scholarly journals On the Origins of the Oceanic Ultraviolet Catastrophe

2021 ◽  
Keyword(s):  
Diffusion Tensor ◽  
Internal Gravity Waves ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Energy Fluxes ◽  
Analytical Treatment ◽  
Turbulent Dissipation ◽  
Inverse Energy Cascade ◽  
The Status ◽  
Direct Energy

Abstract 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’.

scholarly journals Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

2017 ◽  
Vol 114 (9) ◽  
pp. 2119-2124 ◽  
Author(s):  
Jonasz Słomka ◽  
Jörn Dunkel
Keyword(s):  
Symmetry Breaking ◽  
Mirror Symmetry ◽  
Energy Transport ◽  
Fluid Model ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Scale Selection ◽  
Inverse Cascade ◽  
Inverse Energy Cascade ◽  
Self Organized

Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.

Energy Cascades and Loss of Balance in a Reentrant Channel Forced by Wind Stress and Buoyancy Fluxes

2015 ◽  
Vol 45 (1) ◽  
pp. 272-293 ◽  
Author(s):  
Roy Barkan ◽  
Kraig B. Winters ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Kinetic Energy ◽  
Wind Stress ◽  
General Circulation ◽  
Large Fraction ◽  
Energy Cascade ◽  
Turbulence Theory ◽  
Inverse Energy Cascade ◽  
Loss Of Balance ◽  
Small Scales ◽  
Eddy Field

AbstractA large fraction of the kinetic energy in the ocean is stored in the “quasigeostrophic” eddy field. This “balanced” eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a “deep convection” region, where it can be sustained by buoyancy loss.

Three-wave coupling and weak turbulence of kinetic Alfvén waves

1998 ◽  
Vol 60 (3) ◽  
pp. 515-527 ◽  
Author(s):  
Yu. M. VOITENKO
Keyword(s):  
Nonlinear Dynamics ◽  
Wave Interaction ◽  
Energy Cascade ◽  
Alfven Wave ◽  
Space Plasmas ◽  
Weak Turbulence ◽  
Kolmogorov Type ◽  
Inverse Energy Cascade ◽  
Direct Energy ◽  
Kinetic Alfvén Waves

The nonlinear dynamics of kinetic-Alfvén–wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propagating KAWs has a direct energy cascade in the wavenumber domain ks⊥>ρ−1i and an inverse cascade in the domain ks⊥<ρ−1i, resulting in Kolmogorov-type spectra, Wk∼(kz) −1/2(k⊥)−p, with exponents p=4 and p=3.5 respectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k⊥ range and p=2 (at k⊥<ρ−1i) and p=3.5 (for k⊥>ρ−1i) spectra. Three applications concerning KAW turbulence in flaring loops, in the Earth's magnetosphere and in tokamaks are considered. It is suggested that turbulent KAW spectra are common in space plasmas.

scholarly journals Ocean Eddy Energetics in the Spectral Space as Revealed by High-Resolution General Circulation Models

2019 ◽  
Vol 49 (11) ◽  
pp. 2815-2827
Author(s):  
Shengpeng Wang ◽  
Zhao Jing ◽  
Qiuying Zhang ◽  
Ping Chang ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Energy Conversion ◽  
General Circulation ◽  
Surface Wind ◽  
Circulation Model ◽  
General Circulation Models ◽  
Ocean General Circulation Model ◽  
Energy Cascade ◽  
Spectral Space ◽  
Inverse Energy Cascade ◽  
Barotropic Energy Conversion

AbstractIn this study, the global eddy kinetic energy (EKE) budget in horizontal wavenumber space is analyzed based on 1/10° ocean general circulation model simulations. In both the tropical and midlatitude regions, the barotropic energy conversion from background flow to eddies is positive throughout the wavenumber space and generally peaks at the scale (Le) where EKE reaches its maximum. The baroclinic energy conversion is more pronounced at midlatitudes. It exhibits a dipolar structure with positive and negative values at scales smaller and larger than Le, respectively. Surface wind power on geostrophic flow results in a significant EKE loss around Le but deposits energy at larger scales. The interior viscous dissipation and bottom drag inferred from the pressure flux convergence act as EKE sink terms. The latter is most efficient at Le while the former is more dominant at smaller scales. There is an evident mismatch between EKE generation and dissipation in the spectral space especially at the midlatitudes. This is reconciled by a dominant forward energy cascade on the equator and a dominant inverse energy cascade at the midlatitudes.

scholarly journals Inverse Energy Cascade in Advanced MHD Turbulence (the RNG Method)

1993 ◽  
Vol 157 ◽  
pp. 255-261
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Field Effect ◽  
Magnetic Reynolds Number ◽  
Energy Cascade ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
Inverse Energy Cascade ◽  
Large Scale Magnetic Field

The nonlinear (in terms of the large-scale magnetic field) effect of the modification of the magnetic force by an advanced small-scale magnetohydrodynamic (MHD) turbulence is considered. The phenomenon is due to the generation of magnetic fluctuations at the expense of hydrodynamic pulsations. It results in a decrease of the elasticity of the large-scale magnetic field.The renormalization group (RNG) method was employed for the investigation of the MHD turbulence at the large magnetic Reynolds number. It was found that the level of the magnetic fluctuations can exceed that obtained from the equipartition assumption due to the inverse energy cascade in advanced MHD turbulence.This effect can excite an instability of the large-scale magnetic field due to the energy transfer from the small-scale turbulent pulsations. This instability is an example of the inverse energy cascade in advanced MHD turbulence. It may act as a mechanism for the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies.

Infrared Reynolds number dependency of the two-dimensional inverse energy cascade

2011 ◽  
Vol 667 ◽  
pp. 463-473 ◽  
Author(s):  
ANDREAS VALLGREN
Keyword(s):  
Reynolds Number ◽  
Cascade Range ◽  
Energy Cascade ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Linear Friction ◽  
Non Local ◽  
Reynolds Number Dependency

High-resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number, Reα = kf/kα, where kf is the forcing wavenumber and kα is a frictional wavenumber based on linear friction. In the limit of high Reα, the classic k−5/3 scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit Reα → ∞ and Reν = kd/kf → ∞, where kd is the small-scale dissipation wavenumber, will lead to a steeper energy spectrum than k−5/3 in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by non-local triad interactions.

scholarly journals Inverse Energy Cascade in Forced Two-Dimensional Quantum Turbulence

2013 ◽  
Vol 110 (10) ◽  
Author(s):  
Matthew T. Reeves ◽  
Thomas P. Billam ◽  
Brian P. Anderson ◽  
Ashton S. Bradley
Keyword(s):  
Quantum Turbulence ◽  
Energy Cascade ◽  
Two Dimensional ◽  
Inverse Energy Cascade
Sign in / Sign up

Export Citation Format

Share Document