On rectification of randomly forced flows

Author Posting. © Sears Foundation for Marine Research, 2005. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 63 (2005): 497-527, doi:10.1357/0022240054307894.Nonlinear rectification of the ocean circulation driven by random forcing, which simulates the effect of unresolved eddies, is studied in an idealized closed basin. The results are based on the analysis of randomly forced solutions and linear eigenmodes. Depending on the forcing strength, two rectification regimes are found: zonal jets and isolated gyres. It is shown that both regimes are due to nonlinear interactions of resonant basin modes. In the zonal-jet regime, these interactions involve complex interplay between resonant baroclinic modes and some secondary modes. Both Rhines' scaling for zonal jets and prediction of gyres based on the maximum entropy argument are not confirmed

Random-forcing model of the mesoscale oceanic eddies

Author Posting. © Cambridge University Press, 2005. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 529 (2005): 71-95, doi:10.1017/S0022112005003393.The role of mesoscale oceanic eddies in driving large-scale currents is studied in an eddy-resolving midlatitude double-gyre ocean model. The reference solution is decomposed into large-scale and eddy components in a way which is dynamically consistent with a non-eddy-resolving ocean model. That is, the non-eddy-resolving solution driven by this eddy-forcing history, calculated on the basis of this decomposition, correctly approximates the original flow. The main effect of the eddy forcing on the large-scale flow is to enhance the eastward-jet extension of the subtropical western boundary current. This is an anti-diffusive process, which cannot be represented in terms of turbulent diffusion. It is shown that the eddy-forcing history can be approximated as a space–time correlated, random-forcing process in such a way that the non-eddy-resolving solution correctly approximates the reference solution. Thus, the random-forcing model can potentially replace the diffusion model, which is commonly used to parameterize eddy effects on the large-scale currents. The eddy-forcing statistics are treated as spatially inhomogeneous but stationary, and the dynamical roles of space–time correlations and spatial inhomogeneities are systematically explored. The integral correlation time, oscillations of the space correlations, and inhomogeneity of the variance are found to be particularly important for the flow response.Funding for this research was provided by NSF grants OCE 0091836 and OCE 03-44094, by the Royal Society Fellowship, and by WHOI grants 27100056 and 52990035

A hyper-parameterization method for comprehensive ocean models: Advection of the image point

Idealized and comprehensive ocean models at low resolutions cannot reproduce nominally-resolved flow structures similar to those presented in the high-resolution solution. Although there are various underlying physical reasons for this, from the dynamical system point of view all these reasons manifest themselves as a low-resolution trajectory avoiding the phase space occupied by the reference solution (the high-resolution solution projected onto the coarse grid). In order to solve this problem, a set of hyper-parameterization methods has recently been proposed and successfully tested on idealized ocean models. In this work, for the first time we apply one of hyper-parameterization methods (Advection of the image point) to a comprehensive, rather than idealized, general circulation model of the North Atlantic. The results show that the hyper-parameterization method significantly improves a non-eddy-resolving solution towards the reference eddy-resolving solution by reproducing both the large- and small-scale features of the Gulf Stream flow. The proposed method is much faster than even a single run of the coarse-grid ocean model, requires no modification of the model, and is easy to implement. Moreover, the method can take not only the reference solution as input data but also real measurements from different sources (drifters, weather stations, etc.), or combination of both. All this offers a great flexibility to ocean modellers working with mathematical models and/or measurements

The dynamics of an equivalent-barotropic model of the wind-driven circulation

Various steady and time-dependent regimes of a quasi-geostrophic 1.5 layer model of an oceanic circulation driven by a steady wind stress are studied. After being discretized as a numerical model, the quasi-geostrophic equations of motion become a dynamical system with a large dimensional phase space. We find that, for a wide range of parameters, the large-time asymptotic regimes of the model correspond to low-dimensional attractors in this phase space. Motion on these attractors is significant in determining the intrinsic time scales of the system. In two sets of experiments, we explore the dependence of solutions on the viscosity coefficient and the deformation radius. Both experiments yielded a succession of solutions with different forms of time dependence including chaotic solutions. The transition to chaos in this model occurs through a modified classical Ruelle-Takens scenario. We computed some unstable steady regimes of the circulation and the associated fastest growing linear eigenmodes. The structure of the eigenmodes and the details of the energy conversion terms allow us to characterize the primary instability of the steady circulation. It is a complex instability of the western boundary intensification, the western gyre and the meander between the western and central gyres. The model exhibits ranges of parameters in which multiple, stable, time-dependent solutions exist. Further, we note that some bifurcations involve the appearance of variability at climatological time scales, purely as a result of the intrinsic dynamics of the wind-driven circulation

Submesoscale generation by boundaries

An important dynamical question involves how oceanic balanced flows lose energy. Recent numerical and analytical studies suggest topography catalyzes energy exchanges between balanced flows and a variety of unbalanced phenomena, which presumably leads to dissipation. We here develop a general theory of inviscid balanced flow interactions with walls that predicts submesoscale and unbalanced flow generation. Comparison with primitive equation-based numerical experiments supports the basic tenets of the theory

A Framework for Parameterizing Eddy Potential Vorticity Fluxes

A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed. © 2012 American Meteorological Society

Properties and origins of the anisotropic eddy-induced transport in the North Atlantic

Author Posting. © American Meteorological Society, 2015. 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 45 (2015): 778–791, doi:10.1175/JPO-D-14-0164.1.This study examines anisotropic transport properties of the eddying North Atlantic flow, using an idealized model of the double-gyre oceanic circulation and altimetry-derived velocities. The material transport by the time-dependent flow (quantified by the eddy diffusivity tensor) varies geographically and is anisotropic, that is, it has a well-defined direction of the maximum transport. One component of the time-dependent flow, zonally elongated large-scale transients, is particularly important for the anisotropy, as it corresponds to primarily zonal material transport and long correlation time scales. The importance of these large-scale zonal transients in the material distribution is further confirmed with simulations of idealized color dye tracers, which has implications for parameterizations of the eddy transport in non-eddy-resolving models.IK would like to acknowledge support through the NSF Grant OCE-1154923. IR was supported by the NSF OCE-1154641 and NASA Grant NNX14AH29G.2015-09-0

Kelvin wave hydraulic control induced by interactions between vortices and topography

The interaction of a dipolar vortex with topography is examined using a combination of analytical solutions and idealized numerical models. It is shown that an anticyclonic vortex may generate along-topography flow with sufficient speeds to excite hydraulic control with respect to local Kelvin waves. A critical condition for Kelvin wave hydraulic control is found for the simplest case of a 1.5-layer shallow water model. It is proposed that in the continuously stratified case this mechanism may allow an interaction between low mode vortices and higher mode Kelvin waves, thereby generating rapidly converging isopycnals and hydraulic jumps. Thus, Kelvin wave hydraulic control may contribute to the flux of energy from mesoscale to smaller, unbalanced, scales of motion in the ocean

The effects of mesoscale ocean–atmosphere coupling on the large-scale ocean circulation

Author Posting. © American Meteorological Society, 2009. 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 Climate 22 (2009): 4066–4082, doi:10.1175/2009JCLI2629.1.Small-scale variation in wind stress due to ocean–atmosphere interaction within the atmospheric boundary layer alters the temporal and spatial scale of Ekman pumping driving the double-gyre circulation of the ocean. A high-resolution quasigeostrophic (QG) ocean model, coupled to a dynamic atmospheric mixed layer, is used to demonstrate that, despite the small spatial scale of the Ekman-pumping anomalies, this phenomenon significantly modifies the large-scale ocean circulation. The primary effect is to decrease the strength of the nonlinear component of the gyre circulation by approximately 30%–40%. This result is due to the highest transient Ekman-pumping anomalies destabilizing the flow in a dynamically sensitive region close to the western boundary current separation. The instability of the jet produces a flux of potential vorticity between the two gyres that acts to weaken both gyres.AH and WD were supported by an ARC Linkage International Grant (LX0668781). WD was also supported by NSF Grants OCE 0424227 and OCE 0550139. Funding for PB was provided by NSF Grants OCE 0344094 and OCE 0725796 and by the research grant from the Newton Trust of the University of Cambridge. SK was supported by U.S. DOE Grant DE-FG02–02ER63413 and NASA Grant NNG-06- AG66G-1

On dynamically consistent eddy fluxes

Author Posting. © The Author, 2004. This is the author's version of the work. It is posted here by permission of Elsevier B. V. for personal use, not for redistribution. The definitive version was published in Dynamics of Atmospheres and Oceans 38 (2005): 123-146, doi:10.1016/j.dynatmoce.2004.11.003.The role of mesoscale oceanic eddies in driving the large-scale currents is studied in an eddy-resolving, double-gyre ocean model. The new diagnostic method is proposed, which is based on dynamical decomposition of the flow into the large-scale and eddy components. The method yields the time history of the eddy forcing, which can be used as additional, external forcing in the corresponding non-eddy-resolving model of the gyres. The main strength of this approach is in its dynamical consistency: the non-eddy-resolving solution driven by the eddy forcing history correctly approximates the original large-scale flow component. It is shown that statistical decompositions, which are based on space-time filtering diagnostics, are dynamically inconsistent. The diagnostics algorithm is formulated and tested, and the diagnosed eddies are analysed, both statistically and dynamically. It is argued that the main dynamic role of the eddies is to maintain the eastward-jet extension of the subtropical western boundary current (WBC). This is done largely by both the time–mean isopycnal-thickness flux and the relative-vorticity eddy flux fluctuations. The fluctuations drive large-scale flow through the nonlinear rectification mechanism. The relative-vorticity flux contributes mostly to the eastward jet meandering. Finally, eddy fluxes driven by both the eddies and the large-scale flow are found to be important. The latter is typically neglected in the analysis, but here it corresponds to important large-scale feedback on the eddies.Funding for this research was provided by NSF grant OCE 00–91836, by the Royal Society Fellowship, and by WHOI grants 27100056 and 52990035