Spectral Energy Flux Research Articles

Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence

Using a recently developed filtering technique, we study the spatiotemporal properties of the scale-to-scale fluxes of energy and enstrophy in a weakly turbulent experimental quasi-two-dimensional flow. Although these spectral properties vary in time and space, we show that they persist along the Lagrangian trajectories of fluid elements for times that can be nearly as long as the correlation time of the velocity field itself. Additionally, we show that at small scales, the spectral energy flux persists longest for fluid elements in strongly hyperbolic regions of the flow, whereas at large scales it persists in strongly elliptic regions.

Double Cascade Turbulence and Richardson Dispersion in a Horizontal Fluid Flow Induced by Faraday Waves

We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles.

Potential biosignatures in super-Earth atmospheres

Atmospheric temperature and mixing ratio profiles of terres trial planets vary with the spectral energy flux distribution for di fferent types of M-dwarf stars and the planetary gravity. We investigate the resulting effects on the spectral appearance of molecular absorption bands, which are relevant as indicators for potential planetary habitability during primary and secondary eclipse for transiting terrestrial planets with Earth-like biomass emissi ons. Atmospheric profiles are computed using a plane-parallel, 1D climate model coupled with a chemistry model. We then calculate simulated spectra using a line-by-line radiative transfer model. We find that emission spectra during secondary eclipse show i ncreasing absorption of methane, water, and ozone for planets orbiting quiet M0-M3 dwarfs and the active M-type star AD Leo compared with solar-type central stars. However, for planets orbiting very cool and quiet M dwarfs (M4 to M7), increasing temperatures in the mid-atmosphere lead to reduced absorption signals, which impedes the detection of molecules in these scenarios. Transmission spectra during primary eclipse show strong absorption features of CH4, N2O and H2O for planets orbiting quiet M0-M7 stars and AD Leo. The N2O absorption of an Earth-sized planet orbiting a quiet M7 star can even be as strong as the CO2 signal. However, ozone absorption decreases for planets orbiting these cool central stars owing to chemical effects in the atmosphere. To investigate the effect on the spectroscopic detection of absorption bands with potential future satellite missions, we compute signal-to-noise-ratios (SNR) for a James Webb Space Telescope (JWST)-like aperture telescope.

SPECTRAL IRRADIANCE CALIBRATION IN THE INFRARED. XVII. ZERO-MAGNITUDE BROADBAND FLUX REFERENCE FOR VISIBLE-TO-INFRARED PHOTOMETRY

The absolutely calibrated infrared (IR) stellar spectra of standard stars described by Engelke et al. are being extended into the visible and will span a continuous wavelength range from ~0.35 μm to 35.0 μm. This paper, which is a continuation of the series on calibration initiated with Cohen et al., presents the foundation of this extension. We find that due to various irregularities Vega (α Lyr) is not suitable for its traditional role as the primary visible or near-infrared standard star. We therefore define a new zero-point flux that is independent of Vega and, as far as is feasible, uses measured spectral energy distributions (SEDs) and fluxes derived from photometry. The calibrated primary stars now underpinning this zero-point definition are 109 Vir in the visible and Sirius (α CMa) in the infrared. The resulting zero-point SED tests well against solar analog data presented by Rieke et al. while also maintaining an unambiguous link to specific calibration stars, thus providing a pragmatic range of options for any researcher wishing to tie it to a given set of photometry.

Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter

We investigate the scale-locality of subgrid-scale (SGS) energy flux and interband energy transfers defined by the sharp spectral filter. We show by rigorous bounds, physical arguments, and numerical simulations that the spectral SGS flux is dominated by local triadic interactions in an extended turbulent inertial range. Interband energy transfers are also shown to be dominated by local triads if the spectral bands have constant width on a logarithmic scale. We disprove in particular an alternative picture of “local transfer by nonlocal triads,” with the advecting wavenumber mode at the energy peak. Although such triads have the largest transfer rates of all individual wavenumber triads, we show rigorously that, due to their restricted number, they make an asymptotically negligible contribution to energy flux and log-banded energy transfers at high wavenumbers in the inertial range. We show that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain an energy cascade to small scales. Furthermore, nonlocal triads are argued to contribute even less to the space-average energy flux than is implied by our rigorous bounds, because of additional cancellations from scale-decorrelation effects. We can thus recover the −4/3 scaling of nonlocal contributions to spectral energy flux predicted by Kraichnan’s abridged Lagrangian-history direct-interaction approximation and test-field model closures. We support our results with numerical data from a 5123 pseudospectral simulation of isotropic turbulence with phase-shift dealiasing. We also discuss a rigorous counterexample of Eyink [Physica D 78, 222 (1994)], which showed that nonlocal wavenumber triads may dominate in the sharp spectral flux (but not in the SGS energy flux for graded filters). We show that this mathematical counterexample fails to satisfy reasonable physical requirements for a turbulent velocity field, which are employed in our proof of scale locality. We conclude that the sharp spectral filter has a firm theoretical basis for use in large-eddy simulation modeling of turbulent flows.

Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation

We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale forcing and large-scale damping. We employed several types of damping and dissipation mechanisms in simulations up to 20482resolution. For all these simulations we obtained a wavenumber range for which the mean spectral energy flux is a negative constant and the energy spectrum scales ask−5/3, consistent with the predictions of Kraichnan (Phys. Fluids, vol. 439, 1967, p. 1417). To gain further insight, we investigated the energy cascade in physical space, employing a local energy flux defined by smooth filtering. We found that the inverse energy cascade is scale local, but that the strongly local contribution vanishes identically, as argued by Kraichnan (J. Fluid Mech., vol. 47, 1971, p. 525). The mean flux across a length scale ℓ was shown to be due mainly to interactions with modes two to eight times smaller. A major part of our investigation was devoted to identifying the physical mechanism of the two-dimensional inverse energy cascade. One popular idea is that inverse energy cascade proceeds via merger of like-sign vortices. We made a quantitative study employing a precise topological criterion of merger events. Our statistical analysis showed that vortex mergers play a negligible direct role in producing mean inverse energy flux in our simulations. Instead, we obtained with the help of other works considerable evidence in favour of a ‘vortex thinning’ mechanism, according to which the large-scale strains do negative work against turbulent stress as they stretch out the isolines of small-scale vorticity. In particular, we studied a multi-scale gradient (MSG) expansion developed by Eyink (J. Fluid Mech., vol. 549, 2006a, p. 159) for the turbulent stress, whose contributions to inverse cascade can all be explained by ‘thinning’. The MSG expansion up to second order in space gradients was found to predict well the magnitude, spatial structure and scale distribution of the local energy flux. The majority of mean flux was found to be due to the relative rotation of strain matrices at different length scales, a first-order effect of ‘thinning’. The remainder arose from two second-order effects, differential strain rotation and vorticity gradient stretching. Our findings give strong support to vortex thinning as the fundamental mechanism of two-dimensional inverse energy cascade.

Mesoscale to Submesoscale Transition in the California Current System. Part III: Energy Balance and Flux

Abstract This is the last of a suite of three papers about the transition that occurs in numerical simulations for an idealized equilibrium, subtropical, eastern-boundary upwelling current system similar to the California Current. The transition is mainly explained by the emergence of ubiquitous submesoscale density fronts and ageostrophic circulations about them in the weakly stratified surface boundary layer. Here the high-resolution simulations are further analyzed from the perspective of the kinetic energy (KE) spectrum shape and spectral energy fluxes in the mesoscale-to-submesoscale range in the upper ocean. For wavenumbers greater than the mesoscale energy peak, there is a submesoscale power-law regime in the spectrum with an exponent close to −2. In the KE balance an important conversion from potential to kinetic energy takes place at all wavenumbers in both mesoscale and submesoscale ranges; this conversion is the energetic counterpart of the vertical restratification flux and frontogenesis discussed in the earlier papers. A significant forward cascade of KE occurs in the submesoscale range en route to dissipation at even smaller scales. This is contrary to the inverse energy cascade of geostrophic turbulence and it is, in fact, fundamentally associated with the horizontally divergent (i.e., ageostrophic) velocity component. The submesoscale dynamical processes of frontogenesis, frontal instability, and breakdown of diagnostic force balance are all essential elements of the energy cycle of potential energy conversion and forward KE cascade.

Resonant Behavior and Fluctuating Energy Storage in Coronal Loops

The energy balance at large scales in a coronal loop is investigated, using an analytical approach based on the reduced magnetohydrodynamic equations and a simplified model of the loop. The dynamics is regulated by two phenomena: the resonance excited by motions at the loop basis, which stores energy within the loop; and nonlinear couplings, which move energy toward smaller scales. The former phenomenon is studied using a linearized dissipative model; the properties of resonant modes are derived, and the input energy flux is found to be independent of dissipation. The spectral energy flux to small scales is calculated assuming local mode interactions and taking into account the space and time dependence of resonant modes. This flux is determined by interactions among fluctuations at the same order of resonance and the zero-frequency (DC) velocity fluctuation. The DC magnetic field fluctuations do not influence the spectral flux, although they dominate the large-scale fluctuations. An estimate for the velocity fluctuation in the loop is derived from the energy balance, finding an agreement with measures of nonthermal velocity in the solar corona. A peculiar form of the fluctuation spectrum is inferred, formed by an injection range at large scales, a preinertial range where magnetic energy dominates kinetic energy, an inertial range where the turbulence behaves as in an unbounded system, and a dissipative range. These analytical results are compared with those of a numerical model, finding a good agreement, and are discussed with respect to those of previous works.

Lateral Shifts in Near-Field Thermal Radiation with Surface Phonon Polaritons

It is well known that radiative heat transfer in the near field regime can be greatly enhanced because of photon tunneling, during which the classical radiation theory fails to predict the energy propagation direction. In the present article, we investigate the lateral shifts of energy pathways in near-field thermal radiation between two SiC plates separated by a vacuum gap. The energy streamline (ESL) method can be combined with fluctuational electrodynamics to trace the Poynting vector at a fixed parallel wavevector component β. The spectral energy flux exhibits nearly monochromatic enhancement with the excitation of surface phonon polaritons. In the spectral region important for radiative energy transfer, there exist considerable lateral shifts depending on the values of β. The range of β dominantly contributing to the spectral energy flux is identified for different wavelengths by examining the Poynting vector equation. With the use of ESLs, the effect of coupled surface polaritons on the lateral shift is also investigated. Furthermore, the lateral dimension for the SiC plates to be treated as infinitely extended is estimated based on the lateral shifts in the wavelength region that mostly contributes to the total energy flux.

An analysis of the energy transfer and the locality of nonlinear interactions in turbulence

Using the results of direct numerical simulations of isotropic turbulence, we compute detailed energy exchanges between different scales of motion and investigate how they contribute to the global quantities such as the energy transfer, the spectral energy flux, and the subgrid-scale dissipation. The scales of motion are defined by decomposing velocity fields using sharp spectral and smooth, tangent hyperbolic filters. The analysis of detailed interactions reveals that individual nonlocal contributions are large but significant cancellations lead to the global quantities asymptotically dominated by the local interactions. Implications of these results for turbulence modeling are discussed.

Cascade Inequalities for Forced–Dissipated Geostrophic Turbulence

AbstractAnalysis of spectral kinetic energy fluxes in satellite altimetry data has demonstrated that an inverse cascade of kinetic energy is ubiquitous in the ocean. In geostrophic turbulence models, a fully developed inverse cascade results in barotropic eddies with large horizontal scales. However, midocean eddies contain substantial energy in the baroclinic mode and in compact horizontal scales (scales comparable to the deformation radius Ld). This paper examines the possibility that relatively strong bottom friction prevents the oceanic cascade from becoming fully developed. The importance of the vertical structure of friction is demonstrated by contrasting numerical simulations of two-layer quasigeostrophic turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction with turbulence damped by vertically symmetric Ekman friction (equal decay rates in the two layers). “Cascade inequalities” derived from the energy and enstrophy equations are used to interpret the numerical results. In the symmetric system, the inequality formally requires a cascade to large-scale barotropic flow, independent of the stratification. The inequality is less strict when friction is in the bottom layer only, especially when stratification is surface intensified. Accordingly, model runs with surface-intensified stratification and relatively strong bottom friction retain substantial small-scale baroclinic energy. Altimetric data show that the symmetric inequality is violated in the low- and midlatitude ocean, again suggesting the potential impact of the “bottomness” of friction on eddies. Inequalities developed for multilayer turbulence suggest that high baroclinic modes in the mean shear also enhance small-scale baroclinic eddy energy. The inequalities motivate a new interpretation of barotropization in weakly damped turbulence. In that limit the barotropic mode dominates the spatial average of kinetic energy density because large values of barotropic density are found throughout the model domain, consistent with the barotropic cascade to large horizontal scales, while baroclinic density is spatially localized.

Spectral Energy Fluxes in Geostrophic Turbulence: Implications for Ocean Energetics

AbstractThe energy pathways in geostrophic turbulence are explored using a two-layer, flat-bottom, f-plane, quasigeostrophic model forced by an imposed, horizontally homogenous, baroclinically unstable mean flow and damped by bottom Ekman friction. A systematic presentation of the spectral energy fluxes, the mean flow forcing, and dissipation terms allows for a comprehensive understanding of the sources and sinks for baroclinic and barotropic energy as a function of length scale. The key new result is a robust inverse cascade of kinetic energy for both the baroclinic mode and the upper layer. This is consistent with recent observations of satellite altimeter data over the South Pacific Ocean. The well-known forward cascade of baroclinic potential and total energy was found to be very robust. Decomposing the spectral fluxes into contributions from different terms provided further insight. The inverse baroclinic kinetic energy cascade is driven mostly by an efficient interaction between the baroclinic velocity and the barotropic vorticity, the latter playing a crucial catalytic role. This cascade can be further enhanced by the baroclinic mode self-interaction, which is only present with nonuniform stratification (unequal layer depths). When model parameters are set such that modeled eddies compare favorably with observations, the inverse baroclinic kinetic energy cascade is actually much stronger than the well-known inverse cascade in the barotropic mode. The upper-layer kinetic energy cascade was found to dominate the lower-layer cascade over a wide range of parameters, suggesting that the surface cascade and time mean density stratification may be sufficient for estimating the depth-integrated cascade from ocean observations. This may find useful application in inferring the kinetic to gravitational potential energy conversion rate from satellite measurements.

Diagnosing the energy cascade in a model of the North Atlantic

Spectral potential and kinetic energy densities and fluxes in horizontal wavenumber space are estimated in an eddy‐resolving model of the North Atlantic. In agreement to recent observational results near surface kinetic energy fluxes are negative over wide regions of the North Atlantic, indicative of an inverse energy cascade. This inverse kinetic energy cascade is found over a wide depth range but both the spectral kinetic energy density and the corresponding flux show no clear dependency on Rossby radius or Rhines scale. Potential energy fluxes tend to be positive and show a direct potential energy cascade towards a scale which is related to the Rossby radius in the subtropical North Atlantic.

Template-Based Estimation of Time-Varying Tempo

We present a novel approach to automatic estimation of tempo over time. This method aims at detecting tempo at the tactus level for percussive and nonpercussive audio. The front-end of our system is based on a proposed reassigned spectral energy flux for the detection of musical events. The dominant periodicities of this flux are estimated by a proposed combination of discrete Fourier transform and frequency-mapped autocorrelation function. The most likely meter, beat, and tatum over time are then estimated jointly using proposed meter/beat subdivision templates and a Viterbi decoding algorithm. The performances of our system have been evaluated on four different test sets among which three were used during the ISMIR 2004 tempo induction contest. The performances obtained are close to the best results of this contest.

Multiwavelength Observations of the Extreme X-Ray-selected BL Lacertae Object PG 1553+11 (1ES 1553+113)

PG 1553+11 was the target of a coordinated 3 week multiwavelength campaign during 2003 April and May. A significant X-ray flare was observed during the second half of this campaign. Although no optical flare was recorded during the X-ray campaign, optical observations obtained immediately prior to the campaign displayed a flux higher than that recorded during the campaign. An optical flare was observed a few days after the end of the X-ray campaign and may be related to the X-ray flare. Radio observations were made at three frequencies, with no significant changes in flux detected near the times of the optical and X-ray flares. The spectral energy distributions and flux ratios in different wave bands observed for this object are compared to other X-ray-selected blazars to demonstrate that PG 1553+11 is an extreme member of this group.

Radiative energy flux of diffusive supersonic wave in a cylinder

The calculation of radiative energy flux is very important in the study of diffusive supersonic wave transfer when the radiative thermal conduction approximation is used. In this paper, a formula of radial position-dependent spectral energy flux is given for the diffusive supersonic wave in a low density filled cylinder with a high density wall. A geometrical factor is defined to describe the influence of the radial size of the cylinder on the radiative energy flux. From the formula, the geometrical factor decreases with the radial position from center to edge, due to the much shorter mean free path in the wall than in the fill. This is another important reason in causing a significant curvature in the radiation front, which was observed in recent diffusive supersonic wave experiments. In addition, expressions for calculating the averaged spectral energy flux over the cylinder cross-section and the energy flux in local thermal equalibrium are given. The geometrical factor in the expression of the averaged spectral energy flux is compared with the conventional geometrical factor obtained via geometrical free path which people usually used in their simulation. Finally, to make the simulation easy, approximate expressions are given for the geometrical factors.

Direct Evidence of an Oceanic Inverse Kinetic Energy Cascade from Satellite Altimetry

AbstractSea surface height measurements from satellites reveal the turbulent properties of the South Pacific Ocean surface geostrophic circulation, both supporting and challenging different aspects of geostrophic turbulence theory. A near-universal shape of the spectral kinetic energy flux is found and provides direct evidence of a source of kinetic energy near to or smaller than the deformation radius, consistent with linear instability theory. The spectral kinetic energy flux also reveals a net inverse cascade (i.e., a cascade to larger spatial scale), consistent with two-dimensional turbulence phenomenology. However, stratified geostrophic turbulence theory predicts an inverse cascade for the barotropic mode only; energy in the large-scale baroclinic modes undergoes a direct cascade toward the first-mode deformation scale. Thus if the surface geostrophic flow is predominately the first baroclinic mode, as expected for oceanic stratification profiles, then the observed inverse cascade contradicts geostrophic turbulence theory. The latter interpretation is argued for. Furthermore, and consistent with this interpretation, the inverse cascade arrest scale does not follow the Rhines arrest scale, as one would expect for the barotropic mode. A tentative revision of theory is proposed that would resolve the conflicts; however, further observations and idealized modeling experiments are needed to confirm, or refute, the revision. It is noted that no inertial range was found for the inverse cascade range of the spectrum, implying inertial range scaling, such as the established K−5/3 slope in the spectral kinetic energy density plot, is not applicable to the surface geostrophic flow.

On physical constraints for multi-scale turbulence closure models

This paper deals with a generalisation of physical constraints for the family of two-scale eddy viscosity turbulence models, aimed at deriving general model coefficients. The focus is on models in which – next to the transport equation for the turbulence kinetic energy – two additional equations are solved to provide separately the scales of the energy-containing eddies and of the dissipative processes. The natural choice for accounting for spectral dynamics is to solve separate equations for the spectral energy flux dominated by the energy-containing eddies, εp, and for the energy dissipation εT. We give a critical evaluation of the physical constraints derived for three generic turbulent flows, which can be used to determine model coefficients. The analysis is presented for a generic variable φ, which can subsequently be transformed into any other scalar scale variable, allowing one to analyse the properties and performances of different equations.

Turbulent thermal convection in a sphere

Convection in a rotating spherical layer in the Boussinesq approximation is considered. A free rotating solid concentric inner sphere is included. The problem of developed turbulence is solved using the shell model approach. Two sets of equations are used. The Navier–Stokes equation and the thermal flux equation are solved on a large scale due to a coarse grid. The small-scale solution is described by the shell model, which generates another set of equations. This enables us to estimate the spectral energy flux on small scales. The turbulent coefficients, depending on the radial direction, are then calculated and used in the large-scale solution. The behavior of other characteristics (spectra, helicity) is also studied in time and space. The stabilized solution of the largescale convection is obtained for the Rayleigh number Ra = 10 and the Ekman number E = 10−6 based on the molecular values of viscosity and thermal diffusivity. The results correspond to the Reynolds number Re ∼ 10.

Computational Modeling of the Turbulent Penetrative Convection above the Urban Heat Island in a Stably Stratified Environment

A three-equation model of the turbulent transport of momentum and heat for simulating a circulation structure over the heat island in a stably stratified environment under nearly calm conditions is formulated. The turbulent kinetic energy E = (1/2)〈uiui〉 (where 〈 〉 indicates averaging), its spectral flux ϵ (dissipation), and the dispersion of turbulent fluctuations of temperature 〈θ2〉 are found from differential equations; thus the correct modeling of transport processes in the interface layer with the countergradient heat flux is assured. Turbulent fluxes of momentum, −〈uiuj〉, and heat, −〈uiθ〉, are determined from fully explicit “gradient diffusion” models. The E–ϵ–〈θ2〉 turbulence model minimizes difficulties in simulating the turbulent transport in a stably stratified environment and reduces efforts needed for the numerical implementation of the model. Numerical simulation of the turbulent structure of the penetrative convection over the heat island under conditions of stably stratified atmosphere demonstrates that the three-equation model is able to predict the circulation induced by the heat island, temperature distribution, root-mean-square fluctuations of the turbulent velocity and temperature fields, and spectral turbulent kinetic energy flux that are in good agreement with the experimental data and results of large-eddy simulations.