Turbulent Spectrum Research Articles

What is the Role of Gravity, Turbulence and Magnetic Fields in High-mass Star Formation Clouds?

To explore the potential role of gravity, turbulence and magnetic fields in high-mass star formation in molecular clouds, this study revisits the velocity dispersion–size (σ–L) and density–size (ρ–L) scalings and the associated turbulent energy spectrum using an extensive data sample. The sample includes various hierarchical density structures in high-mass star formation clouds, across scales of 0.01–100 pc. We observe σ ∝ L 0.26 and ρ ∝ L −1.54 scalings, converging toward a virial equilibrium state. A nearly flat virial parameter–mass (α vir−M) distribution is seen across all density scales, with α vir values centered around unity, suggesting a global equilibrium maintained by the interplay between gravity and turbulence across multiple scales. Our turbulent energy spectrum (E(k)) analysis, based on the σ–L and ρ–L scalings, yields a characteristic E(k) ∝ k −1.52. These findings indicate the potential significance of gravity, turbulence, and possibly magnetic fields in regulating dynamics of molecular clouds and high-mass star formation therein.

Gravitational Waves of Holographic QCD Phase Transition with Hyperscaling Violation

In this paper, we study the gravitational waves of holographic QCD phase transition with hyperscaling violation. We consider an Einstein–Maxwell Dilaton background and discuss the confinement–deconfinement phase transition between thermally charged AdS and AdS black holes. We find that hyperscaling violation reduces the phase transition temperature. In a further study, we discuss the effect of hyperscaling violation on the GW spectrum. We found that the hyperscaling violation exponent suppresses the peak frequency of the total GW spectrum. Moreover, the results of the GW spectrum may be detected by IPTA, SKA, BBO, and NANOGrav. We also find that the hyperscaling violation exponent suppresses the peak frequency of the bubble-collision spectrum h2Ωenv. Hyperscaling violation enhances the energy densities of the sound wave spectrum h2Ωsw and the MHD turbulence spectrum h2Ωturb. The total GW spectrum is dominated by the contribution of the bubble collision in runaway bubbles case.

The unsolved problem of solar-wind turbulence

The solar wind forms the largest wind tunnel for plasma and magnetofluid turbulence that is accessible to Earth. It evolves from what is thought to be a turbulent source that continues to drive nonlinear turbulent dynamics as it expands outward via large-scale, energy-containing wind shear and shocks. In the outer heliosphere, once the gradients in the flow have coalesced and they no longer provide an adequate source for the turbulence, the excitation of wave energy by the injection of interstellar pickup ions becomes the dominant source of energy that continues to drive the turbulence. While there are established formalisms for the determination of the strength of the turbulence and the evolution of the turbulent spectra is well-established, the actual nonlinear dynamics that are responsible for its formation and evolution remain unresolved and the subject of considerable debate. We examine the evidence and attempt to illuminate the various theories while demonstrating what is needed to resolve the debates and bring the subject of plasma turbulence into a new level of understanding.

Wall-modeled large eddy simulation of a tandem wing configuration in transonic flow

In this study, the interaction between a turbulent wake and the boundary layer of a horizontal tail plane (HTP) in the transonic flow regime is investigated. The setup considered corresponds to a generic tandem wing configuration with an OAT15A airfoil as the main wing and a National Advisory Committee for Aeronautics (NACA) 64A-110 as an HTP. Due to the transonic flow, the suction side of the OAT15A exhibits buffet. The numerical approach consists of a two-stage procedure in which a detached eddy simulation (DES) provides unsteady inflow conditions for a subsequent zonal high-fidelity large eddy simulation (LES) performed for the HTP region only; the turbulent boundary layer is modeled using scale-resolved wall-modeled LES (WMLES). The study mainly pursues two objectives: first, to discuss the influence of wake turbulence on the flow characteristics of the NACA airfoil; and second, to evaluate the capability of WMLES as a low-cost but high-resolution numerical approach in challenging flow conditions. Essentially, the study confirms the expected result that the outer part of the HTP's boundary layer is dominated by the wake of the main wing. Mainly based on a discussion of turbulence spectra, the study further demonstrates the advantage of WMLES over DES, proving that WMLES is able to capture the effects of wake turbulence on boundary layer dynamics, and thus validates the WMLES approach as a cost-effective, high-resolution turbulence modeling approach. On a superordinate level, the study further sketches a possible way on how a flow problem with such a strongly unsteady behavior could be systematically evaluated.

Random walk model for dual cascades in wave turbulence.

Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. Examples for the latter include surface waves and nonlinear Schrödinger equationswith cubic nonlinearity. However, numerical simulations in forced-dissipative equilibrium of two-dimensional turbulence and of a one-dimensional wave system reveal that the physical nature of their cascades is starkly different. This is demonstrated by comparing their spectra in a finite inertial range and by comparing the temporal fluctuations of their spectral fluxes. In particular, the flux fluctuations are much larger in the wave case and frequently lead to instantaneous flux values that have the opposite sign of the mean flux, a phenomenon that is completely absent in the hydrodynamic case. A simple random walk model for the dual cascade in wave turbulence is then formulated that is very successful in explaining these effects. In particular, the model is able to replicate the detailed shape of the observed turbulent spectrum in a finite inertial range, and it also offers a ready explanation for the large flux fluctuations. It is also shown that a nonlinear diffusion model for the wave system cannot explain the observed spectral shapes. Overall, this suggests that in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance.

Unsteady and Inhomogeneous Turbulent Fluctuations around Isotropic Equilibrium

Extracting statistics for turbulent flows directly from the Navier–Stokes equations poses a formidable challenge, particularly when dealing with unsteady or inhomogeneous flows. However, embracing Kolmogorov’s inertial range spectrum for isotropic turbulence as a dynamic equilibrium provides a conceptual starting point for perturbation theory. We review theoretical results, combining perturbation approaches, and phenomenological turbulence closures, which allow us to gain valuable insights into the statistics of unsteady and inhomogeneous turbulence. Additionally, we extend the ideas to the case of the mixing of a passive scalar.

Exploring the daytime boundary layer evolution based on Doppler spectrum width from multiple coplanar wind lidars during CROSSINN

Abstract. Over heterogeneous, mountainous terrain, the determination of spatial heterogeneity of any type of a turbulent layer has been known to pose substantial challenges in mountain meteorology. In addition to the combined effect in which buoyancy and shear contribute to the turbulence intensity of such layers, it is well known that mountains add an additional degree of complexity via non-local transport mechanisms, compared to flatter topography. It is therefore the aim of this study to determine the vertical depths of both daytime convectively and shear-driven boundary layers within a fairly wide and deep Alpine valley during summertime. Specifically, three Doppler lidars deployed during the CROSSINN (Cross-valley flow in the Inn Valley investigated by dual-Doppler lidar measurements) campaign within a single week in August 2019 are used to this end, as they were deployed along a transect nearly perpendicular to the along-valley axis. To achieve this, a bottom-up exceedance threshold method based on turbulent Doppler spectrum width sampled by the three lidars has been developed and validated against a more traditional bulk Richardson number approach applied to radiosonde profiles obtained above the valley floor. The method was found to adequately capture the depths of convective turbulent boundary layers at a 1 min temporal and 50 m spatial resolution across the valley, with the degree of ambiguity increasing once surface convection decayed and upvalley flows gained in intensity over the course of the afternoon and evening hours. Analysis of four intensive observation period (IOP) events elucidated three regimes of the daytime mountain boundary layer in this section of the Inn Valley. Each of the three regimes has been analysed as a function of surface sensible heat flux H, upper-level valley stability Γ, and upper-level subsidence wL estimated with the coplanar retrieval method. Finally, the positioning of the three Doppler lidars in a cross-valley configuration enabled one of the most highly spatially and temporally resolved observational convective boundary layer depth data sets during daytime and over complex terrain to date.

Wind-resistant reliability assessment of a super-high tower crane considering the randomness and correlation of turbulent spectral parameters

The need for wind-sensitive super-high tower cranes during the construction of high-rise structures has been growing, which makes it critical to assess the wind-resistant reliability of cranes. The accuracy of assessment is dominated by the refined simulation of real stochastic wind fields, which is usually based on the deterministic turbulent spectra including fixed spectral parameters. However, it might cause significant errors to estimate extreme responses of structures. Therefore, a simulation method for stochastic wind fields considering the randomness and correlation of turbulent spectral parameters is proposed in this study. The random functions of correlated spectral parameters are constructed based on several independent elementary random variables. A novel simulation method for stochastic wind fields involving the established random turbulent spectral functions is utilized to generate fluctuating wind samples at the Ma'anshan Yangtze River (MYR) Bridge site. In combination with the probability density evolution method, the stochastic response analysis and reliability assessment of wind-induced vibration of the crane are addressed. Results prove the effectiveness of the proposed approach in depicting probabilistic properties of real wind fields. Meanwhile, the wind-resistant comfort reliability of the tower crane is higher when considering the randomness and correlation of turbulent spectral parameters.

Joint-mode diffusion analysis of discontinuous Galerkin methods: Towards superior dissipation estimates for nonlinear problems and implicit LES

We present a new linear eigensolution analysis technique that provides superior estimates of dissipation distribution in wavenumber space for the discontinuous Galerkin (DG) method. The technique builds upon traditional dispersion-diffusion analyses that have been applied to spectral/hp element methods, but in particular is an improvement upon the non-modal eigenanalysis approach proposed by Fernandez et al. in [1]. The present technique takes into account the indirect effects that dispersion may have on dissipation, as recently discussed by Moura et al. in [2], in order to better represent dissipation itself. Also, a concept often used with dynamic mode decomposition (DMD) techniques is invoked to weight the relative contribution of the multiple diffusion curves that stem from temporal eigenanalysis. This allows for obtaining a single dissipation profile in wavenumber space, so that the proposed technique is named joint-mode analysis. Although the non-modal approach also provides a single diffusion curve, the joint-mode dissipation curve is shown to correlate significantly better with the energy spectrum of Burgers' turbulence at large and intermediate scales, which is particularly relevant for implicit large-eddy simulation (LES). The proposed technique is readily extensible to other spectral/hp element methods.

Analysis of coupled energy and helicity spectra in stratified turbulence: Theory and balloon measurements

Analysis of coupled energy and helicity spectra in stratified turbulence: Theory and balloon measurements

Modeling of primary breakup considering turbulent nozzle flow, internal turbulence and surface instability of liquid jet using turbulence decay theory

In heat engines utilizing fuel injection, the processes of atomization and spray formation have a significant impact on the combustion process, thereby determining both efficiency and emission characteristics. Accurate prediction and control of spray formation in fuel injection systems play a key role in improving the efficiency and environmental performance of thermal engines, especially with the emergence of carbon-neutral fuels. To achieve accurate prediction of spray mixture formation, it is imperative to refine the atomization model for the liquid jet within numerical simulations. This requires a phenomenological representation of the atomization process that avoids reliance on computational constants obtained from spray experimental results. Consequently, the present study attempts to mathematically model the turbulent nozzle flow and liquid jet atomization process, leading to the development of a novel primary breakup model. The construction of the primary breakup model involves an analysis of the turbulence at the nozzle inlet. By merging this turbulence with the turbulence resulting from wall shear flow within the nozzle, the model provides insight into the internal turbulence and surface instability of the liquid jet, encompassing the turbulence spectrum. Consequently, the influence of nozzle length on the turbulent flow within the nozzle can be understood, and the droplet formation characteristics of the liquid jet can be predicted along with its multi-wavelength dispersion characteristics. The model effectively captures the experimental results in terms of breakup length and droplet dispersion characteristics, thus adding a higher level of accuracy to numerical simulations. Ultimately, the in-depth study of this model, coupled with its comparison with experimental results, enhances the understanding of the liquid jet atomization process.

On the feasibility of using short-range, high-frequency transmissions to characterize the vertical-spectra of small-scale internal waves and turbulence in a bottom boundary layer

Using weak fluctuation theory, we examine the detectability of small-scale internal waves and turbulence via short-range, high-frequency transmissions to a vertical array. For internal waves the theory needs modification since the ranges of interest are shorter than the internal wave correlation lengths. The turbulence spectra are characterized by thermal dissipation, χ, kinetic energy dissipation, ε, and outer scale L;0 (largest turbulent eddies) and regions of this space can be explored with different ranges and acoustic frequencies. Very little is known of the internal-wave structure when wave breaking starts. As an example, we consider an experimental arrangement atop the Atlantis 2 seamount where there is a strong, tidally driven boundary layer approximately 100-m thick.

Grid Turbulence Measurements with an Acoustic Doppler Current Profiler

The motivation for this study is to investigate the abilities and limitations of a Nortek Signature1000 acoustic Doppler current profiler (ADCP) regarding fine-scale turbulence measurements. Current profilers offer the advantage of gaining more coherent measurement data than available with point acoustic measurements, and it is desirable to exploit this property in laboratory and field applications. The ADCP was tested in a towing tank, where turbulence was generated from a grid towed under controlled conditions. Grid-induced turbulence is a well-studied phenomenon and a good approximation for isotropic turbulence. Several previous experiments are available for comparison and there are developed theories within the topic. In the present experiments, a Nortek Vectrino acoustic Doppler velocimeter (ADV), which is an established instrument for turbulence measurements, was applied to validate the ADCP. It was found that the mean flow measured with the ADCP was accurate within 4% of the ADV. The turbulent variance was reasonably well resolved by the ADCP when large grid bars were towed at a high speed, but largely overestimated for lower towing speed and smaller grid bars. The effective cutoff frequency and turbulent eddy size were characterized experimentally, which provides detailed guidelines for when the ADCP data can be trusted and will allow future experimentalists to decide a priori if the Nortek Signature can be used in their setup. We conclude that the ADCP is not suitable for resolving turbulent spectra in a small-scale grid-induced flow due to the intrinsic Doppler noise and the low spatial and temporal sample resolution relative to the turbulent scales.

Observation of Doppler shift modulated by the internal kink mode using conventional reflectometry in the EAST tokamak

In this paper we present a new experimental observation using a conventional reflectometry technique, poloidal correlation reflectometry (PCR), in the Experimental Advanced Superconducting Tokamak (EAST). The turbulence spectrum detected by the PCR system exhibits an asymmetry and induced Doppler shift during the internal kink mode (IKM) rotation phase. This Doppler shift is the target measurement of Doppler reflectometry, but captured by conventional reflectometry. Results show that the Doppler shift is modulated by the periodic changes in the effective angle between the probing wave and cutoff layer normal, but not by plasma turbulence. The fishbone mode and saturated long-lived mode are typical IKMs, and this modulation phenomenon is observed in both cases. Moreover, the value of the Doppler shift is positively correlated with the amplitude of the IKM, even when the latter is small. However, the positive and negative frequency components of the Doppler shift can be asymmetric, which is related to the plasma configuration. A simulated analysis is performed by ray tracing to verify these observations. These results establish a clear link between and IKM rotation, and are helpful for studying the characteristics of IKM and related physical phenomena.

Coherent structures of beam-driven whistler mode in the presence of magnetic islands in the magnetopause

The Magnetospheric Multiscale Mission (MMS) has perceived whistler wave generation, coherent structures, and related turbulence close to the magnetopause reconnection zones. The current research examines coherent structure of whistler wave driven by an intense electron beam at the magnetopause’s magnetic reconnection sites as well as by the dynamic growth of magnetic islands. A nonlinear model of high-frequency whistler wave and low-frequency magnetosonic wave has been developed by using the two-fluid approximation. Nonlinear dynamics of 3D whistler wave and magnetosonic wave have been solved by the pseudo spectral method along with the predictor-corrector method and finite difference method. The simulation’s outcomes demonstrate the temporal and spatial development of the whistler localized structures and current sheets as a witness to the turbulence’s existence. Moreover, the turbulent power spectra have been investigated. The formation of the thermal tail of energetic electrons has been studied using the power-law scaling of turbulence development. We determined the scale sizes of current sheets and localized structures using a semi-analytic model and showed that these scale sizes rely on the power of whistler wave. We predict that the acceleration of the energetic electrons and heating in the Magnetopause may be caused by whistler wave.

Gust-induced flow perturbations on circular cylinder: Investigating the effects and characteristics

This paper delves into the fascinating realm of gust flow past a circular cylinder, unveiling the dynamic interactions and key features that influence the system's behavior. In this study, ANSYS Fluent is used to perform numerical simulations based on finite volume method. The aim is to investigate the temporal evolution of the aerodynamic forces at different Reynolds numbers (Re) at different gust frequencies. In this study, gusts are generated by harmonically changing the direction of the inlet velocity at different frequencies. Unlike uniform flow, vortices are shed simultaneously from the upper and lower surface of cylinder, sometimes with equal strengths and sometimes with varying strengths depending upon the gust frequency. Cl, Cd and Strouhal number values increase with gust frequency corresponding to any Reynolds number. However, the values remain less than no-gust case under similar flow situations. Fast Fourier transform analysis has been used to examine the energy spectrum and kinetic energy contours of vorticity and turbulence to gain further insight into fluid physics. The results of this study provide valuable insight into the physics of gust flow and circular cylinders.

Analysis of Aerodynamic Loads on Heliostats at Operation Position Using Large Eddy Simulation and the Consistent Discrete Random Flow Generation Method

Abstract This study utilizes the large eddy simulation model (LES) and a synthetic method based on the Fourier technique called consistent discrete random flow generation (CDRFG) to analyze the peak aerodynamic loads on heliostats due to the atmospheric boundary layer. With the CDRFG technique, key flow parameters, including mean velocity profile, turbulent intensities, integral length scales, and turbulent spectra generated in wind tunnels, can be replicated while also satisfying the divergence-free condition. A three-facet heliostat with an elevation angle of α = 45 deg and the rear aligned to the inflow was analyzed. The heliostat behaves like a lifting surface in this orientation, accentuating the aerodynamic effect. The methodology proposed in this study can accurately reproduce flow statistics and predict the peak loads. Compared to experimental data, differences of 2.62% for drag, 7.43% for lift, and 11.0% for overturning were observed. Furthermore, the simulation reveals the generation of wingtip vortices on the sides of the heliostat, which contribute to the aerodynamic load. Overall, this technique has been demonstrated to be effective in replicating the atmospheric boundary layer and predicting the aerodynamic coefficients of heliostats.

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Dissipation closure of fluid turbulence from energy spectrum

Direct method of the turbulence closure consists of obtaining expression for small-scale velocity and inserting this expression in the Reynolds tensor and in the transport equations for turbulent energy, dissipation, eddy and so on, implementing some averaging. Previously such approaches were used for Burgers-Lundgren vortex. Here we used ‘naïve’ perturbation method for the transport equation for small-scale velocity incompressible fluid - the equation suggested by one of the authors earlier. It is assumed that the energy spectrum of turbulence is given.

Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations

In situ observations of turbulence spectra in space plasmas are usually interpreted as wavenumber spectra, assuming that the fluctuation frequency is negligible in the plasma flow frame. We explore the effects of nonzero frequency in the plasma flow frame on turbulence spectral observations. The finite frequency can be caused by either propagating waves or nonlinear broadening of nonpropagating structures. We show that the observed frequency spectrum can be modified by the nonzero frequency of turbulent fluctuations in several ways. Specifically, (i) frequency broadening results in a minor modification to the observed spectrum, primarily acting as a smoothing kernel of the spectrum near the spectral break, while the asymptotic spectral index remains unchanged; (ii) wave propagation can affect the observed spectral index for anisotropic turbulence. The effect is significant at low frequencies and weaker at high frequencies, leading to a “concave” shape of the observed perpendicular spectrum; (iii) the Doppler shift for forward- and backward-propagating Elsasser modes can result in a nonzero cross helicity for critical-balanced turbulence since the effect of the Doppler shift favors outward-propagating waves systematically, resulting in an observed imbalance. These results may have important implications for the interpretation of solar wind flows observed by Parker Solar Probe.