The framework of invariant parameterization is extended to higher-order closure schemes. We also define, for the first time, generalized invariant parameterization schemes, where symmetries of the corresponding original model are preserved as equivalence transformations of related classes of closed system of differential equations. As a particular problem, we consider invariant parameterization schemes for geostrophic eddies in a barotropic ocean. Here the initial model is the barotropic vorticity equation, which is equivalent to the system of incompressible inviscid two-dimensional Euler equations on a midlatitude beta-plane. The maximal Lie invariance algebra of this model is infinite-dimensional, and we intend to preserve it in the course of invariant parameterization, at least partially. The parameterizations proposed for the eddy vorticity flux and the energy flux are of order one and a half since we explicitly consider the equation for the turbulent kinetic energy in the closure models. These parameterizations are therefore the first examples of invariant higher-order closure schemes. Numerical experiments are carried out to assess the performance of these invariant schemes in studies of freely decaying two-dimensional turbulence, and it is verified that the invariant parameterization schemes give, on average, better results than the standard non-invariant closure models do.
The mid-depth ocean stratification was fitted by Munk (1966) to an exponential profile and shown to be consistent with a vertical advective-diffusive balance. However, tracer release experiments show that vertical diffusivity in the mid-depth ocean is an order of magnitude too small to explain the observed 1 km exponential scale. Alternative mechanisms suggested that the overturning is mostly adiabatic, that interior diapycnal upwelling is negligible, and that nearly all mid-depth water upwells adiabatically in the Southern Ocean (SO). In this picture, SO eddies and wind set isopycnal slopes i…
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow …
The accurate representation of geostrophic balance is an essential requirement for numerical modelling of geophysical flows. Significant effort is often put into the selection of accurate or optimal balance representation by the discretisation of the fundamental equations. The issue of accurate balance representation is particularly challenging when applying dynamic mesh adaptivity, where there is potential for additional imbalance injection when interpolating to new, optimised meshes. In the context of shallow-water modelling, we present a new method for preservation of geostrophic balance wh…
Consistent with satellite-tracked trajectories of drogued drifters, but at odds with Eulerian assessment of satellite-altimetry measurements of sea-surface height, we show that North Brazil Currents Rings (NBCRs) are incapable of bypassing the Lesser Antilles as structures that coherently transport material. The nature of the inability of the de-facto oceanographic Eulerian, streamline-based eddy detection technique to produce a correct assessment is rooted in its lack of objectivity. We arrive at this conclusion by applying \emph{geodesic eddy detection} on the altimetric dataset over nearly …
A single-layer, quasi-geostrophic (QG), large-scale ocean circulation model is developed in this paper to study available ocean current energy potentials harnessed by using the ocean current turbines. Power extraction is modeled by adding a parameterized Rayleigh friction term in the barotropic vorticity equation. Numerical assessments are performed by simulating a set of mid-latitude ocean basins in the beta plane, which are standard prototypes of more realistic ocean dynamics considering inter-decadal variability in turbulent equilibrium. A sensitivity analysis with respect to the turbine pa…
Atmospheric transient eddies and low-frequency flow contribution to the ocean surface wave climate in the North Atlantic during boreal winter is investigated (1980 - 2016). We conduct a set of numerical simulations with a state-of-the-art spectral wave model Wavewatch III forced by decomposed wind fields derived from the ERA-Interim reanalysis (0.7° horizontal resolution). Synoptic-scale processes (2-10 day bandpassed winds) are found to have the largest impact on the formation of wind waves in the western mid-latitude North Atlantic along the North American and western Greenland coasts. The e…
Sea surface height anomalies observed by satellites in 1993--2012 are combined with simulation and observations by surface drifters and Argo floats to study water flow pattern in the Near Strait (NS) connected the Pacific Ocean with the Bering Sea. Daily Lagrangian latitudinal maps, computed with the AVISO surface velocity field, and calculation of the transport across the strait show that the flow through the NS is highly variable and controlled by mesoscale and submesoscale eddies in the area. On the seasonal scale, the flux through the western part of the NR is negatively correlated with th…
We present the results of in-situ measurements of $^{134}$Cs and $^{137}$Cs released from the Fukushima Nuclear Power Plant (FNPP) collected at surface and different depths in the western North Pacific in June and July 2012. It was found that 15 month after the incident concentrations of radiocesium in the Japan and Okhotsk seas were at background or slightly increased level, while they had increased values in the subarctic front area east of Japan. The highest concentrations of $^{134}$Cs and $^{137}$Cs up to 13.5 ${\pm}$ 0.9 and 22.7 ${\pm}$ 1.5 Bq m$^{-3}$ have been found to exceed ten time…
An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30km resolution shallow water ocean model are optimised to have the same climatological mean and variance as that of a less viscous 7.5km resolution model. The 5 day lag-covariance is also optimised, leading to a more accurate estimate of the high resolution response to forcing using the low resolution model. The system considered is an idealised barotropic double gyre that is chaotic at both reso…
We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The model supports a steady parallel shear flow as a response to the wind stress. As the maximal velocity of the shear flow (equivalently the maximal amplitude of the wind forcing) exceeds a critical threshold, the zonal jet destabilizes due to baroclinic instability and we numerically demonstrate that a first transition occurs. We obtain reduced equations of the…
A physically plausible lower bound on the spatially varying geostrophic mesoscale eddy energy dissipation time-scale within the ocean, related to the geographical energy transfer rate out of the geostrophic mesoscales, is provided by means of a simple and computational inexpensive inverse calculation. Data diagnosed from a high resolution global configuration ocean simulation is supplied to a parameterized model of the geostrophic mesoscale eddy energy, from which the dissipation time-scale results as a solution to an optimization calculation. We find that the dissipation time-scale is shortes…
Generative data assimilation highlights fronts as key regulators of ocean energy cascade
University of Washington（华盛顿大学）；California Institute of Technology（加州理工学院）；ENS, PSL Université, Ecole Polytechnique, Sorbonne Université, CNRS（法国高等师范学院、巴黎文理研究大学、巴黎综合理工学院、索邦大学、法国国家科学研究中心）
Enhanced Gulf Stream Path Variability Under Intensified Stratification
Université Grenoble Alpes, CNRS, INRAE, IRD, Grenoble-INP, Institut des Géosciences de l’Environnement（格勒诺布尔阿尔卑斯大学）；Sorbonne Universite, CNRS, Institut Jean Le Rond d’Alembert（索邦大学）；ENS de Lyon, CNRS, Laboratoire de Physique (UMR CNRS 5672)（里昂高等师范学院）
The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumb…
Calibration of a neural network ocean closure for improved mean state and variability
Courant Institute School of Mathematics, Computing, and Data Science, New York University, New York, NY, USA（科朗学院数学、计算与数据科学学院，纽约大学，纽约，纽约州，美国）；Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA（大气与海洋科学项目，普林斯顿大学，普林斯顿，新泽西州，美国）
The mesoscale eddy field plays a key role in the mixing and transport of physical and biological properties and redistribute energy budgets in the ocean. Eddy kinetic energy is commonly defined as the kinetic energy of the time-varying component of the velocity field. However, this definition contains all processes that vary in time, including coherent mesoscale eddies, jets, waves, and large-scale motions. The focus of this paper is on the eddy kinetic energy contained in coherent mesoscale eddies. We present a new method to decompose eddy kinetic energy into oceanic processes. The proposed m…
In contrast with the behavior of the eddies in the open-ocean, the sub-mesoscale eddies generated in the constricted Ligurian Basin (NW Mediterranean), are unproductive but their combined effect, arranged in a rim-like fashion, contributes to the containment of a Productive Ligurian Pool (PLP). Data de- rived from MODIS satellite sensor showed persistent higher chlorophyll con- centrations in the centre of the basin, concurrent with high EKE values in its surroundings, derived from AVISO altimetry merged products. This sug- gested that this 'productive pool' is maintained by the intense (sub)m…
The predictability of the atmosphere at short and long time scales, associated with the coupling to the ocean, is explored in a new version of the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), based on a 2-layer quasi-geostrophic atmosphere and a 1-layer reduced-gravity quasi-geostrophic ocean. This version features a new ocean basin geometry with periodic boundary conditions in the zonal direction. The analysis presented in this paper considers a low-order version of the model with 40 dynamical variables. First the increase of surface friction (and the associated heat flux) with th…
Probability density functions and conditional averages of velocity gradients derived from upper ocean observations are compared with results from forced simulations of the two-dimensional Navier-Stokes equations. Ocean data are derived from TOPEX satellite altimeter measurements. The simulations use rapid forcing on large scales, characteristic of surface winds. The probability distributions of transverse velocity derivatives from the ocean observations agree with the forced simulations, though they differ from unforced simulations reported elsewhere. The distribution and cross-correlation of …
Buoyant, finite-size or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey-Riley equation. Derived from first principles - a result of over a century of research since the pioneering work by Sir George Stokes - the Maxey-Riley equation is a Newton-type-law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper we present an overview of recent efforts to port the…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；IMT Atlantique（大西洋矿业电信学校）；Institut Universitaire de France (IUF)（法国大学研究院）；ESIEA（法国高等计算机电子工程与自动化学校）；Sorbonne Université（索邦大学）；Institut Pierre Simon Laplace（皮埃尔-西蒙·拉普拉斯研究所）
Modeling the subgrid-scale dynamics of reduced models is a long standing open problem that finds application in ocean, atmosphere and climate predictions where direct numerical simulation (DNS) is impossible. While neural networks (NNs) have already been applied to a range of three-dimensional flows with success, two dimensional flows are more challenging because of the backscatter of energy from small to large scales. We show that learning a model jointly with the dynamical solver and a meaningful \textit{a posteriori}-based loss function lead to stable and realistic simulations when applied …
Adjoint-based online learning of two-layer quasi-geostrophic baroclinic turbulence
Hong Kong University of Science and Technology（香港科技大学）；Institut de Physique du Globe de Paris（巴黎地球物理研究所）；Université Grenoble-Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；National Oceanography Centre, Southampton（南安普顿国家海洋中心）；Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）
This paper describes a reduced-order quasi-geostrophic coupled ocean-atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows one to easily modify the model physics. Using this new model, coined the "Modular Arbitrary-Order Ocean-Atmosphere Model" (MAOOAM), we analyse the dependence of the model dynamics on the truncation level of the spectral expansion, and unveil spurious behaviour that may exist at low resolution by a comparison with the higher-resolution configurations. In par…
In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with a geostrophically balanced turbulent flow. Advection and refraction by this flow lead to wave scattering, redistributing IGW energy in the position--wavenumber phase space. We give a detailed description of this process by deriving a kinetic equation governing the evolution of the IGW phase-space energy density. The derivation relies on the smallness of the Rossby number characterising the geostrophic flow, which is treated as a random field with known statistics, and makes no as…
The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing Galerkin basis for projecting and reducing complex dynamical models. The POD basis used is the one obtained from the experimental data. We apply the procedure to analyze coherent structures in an oceanic setting, the ones arising from instabilities of the Algerian current, in the western Mediterranean S…
Multistabilities were found in the ocean-atmosphere flow, in a reduced order ocean-atmosphere coupled model, when the non-linear temperature equations were solved numerically. In this paper we explain how the full non-linear Stefan-Bolzmann law was numerically implemented, and the resulting change to the system dynamics compared to the original model where these terms were linearised. Multiple stable solutions were found that display distinct ocean-atmosphere flows, as well as different Lyapunov stability properties. In addition, distinct Low Frequency Variability (LFV) behaviour was observed …
The global stratification and circulation of the ocean and their sensitivities to changes in forcing depend crucially on the representation of the mesoscale eddy field. Here, a geometrically informed and energetically constrained parameterization framework for mesoscale eddies --- termed GEOMETRIC --- is proposed and implemented in three-dimensional primitive equation channel and sector models. The GEOMETRIC framework closes mesoscale eddy fluxes according to the standard Gent--McWilliams scheme, but with the eddy transfer coefficient constrained by the depth-integrated eddy energy field, prov…
