On the Origins of the Oceanic Ultraviolet Catastrophe

We provide a first-principles analysis of the energy fluxes in the oceanic internal wavefield. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber – frequency (m – w) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a ‘local’ and a ‘scale-separated’ contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed ‘no-flux’ solutions are reinstated to the status of ‘constant-downscale-flux’ solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of ‘Oceanic Ultraviolet Catastrophe’.

Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves

Faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. Some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (Couder et al. (2005); Saylor and Kinard (2005)). Moreover, recent studies discovered the existence of a horizontal velocity field at the fluid surface, called Faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von Kameke et al., 2011, 2013; Francois et al., 2013). Additionally, three-dimensionality effects have been part of recent investigations in quasi-2D flows (both electromagnetically-driven (Kelley and Ouellette, 2011; Martell et al., 2019) or produced by parametrically-excited waves (Francois et al., 2014; Xia and Francois, 2017)). Furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2D and 3D turbulence (Biferale et al., 2012; Kokot et al., 2017; Biferale et al., 2017). By performing 2D PIV measurements at horizontal planes beneath the Faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (Colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the Faraday wavelength λF). This in turn reveals that an inverse energy cascade and aspects of a confined 2D turbulence can coexist with a three dimensional bulk flow. In this work, 2D PIV measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in Faraday waves. The results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. Furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one Faraday wavelength) below the fluid surface.

The Seasonal Variability of the Ocean Energy Cycle From a Quasi-Geostrophic Double Gyre Ensemble

With the advent of submesoscale O(1km) permitting basin-scale ocean simulations, the seasonality in the mesoscale O(50km) eddies with kinetic energies peaking in summer has been commonly attributed to submesoscale eddies feeding back onto the mesoscale via an inverse energy cascade under the constraint of stratification and Earth’s rotation. In contrast, by running a 101-member, seasonally forced, three-layer quasi-geostrophic (QG) ensemble configured to represent an idealized double-gyre system of the subtropical and subpolar basin, we find that the mesoscale kinetic energy shows a seasonality consistent with the summer peak without resolving the submesoscales; by definition, a QG model only resolves small Rossby number dynamics (O(Ro)≪1) while as submesoscale dynamics are associated with O(Ro)∼1. Here, by quantifying the Lorenz cycle of the mean and eddy energy, defined as the ensemble mean and fluctuations about the mean respectively, we propose a different mechanism from the inverse energy cascade by which the stabilization and strengthening of the western-boundary current during summer due to increased stratification leads to a shedding of stronger mesoscale eddies from the separated jet. Conversely, the opposite occurs during the winter; the separated jet destablizes and results in overall lower mean and eddy kinetic energies despite the domain being more susceptible to baroclinic instability from weaker stratification.

The Seasonal Variability of the Ocean Energy Cycle From a Quasi-Geostrophic Double Gyre Ensemble

With the advent of submesoscale O(1km) permitting basin-scale ocean simulations, the seasonality in the mesoscale O(50km) eddies with kinetic energies peaking in summer has been commonly attributed to submesoscale eddies feeding back onto the mesoscale via an inverse energy cascade under the constraint of stratification and Earth’s rotation. In contrast, by running a 101-member, seasonally forced, three-layer quasi-geostrophic (QG) ensemble configured to represent an idealized double-gyre system of the subtropical and subpolar basin, we find that the mesoscale kinetic energy shows a seasonality consistent with the summer peak without resolving the submesoscales; by definition, a QG model only resolves small Rossby number dynamics (O(Ro)≪1) while as submesoscale dynamics are associated with O(Ro)∼1. Here, by quantifying the Lorenz cycle of the mean and eddy energy, defined as the ensemble mean and fluctuations about the mean respectively, we propose a different mechanism from the inverse energy cascade by which the stabilization and strengthening of the western-boundary current during summer due to increased stratification leads to a shedding of stronger mesoscale eddies from the separated jet. Conversely, the opposite occurs during the winter; the separated jet destablizes and results in overall lower mean and eddy kinetic energies despite the domain being more susceptible to baroclinic instability from weaker stratification.

Inverse energy cascade in ocean macroscopic turbulence: Energy transfer rate ε and Richardson-Obhukov constant g from an surface drifter experiment in the Benguela upwelling system

<p>We derive the energy transfer rate ε from the 3<sup>rd</sup> order relative (longitudinal)  velocity structure function <Δu<sub>l</sub><sup>3</sup>>=(3/2)εs from ocean surface drifter trajectories in the turbulent mixed layer of the Benguela upwelling region off the coast of Namibia.  Combination with the  mean squared pair separation<s<sup>2</sup>(t)> =gεt<sup>3 </sup>reveals the Richardson-Obhukov constant g≅0.5, which is remarkably close to the one measured in  controlled two-dimensional turbulent flows in laboratory. We verify the  two coupled  cascades of energy (upscale/inverse) and enstrophy (downwscale) by  the  theoretically predicted  slope 1  for <Δu<sub>l</sub><sup>3</sup>> for inertial scales (above the injection scale) and slope 2 for  the 2<sup>nd</sup> order structure function <Δu<sub>l</sub><sup>2</sup>> for non-local scales (below the injection scale) respectively. We detect  additional 'ballistic contributions' in the central regime of the corresponding probability distribution P(st) of relative separations s for fixed time t, leading to an additional  power law factor s<sup>-α</sup> with  α ≅ 5/3. The algebraic decay with 1<α <2 revives  to the relevance of Levy distributions in the stochastic description of the turbulent transport process in contrast to former claims. Our findings  of a positively skewed   probability distribution P(Δu<sub>l</sub>s) of relative longitudinal velocity Δu<sub>l</sub>  for inertial scales s renews the question of intermittency in the  inverse energy cascade.</p>

Field Evidence of Inverse Energy Cascades in the Surfzone

Low-frequency currents and eddies transport sediment, pathogens, larvae, and heat along the coast and between the shoreline and deeper water. Here, low-frequency currents (between 0.1 and 4.0 mHz) observed in shallow surfzone waters for 120 days during a wide range of wave conditions are compared with theories for generation by instabilities of alongshore currents, by ocean-wave-induced sea surface modulations, and by a nonlinear transfer of energy from breaking waves to low-frequency motions via a two-dimensional inverse energy cascade. For these data, the low-frequency currents are not strongly correlated with shear of the alongshore current, with the strength of the alongshore current, or with wave-group statistics. In contrast, on many occasions, the low-frequency currents are consistent with an inverse energy cascade from breaking waves. The energy of the low-frequency surfzone currents increases with the directional spread of the wave field, consistent with vorticity injection by short-crested breaking waves, and structure functions increase with spatial lags, consistent with a cascade of energy from few-meter-scale vortices to larger-scale motions. These results include the first field evidence for the inverse energy cascade in the surfzone and suggest that breaking waves and nonlinear energy transfers should be considered when estimating nearshore transport processes across and along the coast.

Inverse Energy Cascade of Fast Magnetosonic Turbulence in the Heliosheath

<p>The solar wind in the heliosheath beyond the termination shock (TS) is a non-equilibrium collisionless plasma consisting of thermal solar wind ions, suprathermal pickup ions (PUI) and electrons. In such multi-ion plasma, two fast magnetosonic wave modes exist: the low-frequency fast mode that propagates in the thermal ion component and the high-frequency fast mode that propagates in the suprathermal PUI component [<em>Zieger et al.</em>, 2015]. Both fast modes are dispersive on fluid and ion scales, which results in nonlinear dispersive shock waves. In this talk, we briefly review the theory of dispersive shock waves in multi-ion collisionless plasma. We present high-resolution three-fluid simulations of the TS and the heliosheath up to 2.2 AU downstream of the TS. We show that downstream propagating nonlinear magnetosonic waves grow until they steepen into shocklets (thin current sheets), overturn, and start to propagate backward in the frame of the downstream propagating wave, as predicted by theory <em>[McKenzie et al</em>., 1993; <em>Dubinin et al.</em>, 2006]. The counter-propagating nonlinear waves result in fast magnetosonic turbulence far downstream of the shock. Since the high-frequency fast mode is positive dispersive on fluid scale, energy is transferred from small scales to large scales (inverse energy cascade). Thermal solar wind ions are preferentially heated by the turbulence. Forward and reverse shocklets in the heliosheath can efficiently accelerate both ions and electrons to high energies through the shock drift acceleration mechanism. We validate our three-fluid simulations with in-situ high-resolution Voyager 2 magnetic field and plasma observations at the TS and in the heliosheath. Our simulations reproduce the magnetic turbulence spectrum with a spectral slope of -5/3 observed by Voyager 2 in frequency domain [<em>Fraternale et al</em>., 2019]. However, since Taylor’s hypothesis is not true for fast magnetosonic perturbations in the heliosheath, the inertial range of the turbulence spectrum is not a Kolmogorov spectrum in wave number domain. </p>