Investigation of internal intermittency by way of higher-order spectral moments

The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$ . Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.

Complexity of Magnetic-field Turbulence at Reconnection Exhausts in the Solar Wind at 1 au

Magnetic reconnection is a complex mechanism that converts magnetic energy into particle kinetic energy and plasma thermal energy in space and astrophysical plasmas. In addition, magnetic reconnection and turbulence appear to be intimately related in plasmas. We analyze the magnetic-field turbulence at the exhaust of four reconnection events detected in the solar wind using the Jensen–Shannon complexity-entropy index. The interplanetary magnetic field is decomposed into the LMN coordinates using the hybrid minimum variance technique. The first event is characterized by an extended exhaust period that allows us to obtain the scaling exponents of higher-order structure functions of magnetic-field fluctuations. By computing the complexity-entropy index we demonstrate that a higher degree of intermittency is related to lower entropy and higher complexity in the inertial subrange. We also compute the complexity-entropy index of three other reconnection exhaust events. For all four events, the B L component of the magnetic field displays a lower degree of entropy and higher degree of complexity than the B M and B N components. Our results show that coherent structures can be responsible for decreasing entropy and increasing complexity within reconnection exhausts in magnetic-field turbulence.

Boundary-layer evolution over long wind farms

The structure of the internal boundary layer above long wind farms is investigated experimentally. The transfer of kinetic energy from the region above the farm is dominated by the turbulent flux of momentum together with the displacement of kinetic energy operated by the mean vertical velocity: these two have comparable magnitude along the farm opposite to the infinite-farm case. The integration of the energy equation in the vertical highlighted the key role of the energy flux, and how that is balanced by the growth of the internal boundary layer in terms of energy thickness with a small role of the dissipation. The mean velocity profiles seem to follow a universal structure in terms of velocity deficit, while the Reynolds stress does not follow the same scaling structure. Finally, a spectral analysis along the farm identified the leading dynamics determining the turbulent activity: while behind the first row the signature of the tip vortices is dominant, already after the second row their coherency is lost and a single broadband peak, associated with wake meandering, is present until the end of the farm. The streamwise velocity peak is associated with a nearly constant Strouhal number weakly dependent on the farm layout and free stream turbulence condition. A reasonable agreement of the velocity spectra is observed when the latter are normalised by the velocity variance and integral time scale: nevertheless the spectra show clear anisotropy at the large scales and even the small scales remain anisotropic in the inertial subrange.

Characteristics of the Derived Energy Dissipation Rate using the 1-Hz Commercial Aircraft Quick Access Recorder (QAR) Data

The cube root of the energy dissipation rate (EDR), as a standard reporting metric of atmospheric turbulence, is estimated using 1-Hz quick access recorder data from Korean-based national air carriers with two different types of aircraft [Boeing 737 (B737) and B777], archived for 12 months from January to December 2012. Various EDRs are estimated using zonal, meridional, and derived vertical wind components, and the derived equivalent vertical gust (DEVG). Wind-based EDRs are estimated by (i) second-order structure function (EDR1), (ii) power spectral density (PSD), considering the Kolmogorov’s -5/3 dependence (EDR2), and (iii) maximum-likelihood estimation using the von Kármán spectral model (EDR3). DEVG-based EDRs are obtained mainly by vertical acceleration with different conversions to EDR using (iv) the lognormal mapping technique (EDR4) and (v) the predefined parabolic relationship between the observed EDR and DEVG (EDR5). For the EDR1, second-order structure functions are computed for zonal, meridional, and vertical wind within the defined inertial subrange. For the EDR2 and EDR3, individual PSDs for each wind component are computed using the Fast Fourier Transform over every 2-minute time window. Then, two EDR estimates are computed separately by employing the Kolmogorov-scale slope (EDR2) or prescribed von Kármán wind model (EDR3) within the inertial subrange. The resultant EDR estimates from five different methods follow a lognormal distribution reasonably well, which satisfies the fundamental characteristics of atmospheric turbulence. Statistics (mean and standard deviation) of log-scale EDRs are somewhat different from those found in a previous study using a higher frequency (10 Hz) of in situ aircraft data in the United States, likely due to different sampling rates, aircraft types, and locations. Finally, five EDR estimates capture well the intensity and location of three strong turbulence cases that are relevant to clear-air turbulence (CAT), mountain wave turbulence (MWT), and convectively induced turbulence (CIT), with different characteristics of the observed EDRs: 1) zonal (vertical) wind-based EDRs are stronger in the CAT (CIT) case, while MWT has a peak of EDRs in both zonal and vertical wind-based EDRs, and 2) the CAT and MWT cases occurred by large-scale (synoptic-scale) forcing have more variations in EDRs before and after the incident, while the CIT case triggered by smaller mesoscale convective cell has an isolated peak of EDR.

Extending the Frequency Limits of "Postage-Stamp PIV" to MHz Rates

The effective frequency limits of postage-stamp PIV, in which a pulse-burst laser and very small fields of view combine to achieve high repetition rates, have been extended by increasing the PIV acquisition rate to very nearly MHz rates (990 kHz) by using a faster camera. Charge leaked through the camera shift register at these framing rates but this was shown not to bias the measurements. The increased framing rate provided oversampled data and enabled use of multi-frame correlation algorithms for a lower noise floor, increasing the effective frequency response to 240 kHz where the interrogation window size begins to spatially filter the data. The velocity spectra suggest turbulence power-law scaling in the inertial subrange steeper than the theoretical -5/3 scaling, attributed to an absence of isotropy.

Forced Turbulent Convection Along Heated and Cooled Walls with Variable Fluid Properties

The effect of temperature depending material properties on heat and momentum transfer along heated/cooled walls in turbulent pipe flow was investigated using direct numerical simulations (DNS). For the considered thermal wall conditions, always associated with a molecular Prandtl number well over unity Prw = 10, the significantly dampened/enhanced turbulent motion caused by the increase/decrease of the viscosity with distance to the heated/cooled wall, turned out to clearly dominate over the opposite trend of the enthalpy fluctuations. The Nusselt number and, quantitatively less pronounced, the wall friction coefficient are accordingly decreased/increased for the heated/cooled case. A comparison against a well established Nu-correlation unveils the limits of the generally applied approach, which is essentially based on uniform bulk flow conditions and subsequently modified accounting for material property variation, when applied to heated and cooled conditions. An enhanced disparity of the turbulent normal stresses is observed inside the inertial subrange for the heated case, indicating a stronger deviation from isotropic turbulence, which possibly challenges mostly isotropic standard turbulence models.

Revisiting two-dimensional turbulence and mesoscale spectra

<p>Two-dimensional (2D) turbulence is not only a basic research topic that needs further investigations, it is also relevant for wind energy applications as today’s wind farm clusters can be as large as thousands of kilometers squared and individual turbines hundreds of meters tall. This challenges the use of classical turbulence models applicable for scales smaller than ~1 h, or as denoted in Högström et al. (2002) the Kolmogoroff inertial subrange, the shear production range, and for ranges the spectral gap region.</p><p>This study revisits some key characteristics of 2D turbulence and interpretation of the physics behind it, including general literatures as well as a series of our studies in recent years (Larsén et al. 2013, 2016, 2021). This includes</p><ul><li>The respective frequency/wave number range and the spectral behaviours for the wind speed: the synoptic scales where the spectral slope is -3, the mesoscale where the spectral slope is typically -5/3, and the gap region. We analyze at what scales the spectra meet and merge, and how the spectra are affected by weather types, seasons and stability.</li> <li>The 2D-isotropy characteristics. We analyze how the longitudinal and lateral velocities correlate across the scales.</li> <li>The application of stationarity. The validity of an assumption of stationary time series decides to how large scales we can perform the analysis of the longitudinal and lateral velocity components, the Taylor frozen hypothesis and 2D-isotropy.</li> </ul><p>The primary datasets are from several met stations over Denmark and the North Sea region, including both 10-min and sonic measurements from about 10 m up to 240 m.</p><p> </p><p>References:</p><p>Högström U, Hunt J, Smedman AS (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103:101–124</p><p>Larsén, X. G., Larsen, S. E., Petersen, E. L., & Mikkelsen, T. K. (2021). A Model for the Spectrum of the Lateral Velocity Component from Mesoscale to Microscale and Its Application to Wind-Direction Variation. Boundary-Layer Meteorology, 178, 415-434. https://doi.org/10.1007/s10546-020-00575-0</p><p>Larsén X. Larsen S. and Petersen E. (2016): Full-scale spectrum of the boundary layer wind. Boundary-Layer Meteorology, Vol 159, p 349-371</p><p>Larsén X., Vincent C. and Larsen S.E. (2013): Spectral structure of mesoscale winds over the water, Q. J. R. Meteorol. Soc., DOI:10.1002/qj.2003, 139, 685-700.</p>

Hydrodynamic Characteristics of Flow in a Strongly Curved Channel with Gravel Beds

This study experimentally and numerically investigated the hydrodynamic characteristics of a 180° curved open channel over rough bed under the condition of constant downstream water depth. Three different sizes of bed particles (the small, middle and big cases based upon the grain size diameter D50) were selected for flume tests. Three-dimensional instantaneous velocities obtained by the acoustic Doppler velocimeter (ADV) were used to analyze hydrodynamic characteristics. Additionally, the Renormalization-Group (RNG) turbulence model was employed for numerical simulations. Experimental results show that rough bed strengthens turbulence and increases turbulent kinetic energy along curved channels. The power spectra of the longitudinal velocity fluctuation satisfy the classic Kolmogorov −5/3 law in the inertial subrange, and the existence of rough bed shortens the inertial subrange and causes the flow reach the viscous dissipation range in advance. The contributions of sweeps and ejections are more important than those of the outward and inward interactions over a rough bed for the middle case. Flow-3D was adopted to simulate flow patterns on two rough bed settings with same surface roughness (skin drag) but different bed shapes (form drag): one is bed covered with thick bottom sediment layers along the curved part of the flume (the big case) as the experimental condition, and the other one is uniform bed along the entire flume (called the big case_flat only for simulations). Numerical simulations reveal that the secondary flow is confined to the near-bed area and the intensity of secondary flow is improved for both rough bed cases, possibly causing more serious bed erosion along a curved channel. In addition, the thick bottom sediments (the big case), i.e., larger form drag, can enhance turbulence strength near bed regions, enlarge the transverse range of secondary flow, and delay the shifting of the core region of maximum longitudinal velocity towards the concave bank.

A CFD-PBM coupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media

To account for the effect of liquid viscosity, the bubble breakup model considering turbulent eddy collision based on the inertial subrange turbulent spectrum was extended to the entire turbulent spectrum that included the energy-containing, inertial, and energy-dissipation subranges. The computational fluid dynamics-population balance model (CFD-PBM) coupled model was modified to include this extended bubble breakup model for simulations of a bubble column. The effect of turbulent energy spectrum on the bubble breakup and hydrodynamic behaviors was studied in a bubble column under different liquid viscosities. The results showed that when the liquid viscosity was < 80 mPas, the bubble breakup and hydrodynamics were almost independent on the turbulent spectrum. At liquid viscosity > 80 mPas, the bubble breakup rate and gas holdup were significantly under-predicted when the inertial turbulent spectrum was used, and when using the entire turbulent spectrum the predictions were more consistent with experimental data.