The multifractal theory of turbulence is used to investigate the energy cascade in the Northwestern Atlantic ocean. The statistics of singularity exponents of velocity gradients computed from in situ measurements are used to show that the anomalous scaling of the velocity structure functions at depths between 50 ad 500 m has a linear dependence on the exponent characterizing the strongest velocity gradient, with a slope that decreases with depth. Since the distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade, the log-Poisson model, to derive the functional dependence of the anomalous scaling with dissipation. Using this model we can interpret the vertical change of the linear slope as a change in the energy cascade.
Horizontal currents in the Bay of Bengal were measured on eight cruises covering a total of 8600 $km$ using a 300 $kHz$ Acoustic Doppler Current Profiler (ADCP). The cruises are distributed over multiple seasons and regions of the Bay. Horizontal wavenumber spectra of these currents over depths of 12--54 m and wavelengths from 2--400 km were decomposed into vortical and divergent components assuming isotropy. An average of across and along track spectra over all cruises shows that the spectral slope of horizontal kinetic energy for wavelengths of 10--80 $km$ scales with an exponent of $-1.7 \p…
The global ocean overturning circulation, critically dependent on the global density stratification, plays a central role in regulating climate evolution. While it is well-known that the global stratification profile exhibits a strong dependence to Southern Ocean dynamics and in particular to wind and buoyancy forcing, we demonstrate here that the stratification is also acutely sensitive to the mesoscale eddy energy dissipation time-scale. Within the context of a global ocean circulation model with an energy constrained mesoscale eddy parameterization, it is shown that modest variations in the…
Sutherland and Melville (2015a) investigated the relative contributions to the total dissipation rate in the ocean surface wave boundary layer of different breaking wave scales, from large-scale whitecaps to micro-breakers. Based on their measurements of geometric/kinematic properties of breaking waves for a wide range of wave ages, they inferred the dissipation rates from breaking as a function of scale. These results were compared with their complementary measurements of the total dissipation rate in the underlying wave boundary layer. They reported that the total depth-integrated dissipatio…
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In realistic oceanic sea states, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss th…
We calculate the rate of ocean waves energy dissipation due to whitecapping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve the $3D$ Hamiltonian equation that includes three- and four-wave interactions. This model is valid for moderate values of surface steepness only, $μ< 0.09$. Then we solve the exact Euler equation for non-stationary potential flow of an ideal fluid with a free surface in $2D$ geometry. We use the conformal mapping of domain filled with fluid onto the lower hal…
Due to the nonlinear interaction between different flow patterns, for instance, ocean current, meso-scale eddies, waves, etc, the movement of ocean is extremely complex, where a multiscale statistics is then relevant. In this work, a high time-resolution velocity with a time step 15 minutes obtained by the Lagrangian drifter deployed in the Gulf of Mexico (GoM) from July 2012 to October 2012 is considered. The measured Lagrangian velocity correlation function shows a strong daily cycle due to the diurnal tidal cycle. The estimated Fourier power spectrum $E(f)$ implies a dual-power-law behavior…
We present an approximate deconvolution (AD) large eddy simulation (LES) model for the two-layer quasigeostrophic equations. We applied the AD-LES model to mid-latitude two-layer square oceanic basins, which are standard prototypes of more realistic stratified ocean dynamics models. Two spatial filters were investigated in the AD-LES model: a tridiagonal filter and an elliptic differential filter. A sensitivity analysis of the AD-LES results with respect to changes in modeling parameters was performed. The results demonstrate that the AD-LES model used in conjunction with the tridiagonal or di…
Motivated by oceanographic observational datasets, we propose a probabilistic neural network (PNN) model for calculating turbulent energy dissipation rates from vertical columns of velocity and density gradients in density stratified turbulent flows. We train and test the model on high-resolution simulations of decaying turbulence designed to emulate geophysical conditions similar to those found in the ocean. The PNN model outperforms a baseline theoretical model widely used to compute dissipation rates from oceanographic observations of vertical shear, being more robust in capturing the tails…
Ocean turbulence dissipation rate is estimated either by means of microstructure shear measurements, or by adiabatically reordering vertical profiles of density. The latter technique leads to the estimate of the Thorpe scale, which in turn can be used to obtain average turbulence dissipation rate by comparing the Thorpe scale to the Ozmidov scale. In both cases, the turbulence dissipation rate can be estimated using single vertical profiles from shipborne instrumentation. We present here an alternative method to estimate the length scale of overturns by using the Ellison length scale. The Elli…
Could tidal dissipation within Enceladus' subsurface ocean account for the observed heat flow? Earthlike models of dynamical tides give no definitive answer because they neglect the influence of the crust. I propose here the first model of dissipative tides in a subsurface ocean, by combining the Laplace Tidal Equations with the membrane approach. For the first time, it is possible to compute tidal dissipation rates within the crust, ocean, and mantle in one go. I show that oceanic dissipation is strongly reduced by the crustal constraint, and thus contributes little to Enceladus' present heat…
A model-data inversion is applied to a very large observational dataset collected in the Southern Ocean north of the Ross Sea during late autumn to early winter, producing estimates of the frequency-dependent rate of dissipation by sea ice. The modeling platform is WAVEWATCH III(R) which accounts for non-stationarity, advection, wave generation, and other relevant processes. The resulting 9477 dissipation profiles are co-located with other variables such as ice thickness to quantify correlations which might be exploited in later studies to improve predictions. Mean dissipation profiles from th…
New parameterizations for the spectra dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observation of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is non-zero only when a non-dimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short wave dissipation due to…
Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to estimate the dissipation of swell energy for a number of storms. Swells can be very persistent with energy e-folding scales exceeding 20,000 km. For increasing swell steepness this scale shrinks systematically, down to 2800 km for the steepest observed swells, revealing a significant loss of swell energy. This value corresponds to a normalized energy decay in time ß = 4.2 x 10-6 s -1 . Many processes may be responsible for this dissipation. Because no particular trend is found with wind magnitude and …
Lee waves generated by stratified flow over rough bottom topography in the ocean extract momentum and energy from the geostrophic flow, causing drag and enhancing turbulence and mixing in the interior ocean when they break. Inviscid linear theory is generally used to predict the generation rate of lee waves, but the location and mechanism of wave breaking leading to eventual dissipation of energy and irreversible mixing are poorly constrained. In this study, a linear model with viscosity, diffusivity, and an upper boundary is used to demonstrate the potential importance of the surface in refle…
Turbulent and internal wave motions are important for the exchange of momentum, heat and suspended matter in the deep-sea which is generally stably stratified in density. Turbulence-generation models involve shear of vertical current differences that deforms the stratified waters, and convection that is drive by (unstable) buoyancy. Shear-generation is found more general in the well-stratified ocean-interior, while convection is known to occur near the sea-surface, e.g. via nighttime cooling. Far below the surface, the Western-Mediterranean Sea is very weakly stratified and offers opportunity …
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…
The Ocean's turbulent energy cycle has a paradox; large-scale eddies under the control of Earth's rotation primarily transfer kinetic energy (KE) to larger scales via an inverse cascade, while a transfer to smaller scales is needed to accomplish dissipation. It has been argued, using numerical simulations, that fronts, waves and other turbulent structures can produce a forward cascade of KE toward dissipation scales. However, this forward cascade and its coexistence with known inverse cascade were not confirmed in observations. Here we present the first evidence of a dual KE cascade in the Oce…
The dynamic and thermal regimes of climate are regulated by an exchange of energy and momentum between the atmosphere and the ocean. The role exerted by surface waves on this interchange is particularly enigmatic. Waves induce turbulence in the upper ocean by breaking and through Langmuir circulations. However, waves can directly inject energy into subsurface layers. This relates to waves not being truly irrotational and therefore the induced orbital motion being turbulent. The existence, extent and properties of this turbulent oscillatory flow still remain uncertain. Here we present measureme…
Wave attenuation by ice floes is an important parameter for modelling the Arctic Oceans. At present, attenuation coefficients are extracted from linear models as a function of the incident wave period and floe thickness. Recent explorations in the Antarctic Mixed Ice Zone (MIZ) revealed a further dependence on wave amplitude, suggesting that nonlinear contributions are non-negligible. An experimental model for wave attenuation by a single ice floe in a wave flume is here presented. Observations are compared with linear predictions based on wave scattering. Results indicate that linear models p…
Satellite Synthetic Aperture Radar (SAR) observations can provide a global view of ocean swell fields when using a specific "wave mode" sampling. A methodology is presented to routinely derive integral properties of the longer wavelength (swell) portion of the wave spectrum from SAR Level 2 products, and both monitor and predict their evolution across ocean basins. SAR-derived estimates of swell height, and energy-weighted peak period and direction, are validated against buoy observations, and the peak directions are used to project the peak periods in one dimension along the corresponding gre…
Recent research shows that the surface wave energy dissipation, which is the vertical energy flux across the air-sea interface, can be calculated as the product of air density, reference wind speed cubed and an energy transfer coefficient determined by the dimensionless parameters made of wind speed, significant wave height and dominant wave period. In a similar way, the horizontal wave energy flux of wind generated waves can be represented by the same dimensionless wind and wave parameters. Satellite altimeters routinely report reference wind speed and significant wave height. An algorithm to…
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…
A key issue in stratified turbulence theory concerns the nature of the link between D(APE), the dissipation rate of available potential energy APE, and W_{r,turbulent}, the turbulent rate of change of background gravitational potential energy GPE_r, which are both controlled by molecular diffusion. For Boussinesq fluids with a linear equation of state, this link is simply W_{r,turbulent}=D(APE), widely interpreted as implying that GPE_r increases at the expense of APE, in contrast with the laminar case where GPE_r increases at the expense of internal energy (IE). This idea is revisited here by…
Understanding the statistics of ocean geostrophic turbulence is of utmost importance in understanding its interactions with the global ocean circulation and the climate system as a whole. Here, a study of eddy-mixing entropy in a forced-dissipative barotropic ocean model is presented. Entropy is a concept of fundamental importance in statistical physics and information theory; motivated by equilibrium statistical mechanics theories of ideal geophysical fluids, we consider the effect of forcing and dissipation on eddy-mixing entropy, both analytically and numerically. By diagnosing the time evo…
Energy dissipation rates are an important characteristic of turbulence; however, their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data obtained from oceanic turbulence measurements, we demonstrate that the vertical sequences of energy dissipation rates exhibit a scaling property. Utilising this property, we propose a method to estimate the population mean for a profile. For scaling in the observed profiles, we demonstrate that our data exhibit a statistical property consistent with that exhib…
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）
We study the development of mean structures in a nonlinear model of large scale ocean dynamics with bottom topography and dissipation, and forced with a noise term. We show that the presence of noise in this nonlinear model leads to persistent average currents directed along isobaths. At variance with previous works we use a scale unselective dissipation, so that the phenomenon can not be explained in terms of minimum enstrophy states. The effect requires the presence of both the nonlinear and the random terms, and can be though of as an ordering of the stochastic energy input by the combined …
