Cascade Flux Research Articles

Spatially evolving cascades in wall turbulence with and without interface

Direct numerical simulations of channel flow and temporal boundary layer at a Reynolds number $Re_{\tau } = 1500$ are used to assess the scale-by-scale mechanisms of wall turbulence. From the peak of turbulence production embedded at the small scales of the near-wall region, spatially ascending reverse cascades are generated that move through self-similar eddies growing in size with the wall distance. These fluxes are followed by spatially ascending forward cascades through detached eddies thus reaching sufficiently small scales where eventually scale energy is dissipated. This phenomenology is shared by both boundary layer and channel flow and is recognized as a robust physical feature characterizing wall turbulence in general. Specific features related to the flow configuration are indeed identified in the outer region. In particular, the central region of channels is characterized by a generalized Richardson energy cascade where large scales are in equilibrium with small scales at different wall distances through a combined forward cascade and spatial flux. On the contrary, the interface region of boundary layers is characterized by an almost two-dimensional physics where spatially ascending reverse cascades sustain long and wide interface structures with a forward cascade that survives only in the wall-normal scales. The overall scenario consists in a variety of scale motions that while protruding from the turbulent core towards the external region, squeeze at the interface thus sustaining vertical shear in a thin layer. The observed multidimensional physics sheds light on the complex interactions between outer entrainment and near-wall self-sustaining mechanisms with possible repercussions for theories.

A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation

In this note we point out some simple sufficient (plausible) conditions for ‘turbulence’ cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation in a d-dimensional periodic box. Simple characterizations of dissipation anomalies for the wave action and kinetic energy in rough analogy with those that arise for fully developed turbulence in the 2D Navier–Stokes equations are given and sufficient conditions are given which differentiate between a ‘weak’ turbulence regime and a ‘strong’ turbulence regime. The proofs are relatively straightforward once the statements are identified, but we hope that it might be useful for thinking about mathematically precise formulations of the statistically-stationary wave turbulence problem.

Development of a Highly Selective NAD+ -Dependent Glyceraldehyde Dehydrogenase and its Application in Minimal Cell-Free Enzyme Cascades.

Anthropogenic climate change has been caused by over-exploitation of fossil fuels and CO2 emissions. To counteract this, the chemical industry has shifted its focus to sustainable chemical production and the valorization of renewable resources. However, the biggest challenges in biomanufacturing are technical efficiency and profitability. In our minimal cell-free enzyme cascade generating pyruvate as the central intermediate, the NAD+ -dependent, selective oxidation of D-glyceraldehyde was identified as a key reaction step to improve the overall cascade flux. Successive genome mining identified one candidate enzyme with 24-fold enhanced activity and another whose stability is unaffected in 10 % (v/v) ethanol, the final product of our model cascade. Semi-rational engineering improved the substrate selectivity of the enzyme up to 21-fold, thus minimizing side reactions in the one-pot enzyme cascade. The final biotransformation of D-glucose showed a continuous linear production of ethanol (via pyruvate) to a final titer of 4.9 % (v/v) with a molar product yield of 98.7 %. Due to the central role of pyruvate in diverse biotransformations, the optimized production module has great potential for broad biomanufacturing applications.

A Physical Model for the Observed Inverse Energy Cascade in Typhoon Boundary Layers

AbstractThe knowledge of the observed inverse energy cascade in typhoon boundary layers holds significant implications for understanding the formation, enhancement, and deformation of typhoons. This study reveals that the observed inverse energy cascade originates from the rapid rotation of typhoons. The transition from the direct energy cascade regime to the inverse energy cascade regime can be characterized by the Zeman length scale. The turbulence structures behave as two dimensional above the Zeman length scale. Through symmetry analysis, it is discovered that the ratio of the inverse energy cascade flux to the direct energy cascade flux is proportional to the turbulence Rossby number with a power of −2. These findings offer a framework for incorporating the inverse energy cascade into the turbulence parameterizations and improving typhoon modeling.

Seasonal variations of eddy kinetic energy flux in the South Indian Countercurrent region

The inverse cascade flux of kinetic energy (KE) and its length scale in the South Indian Countercurrent (SICC) region were investigated using 24-year satellite altimeter daily data from 1993-2016. The evolution of the eddy life cycle in the SICC was presented systemically. It was found that the arrest and inject scales of inverse cascade were within the baroclinic most unstable scale and observed energy-containing eddy scale. The seasonal cycle of the arrest scale, inject scale, and amplitude of the inverse cascade were compared with the eddy kinetic energy seasonal cycle, which revealed a 1.5-month lag of the eddy kinetic energy to the vertical shear of zonal velocity, implying the existence of nonlinear processes during the eddy growth phase. Meanwhile, the anisotropy of the inverse cascade indicated that kinetic energy might be transferred from meridional motions to zonal motions, which is probably caused by β effect. These results would be beneficial for a better understanding of the KE transfer processes in the SICC region.

Sufficient Conditions for Dual Cascade Flux Laws in the Stochastic 2d Navier–Stokes Equations

We provide sufficient conditions for mathematically rigorous proofs of the third order universal laws capturing the energy flux to large scales and enstrophy flux to small scales for statistically stationary, forced-dissipated 2d Navier-Stokes equations in the large-box limit. These laws should be regarded as 2d turbulence analogues of the $4/5$ law in 3d turbulence, predicting a constant flux of energy and enstrophy (respectively) through the two inertial ranges in the dual cascade of 2d turbulence. Conditions implying only one of the two cascades are also obtained, as well as compactness criteria which show that the provided sufficient conditions are not far from being necessary. The specific goal of the work is to provide the weakest characterizations of the '0-th laws' of 2d turbulence in order to make mathematically rigorous predictions consistent with experimental evidence.

Deletion Timing of Cic Alleles during Hematopoiesis Determines the Degree of Peripheral CD4+ T Cell Activation and Proliferation.

Capicua (CIC) is a transcriptional repressor that regulates several developmental processes. CIC deficiency results in lymphoproliferative autoimmunity accompanied by expansion of CD44hiCD62Llo effector/memory and follicular Th cell populations. Deletion of Cic alleles in hematopoietic stem cells (Vav1-Cre-mediated knockout of Cic) causes more severe autoimmunity than that caused by the knockout of Cic in CD4+CD8+ double positive thymocytes (Cd4-Cre-mediated knockout of Cic). In this study, we compared splenic CD4+ T cell activation and proliferation between whole immune cell-specific Cic-null (Cicf/f;Vav1-Cre) and T cell-specific Cic-null (Cicf/f;Cd4-Cre) mice. Hyperactivation and hyperproliferation of CD4+ T cells were more apparent in Cicf/f;Vav1-Cre mice than in Cicf/f;Cd4-Cre mice. Cicf/f;Vav1-Cre CD4+ T cells more rapidly proliferated and secreted larger amounts of IL-2 upon TCR stimulation than did Cicf/f;Cd4-Cre CD4+ T cells, while the TCR stimulation-induced activation of the TCR signaling cascade and calcium flux were comparable between them. Mixed wild-type and Cicf/f;Vav1-Cre bone marrow chimeras also exhibited more apparent hyperactivation and hyperproliferation of Cic-deficient CD4+ T cells than did mixed wild-type and Cicf/f;Cd4-Cre bone marrow chimeras. Taken together, our data demonstrate that CIC deficiency at the beginning of T cell development endows peripheral CD4+ T cells with enhanced T cell activation and proliferative capability.

Synthetic dissipation and cascade fluxes in a turbulent quantum gas.

Scale-invariant fluxes are the defining property of turbulent cascades, but their direct measurement is a challenging experimental problem. Here we perform such a measurement for a direct energy cascade in a turbulent quantum gas. Using a time-periodic force, we inject energy at a large length scale and generate a cascade in a uniformly trapped three-dimensional Bose gas. The adjustable trap depth provides a high-momentum cutoff k D, which realizes a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius k D, and the tunability of k D allows for a clear demonstration of the zeroth law of turbulence. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.

Simulations of Hot-Gas Flow in Internally Cooled Cascade of Turbine Vanes

Abstract An experiment in cooling of gas turbine nozzle guide vanes was modelled numerically with a conjugate viscous-flow and solid-material heat conduction solver. The nozzle vanes were arranged in a cascade and operated in high-pressure, hot-temperature conditions, typical for first turbine stage in a flow of controlled-intensity, artificially-generated turbulence. The vane cooling was internal, accomplished by 10 channels in each vane with cooling-air flow. Numerical simulations of the experiment were conducted applying two turbulence models of the k-omega family: k-omega-SST and Transition SST implemented in the ANSYS Fluent solver. Boundary conditions for the simulations were set based on conditions of experiment: total pressures and total temperature on inlet to cascade, static pressure on the outlet of the cascade and heat flux on the surface of cooling channels. The values of heat flux on the surface of cooling channels were evaluated based on Nusselt numbers obtained from experiment and varied in time until steady-state conditions were obtained. Two test cases, one with subcritical outlet flow, and another one, with supercritical outlet flow were simulated. The result of experiment – distributions of pressure, surface temperature, and heat transfer coefficients on the vane external surface were compared to results of numerical simulations. Sensitivity of the vane surface temperatures and heat transfer coefficients to turbulence models and to boundary-condition values of parameters of turbulence models: turbulence energy and specific dissipation of turbulence energy was also studied.

Impact of Plasma Instability on Constraint of the Intergalactic Magnetic Field

Abstract A relativistic electron–positron pair beam can be produced in the interaction between TeV photons from a blazar and extragalactic background light. The relativistic e ± pairs lose energy through inverse-Compton scattering (ICS) photons of the cosmic microwave background or plasma instabilities. The dominant energy-loss process is under debate. Based on the assumption that the dominant energy-loss process is ICS, the resulting cascade GeV radiation is usually used to constrain the intergalactic magnetic field (IGMF). Here, we include the energy-loss due to plasma oblique instability in the calculation of cascade gamma-ray flux, and investigate the impact of the plasma instability on the constraint of IGMF. Up-to-date GeV data and archival TeV data of the blazar 1ES 0229+200 are used. The results indicate that even if the oblique instability cooling is dominating ICS cooling, the cascade flux could still be used to constrain the IGMF. It is found that with the ratio between the cooling rates of the oblique instability and the ICS varying from 0.1,1 to 10, the lower limit of the IGMF of the cascade flux and the gamma-ray data changes from 8 × 10−18 G, 5 × 10−18 G to 10−18 G. If the ratio between the two cooling rates is 30, the estimate of IGMF based on the cascade flux is invalid.

Von Kármán–Howarth Equation for Hall Magnetohydrodynamics: Hybrid Simulations

Abstract A dynamical vectorial equation for homogeneous incompressible Hall-magnetohydrodynamic (MHD) turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results of two-dimensional hybrid simulations of plasma turbulence. At large (MHD) scales the simulations exhibit a clear inertial range where the MHD dynamic law is valid. In the sub-ion range the cascade continues via the Hall term, but the dynamic law derived in the framework of incompressible Hall-MHD equations is obtained only in a low plasma beta simulation. For a higher beta plasma the cascade rate decreases in the sub-ion range and the change becomes more pronounced as the plasma beta increases. This break in the cascade flux can be ascribed to nonthermal (kinetic) features or to others terms in the dynamical equation that are not included in the Hall-MHD incompressible approximation.

LOWER BOUND ON THE COSMIC TeV GAMMA-RAY BACKGROUND RADIATION

ABSTRACT The Fermi gamma-ray space telescope has revolutionized our understanding of the cosmic gamma-ray background radiation in the GeV band. However, investigation on the cosmic TeV gamma-ray background radiation still remains sparse. Here, we report the lower bound on the cosmic TeV gamma-ray background spectrum placed by the cumulative flux of individual detected extragalactic TeV sources including blazars, radio galaxies, and starburst galaxies. The current limit on the cosmic TeV gamma-ray background above 0.1 TeV is obtained as 2.8 × 10−8(E/100 GeV)−0.55 exp(−E/2100GeV)[GeV cm−2 s−1 sr−1] < E 2 dN/dE < 1.1 × 10−7(E/100 GeV)−0.49 [GeV cm−2 s−1 sr−1], where the upper bound is set by requirement that the cascade flux from the cosmic TeV gamma-ray background radiation can not exceed the measured cosmic GeV gamma-ray background spectrum. Two nearby blazars, Mrk 421 and Mrk 501, explain ∼70% of the cumulative background flux at 0.8–4 TeV, while extreme blazars start to dominate at higher energies. We also provide the cumulative background flux from each population, i.e., blazars, radio galaxies, and starburst galaxies which will be the minimum requirement for their contribution to the cosmic TeV gamma-ray background radiation.

CONSTRAINTS ON THE INTERGALACTIC MAGNETIC FIELD WITH GAMMA-RAY OBSERVATIONS OF BLAZARS

Distant BL Lacertae objects emit $\gamma$ rays which interact with the extragalactic background light (EBL), creating electron-positron pairs, and reducing the flux measured by ground-based imaging atmospheric Cherenkov telescopes (IACTs) at very-high energies (VHE). These pairs can Compton-scatter the cosmic microwave background, creating a $\gamma$-ray signature at slightly lower energies observable by the \fermi\ Large Area Telescope (LAT). This signal is strongly dependent on the intergalactic magnetic field (IGMF) strength ($B$) and its coherence length ($L_B$). We use IACT spectra taken from the literature for 5 VHE-detected BL Lac objects, and combine it with LAT spectra for these sources to constrain these IGMF parameters. Low $B$ values can be ruled out by the constraint that the cascade flux cannot exceed that observed by the LAT. High values of $B$ can be ruled out from the constraint that the EBL-deabsorbed IACT spectrum cannot be greater than the LAT spectrum extrapolated into the VHE band, unless the cascade spectrum contributes a sizable fraction of the LAT flux. We rule out low $B$ values ($B< 10^{-19}$ G for $L_B\ge1$\ Mpc) at $>5\sigma$ in all trials with different EBL models and data selection, except when using $>1$ GeV spectra and the lowest EBL models. We were not able to constrain high values of $B$.

The effect of viscoelasticity on the turbulent kinetic energy cascade

AbstractDirect numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model, such as those laden with polymers, are presented. It is shown that the strong depletion of the turbulence dissipation reported by previous authors does not necessarily imply a depletion of the nonlinear energy cascade. However, for large relaxation times, of the order of the eddy turnover time, the polymers remove more energy from the large scales than they can dissipate and transfer the excess energy back into the turbulent dissipative scales. This is effectively a polymer-induced kinetic energy cascade which competes with the nonlinear energy cascade of the turbulence leading to its depletion. It is also shown that the total energy flux to the small scales from both cascade mechanisms remains approximately the same fraction of the kinetic energy over the turnover time as the nonlinear energy cascade flux in Newtonian turbulence.

Search for extendedγ-ray emission around AGN with H.E.S.S. andFermi-LAT

Context: Very-high-energy (VHE; E>100 GeV) {\gamma}-ray emission from blazars inevitably gives rise to electron-positron pair production through the interaction of these {\gamma}-rays with the Extragalactic Background Light (EBL). Depending on the magnetic fields in the proximity of the source, the cascade initiated from pair production can result in either an isotropic halo around an initially beamed source or a magnetically broadened cascade flux. Aims: Both extended pair halo (PH) and magnetically broadened cascade (MBC) emission from regions surrounding the blazars 1ES 1101-232, 1ES 0229+200 and PKS 2155-304 were searched for, using VHE {\gamma}-ray data taken with the High Energy Stereoscopic System (H.E.S.S.), and high energy (HE; 100 MeV<E<100 GeV) {\gamma}-ray data with the Fermi Large Area Telescope (LAT). Methods: By comparing the angular distributions of the reconstructed gamma-ray events to the angular profiles calculated from detailed theoretical models, the presence of PH and MBC was investigated. Results: Upper limits on the extended emission around 1ES 1101-232, 1ES 0229+200 and PKS 2155-304 are found to be at a level of few percent of the Crab nebula flux above 1 TeV, depending on the assumed photon index of the cascade emission. Assuming strong Extra-Galactic Magnetic Field (EGMF) values, > 10$^{-12}$G, this limits the production of pair halos developing from electromagnetic cascades. For weaker magnetic fields, in which electromagnetic cascades would result in magnetically broadened cascades, EGMF strengths in the range (0.3 - 3)$\times 10^{-15}$G were excluded for PKS 2155-304 at the 99% confidence level, under the assumption of a 1 Mpc coherence length.

On Lagrangian single-particle statistics

In turbulence, ideas of energy cascade and energy flux, substantiated by the exact Kolmogorov relation, lead to the determination of scaling laws for the velocity spatial correlation function. Here we ask whether similar ideas can be applied to temporal correlations. We critically review the relevant theoretical and experimental results concerning the velocity statistics of a single fluid particle in the inertial range of statistically homogeneous, stationary and isotropic turbulence. We stress that the widely used relations for the second structure function, D2(t) ≡ ⟨[v(t) − v(0)]2⟩∝εt, relies on dimensional arguments only: no relation of D2(t) to the energy cascade is known, neither in two- nor in three-dimensional turbulence. State of the art experimental and numerical results demonstrate that at high Reynolds numbers, the derivative \documentclass[12pt]{minimal}\begin{document}$\frac{d D_2(t)}{dt}$\end{document}dD2(t)dt has a finite non-zero slope starting from t ≈ 2τη. The analysis of the acceleration spectrum ΦA(ω) indicates a possible small correction with respect to the dimensional expectation ΦA(ω) ∼ ω0 but present data are unable to discriminate between anomalous scaling and finite Reynolds effects in the second order moment of velocity Lagrangian statistics.

Reynolds number effects on scale energy balance in wall turbulence

The scale energy budget utilizes a modified version of the classical Kolmogorov equation of wall turbulence to develop an evolution equation for the second order structure function [R. J. Hill, “Exact second-order structure-function relationships,” J. Fluid Mech. 468, 317 (2002)]. This methodology allows for the simultaneous characterization of the energy cascade and spatial fluxes in turbulent shear flows across the entire physical domain as well as the range of scales. The present study utilizes this methodology to characterize the effects of Reynolds number on the balance of energy fluxes in turbulent channel flows. Direct numerical simulation data in the range Reτ = 300–934 are compared to previously published results at Reτ = 180 [N. Marati, C. M. Casciola, and R. Piva, “Energy cascade and spatial fluxes in wall turbulence,” J. Fluid Mech. 521, 191 (2004)]. The present results show no Reynolds number effects in the terms of the scale energy budget in either the viscous sublayer or buffer regions of the channel. In the logarithmic layer, the transfer of energy across scales clearly varies with Reynolds number, while the production of turbulent kinetic energy is not dependent on Reynolds number. An envelope of inverse energy cascade is quantified in the buffer region within which energy is transferred from small to larger scales. This envelope is observed in the range 6 &amp;lt; y+ &amp;lt; 37, where all scales except the smallest scales display characteristics of an inverse energy cascade. The cross-over scale lc+, which indicates the transition between production dominated and scale transfer dominated regimes, increases with Reynolds number, implying a larger range of transfer dominated scales, before the dominant mechanism switches to production. At higher Reynolds numbers, two distinct regimes of lc+ as a function of wall-normal location are observed, which was not captured at Reτ = 180. The variations of lc+ match the trends of the shear scale, which is a representation of the mean shear in the flow. Thus, this study demonstrates the utility and importance of the use of higher Reynolds number data in order to accurately characterize and understand the energy dynamics of various scales across the entire boundary layer.

TIME DELAY OF CASCADE RADIATION FOR TeV BLAZARS AND THE MEASUREMENT OF THE INTERGALACTIC MAGNETIC FIELD

Recent claims that the strength B_IGMF of the intergalactic magnetic field (IGMF) is >~ 1e-15 G are based on upper limits to the expected cascade flux in the GeV band produced by blazar TeV photons absorbed by the extragalactic background light. This limit depends on an assumption that the mean blazar TeV flux remains constant on timescales >~2 (B_ IGMF/1e-18 G)^2 / (E/{10 GeV})^2 yr for an IGMF coherence length ~ 1 Mpc, where E is the measured photon energy. Restricting TeV activity of 1ES 0229+200 to ~3 -- 4 years during which the source has been observed leads to a more robust lower limit of B_IGMF >~ 1e-18 G, which can be larger by an order of magnitude if the intrinsic source flux above ~5 -- 10 TeV from 1ES 0229+200 is strong.

Non-statistical population of 1s2s2p4PJ states by charge transfer into multiply charged ions

The experimentally observed enhancement of (1s2s3s)ml4P to (1s2s3S)ml2P populations in collisions of He-like ions with H2 and He targets is discussed and explained by a state-selective cascade feeding mechanism. Continuum Distorted Wave (CDW) and Classical Trajectory Monte Carlo (CTMC) calculations show that large populations of higher lying (1s2s 3S)nℓ2'4L Rydberg states for ℓ = L = 0, n-1 and n = 2 - 8 can be formed in 0.25-2 MeV/u collisions by direct capture to metastable F7+(1s2s3S) ions. These states subsequently decay through a cascade sequence of radiative or Auger transitions dictated by angular momentum and spin selection rules. All radiative (E1) and Auger transitions for n = 5 were evaluated using the Cowan package for Hartree-Fock calculations. The (1s2s3S)ml2L doublets were found to Auger decay rapidly to the 1s2 level allowing for negligible cascade feeding of lower lying doublets including the 1s2s2p2P±. Alternatively, Auger decay of the (1s2s3S)ml4L quartets is blocked by spin selection rules. Decay can proceed, however, through dipole transitions, but only to other quartets, including the lowest lying 1s2s2p4P state, which in this way acts as an "excited ground state" eventually collecting most cascade flux. This selective cascade feeding mechanism thus leads to the non-statistical enhancement of the 1s2s2p4P quartet population over those of the 1s2s2p2P± doublet populations providing an alternative explanation to the recently suggested novel mechanism of dynamical Pauli exchange.

Energy cascade and spatial fluxes in wall turbulence

Real turbulent flows are difficult to classify as either spatially homogeneous or isotropic. Nonetheless these idealizations allow the identification of certain universal features associated with the small-scale motions almost invariably observed in a variety of different conditions. The single most significant aspect is a flux of energy through the spectrum of inertial scales related to the phenomenology commonly referred to as the Richardson cascade. Inhomogeneity, inherently present in near-wall turbulence, generates additional energy fluxes of a different nature, corresponding to the spatial redistribution of turbulent kinetic energy. Traditionally the spatial flux is associated with a single-point observable, namely the turbulent kinetic energy density. The flux through the scales is instead classically related to two-point statistics, given in terms of an energy spectrum or, equivalently, in terms of the second-order moment of the velocity increments. In the present paper, starting from a suitably generalized form of the classical Kolmogorov equation, a scale-by-scale balance for the turbulent fluctuations is evaluated by examining in detail how the energy associated with a specific scale of motion – hereafter called the scale energy – is transferred through the spectrum of scales and, simultaneously, how the same scale of motion exchanges energy with a properly defined spatial flux. The analysis is applied to a data set taken from a direct numerical simulation (DNS) of a low-Reynolds-number turbulent channel flow. The detailed scale-by-scale balance is applied to the different regions of the flow in the various ranges of scales, to understand how – i.e. through which mechanisms, at which scales and in which regions of the flow domain – turbulent fluctuations are generated and sustained. A complete and formally precise description of the dynamics of turbulence in the different regions of the channel flow is presented, providing rigorous support for previously proposed conceptual models.