Wave Turbulence
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2022 ◽  
Vol 933 ◽  
Zhou Zhang ◽  
Yulin Pan

In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay and narrow-band and broad-band forcing) that we consider, we find that the spectral forms approach the wave turbulence theory (WTT) solution $S_\eta \sim k^{-5/2}$ and $S_\eta \sim P^{1/3}$ at high nonlinearity levels. With a decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. We investigate bound waves and the finite-size effect as possible mechanisms causing the spectral variations. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and the reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at a critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.

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’.

2021 ◽  
pp. 104981
Adil Jhangeer ◽  
Muhammad Muddassar ◽  
Jan Awrejcewicz ◽  
Zarmeena Naz ◽  
Muhammad Bilal Riaz

2021 ◽  
Vol 923 (1) ◽  
pp. 103
C. Krafft ◽  
A. S. Volokitin

Abstract Solar coronal and wind plasmas often contain density fluctuations of various scales and amplitudes. The scattering of Langmuir wave turbulence on these inhomogeneities modifies the properties of the radiated electromagnetic emissions traveling from the Sun to the Earth. This paper shows the similarities between the physical results obtained by (i) a model based on the Zakharov equations, describing the self-consistent dynamics of Langmuir wave turbulence spectra in a plasma with external density fluctuations, and (ii) a modeling, within the framework of geometric optics approximation, of quasi-particles (representing plasmon quanta) moving in a fluctuating potential. It is shown that the dynamics of the Langmuir spectra is governed by anomalous diffusion processes, as a result of multiple scattering of waves on the density fluctuations; the same dynamics are observed in the momenta distributions of quasi-particles moving in potential structures with random inhomogeneities. These spectra and distributions are both characterized by a fast broadening during which energy is transported to larger wavevectors and momenta, exhibiting nonlinear time dependence of the average squares of wavevectors and quasi-particle momenta as well as non-Gaussian tails in the asymptotic stage. The corresponding diffusion coefficients depend on the time and are proportional to the square of the average level of density (or potential) fluctuations. It appears that anomalous transport and superdiffusion phenomena are responsible for the spectral broadening.

2021 ◽  
Vol 9 (11) ◽  
pp. 1300
Troels Aagaard ◽  
Joost Brinkkemper ◽  
Drude F. Christensen ◽  
Michael G. Hughes ◽  
Gerben Ruessink

The existence of sandy beaches relies on the onshore transport of sand by waves during post-storm conditions. Most operational sediment transport models employ wave-averaged terms, and/or the instantaneous cross-shore velocity signal, but the models often fail in predictions of the onshore-directed transport rates. An important reason is that they rarely consider the phase relationships between wave orbital velocity and the suspended sediment concentration. This relationship depends on the intra-wave structure of the bed shear stress and hence on the timing and magnitude of turbulence production in the water column. This paper provides an up-to-date review of recent experimental advances on intra-wave turbulence characteristics, sediment mobilization, and suspended sediment transport in laboratory and natural surf zones. Experimental results generally show that peaks in the suspended sediment concentration are shifted forward on the wave phase with increasing turbulence levels and instantaneous near-bed sediment concentration scales with instantaneous turbulent kinetic energy. The magnitude and intra-wave phase of turbulence production and sediment concentration are shown to depend on wave (breaker) type, seabed configuration, and relative wave height, which opens up the possibility of more robust predictions of transport rates for different wave and beach conditions.

Jonathan Skipp ◽  
Sergey Nazarenko

Abstract We study the thermodynamic equilibrium spectra of the Charney- Hasegawa-Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross-Pitaevskii equations, which are examples for comparison. We explore how the third invariant considerably enriches the variety of equilibrium spectra that the CHM system can access. In particular we characterise the singular limits of these spectra in which condensates occur, i.e. a single Fourier mode (or pair of modes) accumulate(s) a macroscopic fraction of the total invariants. We show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in CHM systems of finite size: highly anisotropic zonal flows, large-scale isotropic vortices, and vortices at small scale. We show how these condensates are associated with combinations of negative thermodynamic potentials (e.g. temperature).

Simon Thalabard ◽  
Sergey Medvedev ◽  
Vladimir Grebenev ◽  
Sergey Nazarenko

Abstract We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

S. A Matthews ◽  
H. A. S. Reid ◽  
D. Baker ◽  
D. S. Bloomfield ◽  
P. K. Browning ◽  

AbstractAs a frequent and energetic particle accelerator, our Sun provides us with an excellent astrophysical laboratory for understanding the fundamental process of particle acceleration. The exploitation of radiative diagnostics from electrons has shown that acceleration operates on sub-second time scales in a complex magnetic environment, where direct electric fields, wave turbulence, and shock waves all must contribute, although precise details are severely lacking. Ions were assumed to be accelerated in a similar manner to electrons, but γ-ray imaging confirmed that emission sources are spatially separated from X-ray sources, suggesting distinctly different acceleration mechanisms. Current X-ray and γ-ray spectroscopy provides only a basic understanding of accelerated particle spectra and the total energy budgets are therefore poorly constrained. Additionally, the recent detection of relativistic ion signatures lasting many hours, without an electron counterpart, is an enigma. We propose a single platform to directly measure the physical conditions present in the energy release sites and the environment in which the particles propagate and deposit their energy. To address this fundamental issue, we set out a suite of dedicated instruments that will probe both electrons and ions simultaneously to observe; high (seconds) temporal resolution photon spectra (4 keV – 150 MeV) with simultaneous imaging (1 keV – 30 MeV), polarization measurements (5–1000 keV) and high spatial and temporal resolution imaging spectroscopy in the UV/EUV/SXR (soft X-ray) regimes. These instruments will observe the broad range of radiative signatures produced in the solar atmosphere by accelerated particles.

Ningfei Chen ◽  
Shizhao Wei ◽  
Guangyu Wei ◽  
Zhiyong Qiu

Abstract The two-field equations governing fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived in the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed by both analytical and numerical approaches. In the linear growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability (PDI), accounting for the spontaneous resonant excitation of GAM by DW. The main results of previous works on spontaneous GAM excitation, e.g., the much enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of DW. The soliton structures enhance turbulence spreading from DW linearly unstable to stable region, exhibiting convective propagation instead of typical linear dispersive process, and is thus, expected to induce core-edge interaction and nonlocal transport.

2021 ◽  
Vol 28 (10) ◽  
pp. 102304
M. Sasaki ◽  
H. Arakawa ◽  
T. Kobayashi ◽  
F. Kin ◽  
Y. Kawachi ◽  

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