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 context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived \emph{Sargassum} distributions.
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…
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…
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 …
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…
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 equa…
"Eddy saturation" is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic …
We analyze the distortion of wind-generated near-inertial waves by steady and unsteady barotropic quasi-geostrophic eddies, with a focus on the evolution of the horizontal wavevector $\boldsymbol{k}$ under the effects of mesoscale strain and refraction. The model is initialized with a horizontally-uniform ($\boldsymbol{k}=0$) surface-confined near-inertial wave which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Nearly monochromatic shear bands appear in the jet region as wave energy propagate downwards and t…
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）
A framework for the study of surface ocean inertial particle motion is built from the Maxey--Riley set. A new set is obtained by vertically averaging each term of the original set, adapted to account for Earth's rotation effects, across the extent of a sufficiently small spherical particle that floats at an assumed unperturbed air--sea interface with unsteady nonuniform winds and ocean currents above and below, respectively. The inertial particle velocity is shown to exponentially decay in time to a velocity that lies close to an average of seawater and air velocities, weighted by a function o…
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…
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…
We present results from an experiment designed to better understand the mechanism by which ocean currents and winds control flotsam drift. The experiment consisted in deploying in the Florida Current and subsequently satellite tracking specially designed drifting buoys of varied sizes, buoyancies, and shapes. We explain the differences in the trajectories described by the special drifters as a result of their inertia, primarily buoyancy, which constrains the ability of the drifters to adapt their velocities to instantaneous changes in the ocean current and wind that define the carrying flow fi…
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）
This study describes a specific type of critical layer for near-inertial waves (NIWs) that forms when isopycnals run parallel to sloping bathymetry. Upon entering this slantwise critical layer, the group velocity of the waves decreases to zero and the NIWs become trapped and amplified, which can enhance mixing. A realistic simulation of anticyclonic eddies on the Texas-Louisiana shelf reveals that such critical layers can form where the eddies impinge onto the sloping bottom. Velocity shear bands in the simulation indicate that wind-forced NIWs are radiated downward from the surface in the edd…
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…
The inertial subrange of turbulence in a density stratified environment is the transition from internal waves to isotropic turbulence, but it is unclear how to interpret its extension to anisotropic stratified turbulence. Knowledge about stratified turbulence is relevant for the dispersal of suspended matter in geophysical flows, such as in most of the ocean. For studying internal-wave-induced ocean-turbulence moored high-resolution temperature (T-)sensors are used. Spectra from observations on episodic quasi-convective internal wave breaking above a steep slope of large seamount Josephine in …
The role of mesoscale eddies in transporting Agulhas leakage is investigated using a recent technique from nonlinear dynamical systems theory applied on geostrophic currents inferred from the over two-decade-long satellite altimetry record. Eddies are found to acquire material coherence away from the Agulhas retroflection, near the Walvis Ridge in the South Atlantic. Yearly, 1 to 4 coherent material eddies are detected with diameters ranging from 40 to 280 km. A total of 23 eddy cores of about 50 km in diameter and with at least 30\pct of their contents traceable into the Indian Ocean were fou…
An idealized storm scenario is examined in which a wind-generated inertial wave interacts with a turbulent baroclinic quasi-geostrophic flow. The flow is initialized by spinning up a Eady model with a realistic stratification profile. The storm is modeled as an initial value problem for a mixed-layer confined, horizontally-uniform inertial oscillation. The primordial inertial oscillation then evolves under the effects of advection, refraction, dispersion and dissipation. Waves feedback onto the flow by modifying its potential vorticity. In the first few days, refraction dominates and wave ener…
Any type of non-buoyant material in the ocean is transported horizontally by currents during its sinking journey. This lateral transport can be far from negligible for small sinking velocities. To estimate its magnitude and direction, the material is often modelled as a set of Lagrangian particles advected by current velocities that are obtained from Ocean General Circulation Models (OGCMs). State-of-the-art OGCMs are strongly eddying, similar to the real ocean, providing results with a spatial resolution on the order of 10 km on a daily frequency. While the importance of eddies in OGCMs is we…
The output from an eddy-resolved multi-layered circulation model is used to analyze the vertical structure of simulated deep-sea eddies in the Japan Basin of the Japan/East Sea constrained by bottom topography. We focus on Lagrangian analysis of anticyclonic eddies, generated in the model in a typical year approximately at the place of the mooring and the hydrographic sections, where such eddies have been regularly observed in different years (1993--1997, 1999--2001). Using a quasi-3D computation of the finite-time Lyapunov exponents and displacements for a large number of synthetic tracers in…
Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the unresolved small scales of motion on the explicitly resolved large scale motions. Complimentary to this mainstream physics-based perspective, we propose to address this failure from the dynamical systems point of view, namely, as the persistent tendency of phase space trajectories representing the low-resolution solution to escape the right region of the correspond…
Drifters designed to mimic floating marine debris and small patches of pelagic \emph{Sargassum} were satellite tracked in four regions across the North Atlantic. Though subjected to the same initial conditions at each site, the tracks of different drifters quickly diverged after deployment. We explain the clustering of drifter types using a recent Maxey-Riley theory for surface ocean inertial particle dynamics applied on multidata-based mesoscale ocean currents and winds from reanalysis. Simulated trajectories of objects at the air-sea interface are significantly improved when represented as i…
The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales comparable to the wavelengths, we derive a transport (or kinetic) equation governing wave-energy transfers in both physical and spectral spaces. This equation describes the scattering of the waves by the flow which results in a redistribution of energy between waves with the same frequency (or, equivalently, with the same wavenumber) and, for isotropic flows, in the …
The three-dimensional transport pathways, the time scales of vertical transport, and the dispersion characteristics of submesoscale currents at an upper-ocean front are investigated using material points (tracer particles) that advect with the local fluid velocity. Coherent submesoscale vortex filaments and eddies which dominate submesoscale (0.1 - 10 km) dynamics are found to play a crucial role which is quantified here. These coherent structures are generated and sustained through nonlinear evolution of baroclinic instability. The collective motion of particles helps identify common features…
A one-year time series of moored high-resolution temperature T-sensor data from 1455 m depth on a 3900 m long line in about 5300 m of water in the NE-Atlantic Canary Basin are dominated by salinity (over-)compensated intrusions arising from the effects of Mediterranean outflow waters, which are commonly organized as Meddies. During the passage of a Meddy-core above the T-sensors, no intrusions were observed, thereby making it possible to use the temperature records to quantify turbulence parameters. The present data show that these ocean-interior turbulence estimates are from short-lived (less…
Inertial particles in stably stratified flows play a fundamental role in geophysics, from the dynamics of nutrients in the ocean to the dispersion of pollutants in the atmosphere. We consider the Maxey-Riley equation for small neutrally buoyant inertial particles in the Boussinesq approximation, and discuss its limits of validity. We show that particles behave as forced damped oscillators, with different regimes depending on the particles Stokes number and the fluid Brunt-Väisälä frequency. Using direct numerical simulations we study the particles dynamics and we show that small neutrally buoy…
Oceanic near-inertial waves - internal waves with frequencies close to the local Coriolis frequency $f_0$ - are strongly influenced by the presence of mean currents. To study this influence, Young and Ben Jelloul (1997) derived an asymptotic model that describes the slow modulation of the amplitude of these waves about their rapid oscillation at frequency $f_0$. Here we show that this model can be obtained within a variational framework, by (Whitham) averaging the Lagrangian of the hydrostatic-Boussinesq equations over the wave period $2π/f_0$. The derivation leads to a variational formulation…
Since the advent of satellite altimetry, our perception of the oceanic circulation has brought into focus the pervasiveness of mesoscale eddies that have typical scales of tens to hundreds of kilometers [5], are the ocean's analogue of weather systems, and are often thought of as the peak of the ocean's kinetic energy (KE) wavenumber spectrum [7, 19, 23]. Yet, our understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small representative regions (e.g. [16, 14, 4]), typically a few hundred kilometers in size, that cannot capture the vast dynamic range at p…
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer important physical parameters of inertial oscillations and other ocean processes. Nonstationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the datasets are large, we construct computationally efficient methods through the use of frequency-domain modelling and estimation, with the data expressed as…
In this paper we use the finite size Lyapunov Exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3d) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. Three-dimensional FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by numerical solution of the primitiv…
Inertial particles (i.e. with mass and of finite size) immersed in a fluid in motion are unable to adapt their velocities to the carrying flow and thus they have been the subject of much interest in fluid mechanics. In this paper we consider an ocean setting with inertial particles elastically connected forming a network that floats at the interface with the atmosphere. The network evolves according to a recently derived and validated Maxey--Riley equation for inertial particle motion in the ocean. We rigorously show that, under sufficiently calm wind conditions, rotationally coherent quasigeo…
