lacking the parameterization. The MLE parameterization behaves as expected and fairly consistently in models differing in discretization, boundary layer mixing, resolution, and other parameterizations. The primary impact of the parameterization is a shoaling of the mixed layer, with the largest effect in polar winter regions. Secondary impacts include strengthening the Atlantic meridional overturning while reducing its variability, reducing CFC and tracer ventilation, modest changes to sea surface temperature and air–sea fluxes, and an apparent reduction of sea ice basal melting.National Science Foundation (U.S.) (Grant OCE-0612143)National Science Foundation (U.S.) (Grant OCE-0612059)National Science Foundation (U.S.) (Grant OCE-0825376)National Science Foundation (U.S.) (Grant DMS-0855010)National Science Foundation (U.S.) (Grant OCE-0934737

Atmospheric predictability: revisiting the inherent finite-time barrier

The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier-Stokes (N-S) equations suggest that one can skilfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work re-examines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than -3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved – which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than -3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled

Logarithmic Correlation Functions in Two Dimensional Turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the persence of three dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory $c_{8,1}$ describes the 2D- turbulence both in the absence and the presence of the perturbation. We obtain the following energy spectrum $E(k) \sim k^{-5.125 } \ln(k )$ for perturbed 2D - turbulence and $E(k) \sim k^{-5 } \ln(k )$ for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.Comment: 14 pages ,latex , no figure