Intermittent Turbulence Research Articles

On the connection between intermittency and dissipation in ocean turbulence: a multifractal approach

AbstractThe multifractal theory of turbulence is used to investigate the energy cascade in the Northwestern Atlantic ocean. The statistics of singularity exponents of horizontal velocity gradients computed from in situ measurements at 2 km resolution are used to characterize the anomalous scaling of the velocity structure functions at depths between 50 ad 500 m. Here, we show that the degree of anomalous scaling can be quantified using singularity exponents. Observations reveal, on one side, that the anomalous scaling has a linear dependence on the exponent characterizing the strongest velocity gradient and, on the other side, that the slope of this linear dependence decreases with depth. Since the observed distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade, the log-Poisson model, to derive the functional dependence of the anomalous scaling with the exponent of the strongest velocity gradient, as well as the dependence with dissipation. Using this model we can interpret the vertical change of the linear slope between the anomalous scaling and the exponents of the strongest velocity gradients as a change in the energy cascade. This interpretation assumes the validity of the multifractal theory of turbulence, which has been assessed in previous studies.

Log-Skew-Normality of Ocean Turbulence.

The statistics of intermittent ocean turbulence is the key link between physical understanding of turbulence and its global implications. The log-normal distribution is the standard but imperfect assumed distribution for the turbulent kinetic energy dissipation rate. We argue that as turbulence is often generated by multiple changing sources, a log-skew-normal (LSN) distribution is more appropriate. We show the LSN distribution agrees excellently and robustly with observations. The heavy tail of the LSN distribution has important implications for sampling of turbulence in terrestrial and extraterrestrial analogous systems.

Near-wall flow structures and related surface quantities in wall-bounded turbulence

By applying the Taylor-series expansion solution of the Navier–Stokes equations, an analysis is given to elucidate the relationships between near-wall flow structures and the fundamental surface quantities (skin friction and surface pressure). The derived results are used to understand the physical features of near-wall flow structures around a typical strong wall-normal velocity event (SWNVE) in a turbulent channel flow based on the direct numerical simulation data at Reτ=180. The simulation is carefully done using a multiple-relaxation-time lattice Boltzmann method combined with an improved on-wall bounce-back implementation. It is found that both the skin friction divergence and the Laplacian of surface pressure have good correspondence with sweep and ejection motions induced by the quasi-streamwise vortex above the viscous sublayer. Interestingly, the surface pressure variation induced by a quasi-streamwise vortex tends to attenuate the wall-normal velocity magnitude in both the sweep and ejection sides through the Laplacian of surface pressure. Similar physical effects of surface-pressure-related terms are also observed for the near-wall Reynolds stress. The concentrated enstrophy and dissipation are associated with the SWNVE and high skin friction magnitude. It is found that the SWNVE is dynamically important in generating the boundary enstrophy flux, greatly enhancing the intermittency of turbulence inside the viscous sublayer. In addition, by applying the methods of differential geometry, the near-wall Taylor-series expansions are generalized for a stationary curved surface in a general curvilinear coordinate system. The generalized results could be useful in evaluating the curvature effect in the near-wall region for complex flows.

Evolution of Solar Wind Turbulence from 0.1 to 1 au during the First Parker Solar Probe–Solar Orbiter Radial Alignment

Abstract The first radial alignment between Parker Solar Probe and Solar Orbiter spacecraft is used to investigate the evolution of solar wind turbulence in the inner heliosphere. Assuming ballistic propagation, two 1.5 hr intervals are tentatively identified as providing measurements of the same plasma parcels traveling from 0.1 to 1 au. Using magnetic field measurements from both spacecraft, the properties of turbulence in the two intervals are assessed. Magnetic spectral density, flatness, and high-order moment scaling laws are calculated. The Hilbert–Huang transform is additionally used to mitigate short sample and poor stationarity effects. Results show that the plasma evolves from a highly Alfvénic, less-developed turbulence state near the Sun, to fully developed and intermittent turbulence at 1 au. These observations provide strong evidence for the radial evolution of solar wind turbulence.

Multi‐Spacecraft Measurement of Anisotropic Spatial Correlation Functions at Kinetic Range in the Magnetosheath Turbulence

AbstractWe investigate spatial correlation functions (SCFs) at kinetic range in the terrestrial magnetosheath because of wide angular distributions of the magnetic field fluctuations and the high Signal‐to‐Noise‐Ratio. We employ four‐point measurements of magnetic fluctuations from the Cluster and MMS concerning a spatiotemporally varying background magnetic field to constitute the two‐dimensional (2‐D) SCFs between ion and electron scales. It is found that two populations exist in the 2‐D SCFs, with the minority elongated along the perpendicular coordinate (S⊥) and the majority of population elongated along the coordinate parallel to average magnetic field (S||). This kind of phenomenon indicates that the distribution of magnetosheath turbulence in the wavenumber space is dominantly transverse to the background magnetic field, simultaneously partly along the field (i.e., k⊥ >> k||). In addition, we find that magnetosheath turbulence is the dominance of shear Alfvénic‐like fluctuations, and is quasi‐monofractal intermittent turbulence at kinetic range for both the Cluster case and the MMS case, indicating that strong spatially anisotropic fluctuations may be universal in the magnetosheath. Our observations pose new challenges to the theoretical modeling of turbulence and dissipation at kinetic range in the collisionless magnetized plasma.

Plume Dynamics Structure the Spatiotemporal Activity of Mitral/Tufted Cell Networks in the Mouse Olfactory Bulb.

Although mice locate resources using turbulent airborne odor plumes, the stochasticity and intermittency of fluctuating plumes create challenges for interpreting odor cues in natural environments. Population activity within the olfactory bulb (OB) is thought to process this complex spatial and temporal information, but how plume dynamics impact odor representation in this early stage of the mouse olfactory system is unknown. Limitations in odor detection technology have made it difficult to measure plume fluctuations while simultaneously recording from the mouse's brain. Thus, previous studies have measured OB activity following controlled odor pulses of varying profiles or frequencies, but this approach only captures a subset of features found within olfactory plumes. Adequately sampling this feature space is difficult given a lack of knowledge regarding which features the brain extracts during exposure to natural olfactory scenes. Here we measured OB responses to naturally fluctuating odor plumes using a miniature, adapted odor sensor combined with wide-field GCaMP6f signaling from the dendrites of mitral and tufted (MT) cells imaged in olfactory glomeruli of head-fixed mice. We precisely tracked plume dynamics and imaged glomerular responses to this fluctuating input, while varying flow conditions across a range of ethologically-relevant values. We found that a consistent portion of MT activity in glomeruli follows odor concentration dynamics, and the strongest responding glomeruli are the best at following fluctuations within odor plumes. Further, the reliability and average response magnitude of glomerular populations of MT cells are affected by the flow condition in which the animal samples the plume, with the fidelity of plume following by MT cells increasing in conditions of higher flow velocity where odor dynamics result in intermittent whiffs of stronger concentration. Thus, the flow environment in which an animal encounters an odor has a large-scale impact on the temporal representation of an odor plume in the OB. Additionally, across flow conditions odor dynamics are a major driver of activity in many glomerular networks. Taken together, these data demonstrate that plume dynamics structure olfactory representations in the first stage of odor processing in the mouse olfactory system.

Laser induced incandescence measurement of soot in ethylene buoyant turbulent diffusion flames under normal and reduced oxygen concentrations

There is a lack of published soot measurement data in buoyant turbulent flames under reduced oxygen conditions. In this work, the laser induced incandescence (LII) technique is used to investigate the soot volume fraction (fv) and soot sheet thickness in buoyant turbulent diffusion flames in atmospheres with different oxygen concentrations (OC, oxygen molar fraction in oxidizer). The experiments establish an extensive database of quantitative fv spatial distribution in ethylene flames under three OCs (20.9%, 16.8%, and 15.2%) and two heat release rates (HRR = 10 kW and 15 kW). Mean, fluctuation, and probability density function of fv, as well as local soot intermittency are studied and compared across different conditions. The results show that the maximum instantaneous fv in normal air can be ~8 ppm; but the corresponding mean fv only reaches up to 0.58 ppm due to turbulence and flame intermittency. As the oxygen concentration is reduced from 20.9% to 15.2%, the mean fv decreases, and this effect is more significant at lower heights above the burner (e.g., ~75% reduction in the mean fv at a height of half a burner outer diameter). Soot is found to be distributed unevenly in the flame, appearing in sheet-like regions with irregular and complicated shapes. The soot sheet thickness is quantified to better understand soot-turbulence interactions. This soot dataset, along with other accompanying radiation and flow field measurements, provides a comprehensive understanding of the dynamics of turbulent buoyant flame dynamics under normal and vitiated conditions, and can be used to develop and validate models for soot formation and radiative heat transfer in such flames.

The Influence of Magnetic Turbulence on the Energetic Particle Transport Upstream of Shock Waves

Energetic particles are ubiquitous in the interplanetary space and their transport properties are strongly influenced by the interaction with magnetic field fluctuations. Numerical experiments have shown that transport in both the parallel and perpendicular directions with respect to the background magnetic field is deeply affected by magnetic turbulence spectral properties. Recently, making use of a numerical model with three dimensional isotropic turbulence, the influence of turbulence intermittency and magnetic fluctuations on the energetic particle transport was investigated in the solar wind context. Stimulated by this previous theoretical work, here we analyze the parallel transport of supra-thermal particles upstream of interplanetary shock waves by using in situ particle flux measurements; the aim was to relate particle transport properties to the degree of intermittency of the magnetic field fluctuations and to their relative amplitude at the energetic particle resonant scale measured in the same regions. We selected five quasi-perpendicular and five quasi-parallel shock crossings by the ACE satellite. The analysis clearly shows a tendency to find parallel superdiffusive transport at quasi-perpendicular shocks, with a significantly higher level of the energetic particle fluxes than those observed in the quasi-parallel shocks. Furthermore, the occurrence of anomalous parallel transport is only weakly related to the presence of magnetic field intermittency.

Subproton-scale Intermittency in Near-Sun Solar Wind Turbulence Observed by the Parker Solar Probe

Abstract High time-resolution solar wind magnetic field data are employed to study statistics describing intermittency near the first perihelion (∼35.6 R ⊙) of the Parker Solar Probe mission. A merged data set employing two instruments on the FIELDS suite enables broadband estimation of higher-order moments of magnetic field increments, with five orders established with reliable accuracy. The duration, cadence, and low noise level of the data permit evaluation of scale dependence of the observed intermittency from the inertial range to deep subproton scales. The results support multifractal scaling in the inertial range, and monofractal but non-Gaussian scaling in the subproton range, thus clarifying suggestions based on data near Earth that had remained ambiguous due to possible interference of the terrestrial foreshock. The physics of the transition to monofractality remains unclear but we suggest that it is due to a scale-invariant population of current sheets between ion and electron inertial scales; the previous suggestion of incoherent kinetic-scale wave activity is disfavored as it presumably leads re-Gaussianization that is not observed.

Co-seismic eruption and intermittent turbulence of a subglacial discharge plume revealed by continuous subsurface observations in Greenland

In the Arctic, subglacial discharge plumes have been recently recognised as a key driver of fjord-scale circulation. However, owing to the danger that accompanies prolonged observations at plumes, no time-series data are available. Here, we present results showing the chaotic and irregular dynamics of a plume revealed by continuous subsurface monitoring directly on the calving front of a Greenlandic glacier. We found intense fluctuations in the current and scalars (temperature and salinity), recognised shallow and deep tidal modulation and anomalies due to co-seismic drainage of an ice-dammed lake via the plume, and observed rapid and marked changes in stratification. Our analysis uncovers energy cascade intermittency with coherent structures, corresponding to upwelling pulses of warm water. Prior to our research, in situ evidence of time-variable plume dynamics was absent and limited to snapshots, therefore, our study and approach will enable researchers to transition from an episodic view of a plume to a continuously updated image.

A study on flow characteristics around a hemispherical dome

Large eddy simulation (LES) is used to investigate the unsteady flow around a hemispherical dome. The Reynolds number based on the diameter of the hemisphere is 2.4 × 104. The mean velocity field and fluctuation velocity field were systematically studied. By means of the distribution of mean pressure coefficient, the vulnerable position on the hemispherical dome was found. By means of mean velocity profile, three regions of different properties were divided, and their effects on other creatures and buildings were considered. The probability density function (PDF), joint probability density function (JPDF) and Lumley triangle are further studied. The different intensity of the intermittency of turbulence, the different proportion of ejection (Q2) and sweeping (Q4) events and the anisotropy of Reynolds stress are explained respectively in these three regions.

An investigation of the impact of turbulence intermittency on the rotor loads of a small wind turbine

Small wind turbines (SWT) are designed according to the IEC 61400–2, which assumes the SWT experiences a set of standard wind conditions, developed through assumptions of flat terrain and normal turbulence models. In practice, other wind conditions can exist at SWT sites including winds, influenced by terrain, that feature speed and turbulence behaviour outside the set of standard conditions. In this study, wind conditions at two contrasting locations; one from built environment (Port Kennedy) and another from open terrain (Östergarnsholm), are analysed using two-point statistical approach for small-scale fluctuations. The probability density function (PDF) of the wind speed increments obtained from the two-point statistics reveals that the PK wind cases show the highest intermittency of turbulence at small timescales and this appears to manifest as higher intermittency of the rotor dynamic loads. The PDFs of rotor torque, thrust, and blade flapwise bending moment all show an increased likelihood of larger load fluctuations and occurrence of more extreme events for the turbine operating in the built environment site. The heavier tails of their PDF suggest that the turbine needs to be structurally robust and have better control system to handle these extreme events when operated in sites with complex terrain.

Hidden scale invariance of intermittent turbulence in a shell model

A study shows that the shell model of turbulence has a hidden scaling symmetry, which involves nonlinear transformations of shell speeds and time. This symmetry is restored statistically in the developed turbulence despite all original scaling symmetries being broken by the intermittency.

Assessing intermittency characteristics via cumulant analysis of floating wind turbines wakes

Turbulence intermittency in the wake behind a single floating wind turbine as well as merging wakes due to a pair of floating turbines is investigated using magnitude cumulant analysis and non-analytical cumulant analysis. This low-order statistical approach is used to compute the intermittency for its impact on fatigue loading and power output signals. In the near wake, a 60% increase in the intermittency coefficient compared to the inflow is found. Pitch motion causes a 17% increase in intermittency compared to fixed turbines. The pitch-induced intermittency depletes in the far-wake, and hence, investigating whether a pitch-induced intermittency of one turbine affects a successive one in a wind array setting is recommended. Non-local scale interactions near rotor tips are observed as undulations in the cumulant profiles, referred to as tip-effect fluctuations. The impact of turbulence intensity on intermittency is also examined, and a positive correlation between the two is found in the near-wake. In the far-wake, however, it is found to speed up the pitch-induced intermittency depletion. The wake merging region between two neighboring turbines experiences lower intermittency and damps tip-effect fluctuations. This work provides more reliable intermittency estimation by utilizing lower moment statistics. The findings aid description, turbulent loading quantification, and stochastic modeling for floating wind farm wakes as well as fixed ones for both single and merging wakes.

Numerical simulation of the transient behavior of the turbulent flow in a microfluidic oscillator

In this study, the transient numerical simulation of the flow in a fluidic oscillator has been performed. The proposed device includes several geometrical modifications of a previously patented apparatus intended for the synthesis of ozone-rich bubbles in an oxygen plasma. Prior to the experimental construction of the proposed fluidic oscillator, the present work performs a numerical study of the internal flow in the proposed design, aimed to determine its feasibility. The unsteady simulations are based on the unsteady Reynolds averaged Navier–Stokes equations coupled to the transition Shear Stress Transport (transition SST) turbulence model due to the low Reynolds numbers considered (3500 and 5000 based on flow bulk velocity). The behavior of the complex fluid flow inside the device, where four main vertical structures develop and interact, along one cycle is described in detail including the turbulent kinetic energy and intermittency in the analysis. Moreover, the effect of increasing the Reynolds number on the pressure oscillation frequency and amplitude is analyzed. In particular, the frequency is increased around a 38% and the amplitude a 100% when switching from a Reynolds number of 3500–5000. The numerical results obtained are encouraging, and the evaluated fluidic oscillator design will be fabricated and analyzed in an upcoming experimental study.

Fractal dimension of premixed flames in intermittent turbulence

In turbulent premixed flames, the fractal dimension of flame iso-surface is argued to be D=7/3 for Damköhler’s large-scale limit (Da>>1) and D=8/3 for Damköhler’s small-scale limit (Da∼O(1)) based on heuristic scaling arguments. However, such scaling arguments do not consider the effect of the intermittent nature of turbulent kinetic energy dissipation on the flame surface. In this paper, we account for the effects of intermittent dissipation on the fractal dimension of low Da turbulent premixed flames. Intermittent dissipation leads to variability in the inner cut-off, which then affects the scalar flux and total interface area. We account for these variabilities through two approaches: coarse-grained approach based on the moments of the dissipation and fine-scale analysis by adopting the multifractal formalism. We derive two corrections to the upper-limit of fractal dimension – D=8/3+3/4(1−D1/4) and D=8/3+2/3(3−D1/3). We further show that the second correction leads to an explicit dependence of the fractal dimension (D) on the scaling exponent (ξ) of the velocity structure function through the relation: D=7/3+ξ. Thus, we explicitly quantify the effect of the intermittent nature of turbulence upon low Da premixed combustion.

Spatiotemporal Intermittency in Pulsatile Pipe Flow.

Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (, ) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile.

A comprehensive assessment of fractal wrinkling/eddy dissipation based combustion model for simulating conventional turbulent premixed and non-premixed flames

This paper presents a step-forward extension of the well-known chemistry/flow interaction Eddy Dissipation Concept approach for modelling both, non-premixed and premixed, combustion regimes in a Reynolds-Averaged Navier Stokes framework. The Eddy Dissipation Concept approach and its extended versions (e.g. Partially Stirred reactors, PaSR) are widely used for CFD modelling of a variety of combustion systems. This is mainly due to their capability of incorporating chemical kinetic rates in turbulent flows. However, in defining the averaged chemical reaction rates, EDC describes the fine-scale of turbulent reacting flowfield based on the so-called mixing-rate calculated from turbulent velocity field, which consequently makes this model more suitable for diffusion flame/combustion regimes. In a recent study by the present authors, a hybrid Wrinkling-EDC approach is introduced to model fine scales of turbulent reacting flows in MILD combustion regimes based on flame surface density in premixed flame regimes and turbulent intermittency in diffusion flame regimes. In the present study, we study the performance of this newly developed approach for the simulation of conventional turbulent flames. The simulations are performed and validated using well-documented turbulent premixed and predominantly non-premixed flames (e.g. Flame F3 of Chen et al. and Sandia Flame D). In addition, all cases are simulated using a recently developed EDC model (referred to as extended EDC) along with the standard EDC version where both their results are used as a reference. The obtained results reveal better performance of the Wrinkling-EDC approach over the standard and extended versions of EDC model for the simulation of turbulent premixed flame, and a comparable performance between the extended EDC and wrinkling-EDC approach for the predictions of species concentration and temperature fields of turbulent non-premixed flames.

Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not

Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as outer time units. The characterization as a directed-percolation universal class was also discussed.

Multiscale Shear Forcing of Turbulence in the Nocturnal Boundary Layer: A Statistical Analysis

The lower nocturnal boundary layer is governed by intermittent turbulence which is thought to be triggered by sporadic activity of so-called sub-mesoscale motions in a complex way. We analyze intermittent turbulence based on an assumed relation between the vertical gradients of the sub-mean scales and turbulence kinetic energy. We analyze high-resolution nocturnal eddy-correlation data from 30-m tower collected during the Fluxes over Snow Surfaces II field program. The non-turbulent velocity signal is decomposed using a discrete wavelet transform into three ranges of scales interpreted as the mean, jet and sub-mesoscales. The vertical gradients of the sub-mean scales are estimated using finite differences. The turbulence kinetic energy is modelled as a discrete-time autoregressive process with exogenous variables, where the latter ones are the vertical gradients of the sub-mean scales. The parameters of the discrete model evolve in time depending on the locally-dominant turbulence-production scales. The three regimes with averaged model parameters are estimated using a subspace-clustering algorithm which illustrates a weak bimodal distribution in the energy phase space of turbulence and sub-mesoscale motions for the very stable boundary layer. One mode indicates turbulence modulated by sub-mesoscale motions. Furthermore, intermittent turbulence appears if the sub-mesoscale intensity exceeds 10 % of the mean kinetic energy in strong stratification.