Kinetic Energy Scale Research Articles

4D particle tracking velocimetry of an undular hydraulic jump

Undular hydraulic jumps are characterized by a three-dimensional flow field due to shock waves generated near the sidewalls. Basic flow properties have been described in the literature with experimental data, mostly gathered with classical sensors which provide local information only. A continuous description of the 3D flow field is still missing. In this study, instantaneous and three-dimensional velocity data in an undular jump were obtained between the inflow section and second wave crest using a volumetric particle tracking velocimetry method with high sample rates. A special feature of the tracking algorithm is its capability to process images with very high particle density yielding a highly resolved Lagrangian description of the flow. Velocity fields, turbulent kinetic energy, dissipation rates, Reynolds stresses and turbulent scales are presented for a volume of 10 cm width in cross-direction. Some differences were found when compared to data obtained with an intrusive acoustic Doppler velocimeter.

A filtered Rankine–Hugoniot method for consistent stochastic particle LES-FDF modelling of combustion in high-speed flows

A new model consistency scheme based on the filtered form of the Rankine–Hugoniot (R–H) relation is developed for hybrid Eulerian/Lagrangian Large Eddy Simulation-Filtered Density Function (LES-FDF) methods to model combustion in compressible high-speed flows. The approach particularly pertains to the evolution of the FDF stochastic Lagrangian particles in enthalpy space, accounting for the subgrid effects in the filtered R–H relation to ensure stable solutions and model consistency with the total energy field solved by an Eulerian compressible finite volume scheme. An analytical form of the subgrid term appearing in the filtered R–H relation is derived and it is shown to have a significant effect on the ability to accurately produce the post-shock thermochemical state. Subsequently, two novel numerical schemes are proposed based on either a modelled subgrid scale kinetic energy or a relaxation over a physical timescale. In testing for 1D normal shock cases, the former approach is found to be strongly dependent on the filter width and Mach number, while the latter approach produces consistent results. The relaxation method is further tested for a turbulent 3D shock tube case and a 1D detonation case and found to produce numerically consistent and accurate temperature and species fields. It is shown that the subgrid term is critical for accurately and consistently predicting the temperature fields in both cases and for achieving the correct detonation structure involving a leading shock and autoignition in the second case.Novelty and significance statementLES-FDF methods have not been widely used for high-speed combusting flows with strong shocks. Such flows are common in aerospace combustors and accurate modelling of these is essential for their optimisation, especially with rapid transition to alternative fuels. The first novelty is the development of a filtered Rankine–Hugoniot model to ensure energy consistency between the Eulerian LES and the FDF modelled through Lagrangian particles. The inclusion of a subgrid kinetic energy term in the Lagrangian particle energy equation is shown to be essential for producing consistent solutions and accurate prediction of thermodynamics states through discontinuities. This subgrid term is not closed and, therefore, the second novelty lies in proposing a practical numerical scheme which accounts for it. The consistent model and numerical scheme is validated in canonical shock tube and detonation cases.

A Reverse Nonequilibrium Molecular Dynamics Algorithm for Coupled Mass and Heat Transport in Mixtures.

We present a new method for introducing stable nonequilibrium concentration gradients in molecular dynamics simulations of mixtures. This method extends earlier reverse nonequilibrium molecular dynamics (RNEMD) methods, which use kinetic energy scaling moves to create temperature or velocity gradients. In the new scaled particle flux (SPF-RNEMD) algorithm, energies and forces are computed simultaneously for a molecule existing in two nonadjacent regions of a simulation box, and the system evolves under a linear combination of these interactions. A continuously increasing particle scaling variable is responsible for the migration of the molecule between the regions as the simulation progresses, allowing for simulations under an applied particle flux. To test the method, we investigate diffusivity in mixtures of identical but distinguishable particles and in a simple mixture of multiple Lennard-Jones particles. The resulting concentration gradients provide Fick diffusion constants for mixtures. We also discuss using the new method to obtain coupled transport properties using simultaneous particle and thermal fluxes to compute the temperature dependence of the diffusion coefficient and activation energies for diffusion from a single simulation. Lastly, we demonstrate the use of this new method in interfacial systems by computing the diffusive permeability of a molecular fluid moving through a nanoporous graphene membrane.

Broadband Noise Reduction of a Two-Stage Fan with Wavy Trailing-Edge Blades

In this paper, a numerical investigation is performed to study the broadband noise of a fan stage with wavy trailing-edge blades. A study of the wavelength and ratio of amplitude to wavelength (H/L) is conducted to better understand the noise reduction effect of wavy trailing-edge blades. A rotor–stator interaction broadband noise prediction method based on the result of a Reynolds-averaged Navier–Stokes equation is used. The results show that all wavy trailing-edge configurations reduce the sound power level of the fan stage. The noise reduction effect of H20L10 is the best among all the wavy trailing-edge configurations, and the sound power level is reduced by 2.4 dB at 1000 Hz. When the H/L remains unchanged, the noise reduction effect of the wavy trailing-edge configuration increases with the increase in wavelength. When the wavelength remains unchanged, the noise reduction effect of the wavy trailing-edge configuration with an H/L of 2 is the best. The use of wavy trailing-edge configurations reduces the turbulent kinetic energy and turbulent integral length scale upstream of the stator by changing the wake of the rotor, thereby reducing the rotor–stator interaction broadband noise of the fan stage.

Nonlinear scaling of fluctuation kinetic energy for shock–vorticity wave interaction

Turbulent kinetic energy (TKE) is a quantity of primary importance in shock–turbulence interaction (STI). Linear interaction analysis (LIA) serves as a theoretical method to predict the amplification of TKE in STI. LIA is constrained by low-amplitude fluctuations and neglects nonlinear effects. In this paper, we explore the nonlinear amplification of the kinetic energy of fluctuations in the interaction between a vorticity wave and a shock wave that serves as a building block flow for STI. A weakly nonlinear framework (WNLF) is introduced to analyze nonlinear effects in fluctuation kinetic energy (FKE) and identify the dominant physical mechanisms driving its amplification. The theoretical framework is validated through high-accuracy numerical simulations of shock–vorticity wave interactions. The simulation results are compared with the predictions derived from the WNLF for a range of intensities and inclinations of shock-upstream vorticity fluctuations at different Mach numbers, and WNLF is found to successfully scale the numerical data for FKE, thus confirming the validity and applicability of the framework. According to WNLF findings, at lower supersonic Mach numbers, the intermodal interaction between vorticity–vorticity modes is important, whereas the interaction between vorticity and acoustic modes becomes dominant at higher Mach numbers. Using the intermodal interactions, a model based on WNLF is proposed to predict TKE amplification in STI. In comparison to direct numerical simulation, the WNLF based model predicts the TKE amplification for moderate turbulent Mach number and lower supersonic flow Mach numbers. This is a significant improvement over the LIA results available in the literature.

Energy spectra and fluxes of turbulent rotating Bose–Einstein condensates in two dimensions

We investigate the scaling of the energy cascade in a harmonically trapped, turbulent, rotating Bose-Einstein condensate in two dimensions. We achieve turbulence by injecting a localized perturbation into the condensate and gradually increasing its rotation frequency from an initial value to a maximum. The main characteristics of the resulting turbulent state depend on the initial conditions, rotation frequency, and ramp-up time. We analyze the energy and the fluxes of kinetic energy by considering initial profiles without vortices and with vortex lattices. In the case without initial vortices, we find the presence of Kolmogorov-like scaling (k−5/3) of the incompressible kinetic energy in the inertial range. However, with initial vortex lattices, the energy spectrum follows Vinen scaling (k−1) at transient iterations. For cases with high rotating frequencies, Kolmogorov-like scaling emerges at longer durations. We observe positive kinetic energy fluxes with both initial states across all final frequencies, indicating a forward cascade of incompressible and compressible kinetic energy.

A grid-independent dispersion approach for large-eddy simulation of spray

This study proposes a subgrid-scale (SGS) dispersion approach for large-eddy simulation (LES) of spray. Rather than associating the turbulence correlation timescale used in the dispersion approach with the computational grid, we put forward an approximation of this timescale proportional to the Kolmogorov timescale. The Kolmogorov scale kinetic energy is added to the variance of the stochastic part of the SGS dispersion velocity to account for the effects of micro-scale flows on droplets. The proposed approach supports the notion of grid-independent LES and is illustrated for two benchmark Engine Combustion Network's Spray-A cases, including a vaporizing spray case and a non-vaporizing spray case. We investigate the performance of the approach in LESs of two cases by comparing it with other dispersion approaches. In particular, the investigation mainly covers spray structures, vapor and liquid penetrations, and mass fraction profiles. Results obtained using the proposed approach shows the statistics of the simulated spray cases that exhibit both good agreement with measurements and a noticeable improvement over simulations based on other tested approaches. The approach also yields more consistent results under different grid resolutions, which shows its ability to achieve LESs in non-uniform grids.

The impact of rough topography on behaviors of mesoscale eddies as revealed by submesoscale resolving simulations

Mesoscale eddies are ubiquitous in the world ocean and are a key factor in maintaining the global oceanic energy balance. Geophysical turbulence theory predicts that the eddy length scale should increase to Rhines scale as it inherits the inverse energy cascade from smaller scales that help to stabilize the ocean circulation system. However, satellite-observed mesoscale eddies are much smaller than predicted, which indicates that unclear forward energy cascades prevail in their life cycles. In this study, we explore the role of finite rough topography in modulating eddy kinetic energy and horizontal length scales by using a series of submesoscale resolving numerical simulations with parameters typical of the Drake Passage. Our results show that, when compared with those generated over a flat bottom, the presence of rough topography can substantially reduce the horizontal length scales of eddies by approximately 60%–70%, even in upper layers 2–3 km above the bottom. Rough topography also consumes significant amounts of eddy kinetic energy, as the volume-mean eddy kinetic energy over a rough bottom decreases by about 70%–80% when compared with that over a flat bottom. By using a dynamics-based decomposition method, we subtracted the submesoscale motions from total flow and found that, in addition to energetic internal lee waves, deep-ocean submesoscale processes (integrated over the bottommost 1 km) contributed roughly 22% of the total viscosity dissipation across the whole research domain over a rough bottom. Therefore, this study indicates that the role of deep-ocean submesoscale motions in the energy cascade and abyssal mixing should be considered in ocean model parameterizations in the future.

On a model-based approach to improve intranasal spray targeting for respiratory viral infections

The nasopharynx, at the back of the nose, constitutes the dominant initial viral infection trigger zone along the upper respiratory tract. However, as per the standard recommended usage protocol (“Current Use”, or CU) for intranasal sprays, the nozzle should enter the nose almost vertically, resulting in sub-optimal nasopharyngeal drug deposition. Through the Large Eddy Simulation technique, this study has replicated airflow under standard breathing conditions with 15 and 30 L/min inhalation rates, passing through medical scan-based anatomically accurate human airway cavities. The small-scale airflow fluctuations were resolved through use of a sub-grid scale Kinetic Energy Transport Model. Intranasally sprayed droplet trajectories for different spray axis placement and orientation conditions were subsequently tracked via Lagrangian-based inert discrete phase simulations against the ambient inhaled airflow field. Finally, this study verified the computational projections for the upper airway drug deposition trends against representative physical experiments on sprayed delivery performed in a 3D-printed anatomic replica. The model-based exercise has revealed a new “Improved Use” (or, IU) spray usage protocol for viral infections. It entails pointing the spray bottle at a shallower angle (with an almost horizontal placement at the nostril), aiming slightly toward the cheeks. From the conically injected spray droplet simulations, we have summarily derived the following inferences: (a) droplets sized between 7–17 μm are relatively more efficient at directly reaching the nasopharynx via inhaled transport; and (b) with realistic droplet size distributions, as found in current over-the-counter spray products, the targeted drug delivery through the IU protocol outperforms CU by a remarkable 2 orders-of-magnitude.

Production and transport of turbulent kinetic energy from premixed flames subjected to mean pressure gradients

The influence of mean favorable pressure gradients on the production and transport of turbulent kinetic energy is experimentally investigated in a premixed bluff-body combustor. The combustor wall geometry is modified into converging, straight, or diverging configurations to experimentally alter the mean pressure gradient in the reacting flow field. For each configuration, turbulent kinetic energy production and transport dynamics are characterized with high-speed particle image velocimetry and simultaneous CH* chemiluminescence imaging. For all cases, the premixed reaction increases the turbulent kinetic energy and integral length scales in the flow. However, increasing the magnitude of the mean favorable pressure gradient increases the turbulent kinetic energy produced by the flame. The source of increased turbulent fluctuations from reactants to products is first investigated with a steady flow energy analysis, and is accompanied with a Reynolds decomposed investigation of the kinetic energy in the flow. As the mean pressure gradient increases, the turbulent kinetic energy in the flow increases due to stronger magnitudes of flame-generated turbulence in the form of baroclinic torque. The evolution of the flame-generated turbulence is examined by decomposing the transport equation of turbulent kinetic energy. Increasing the mean favorable pressure gradient augments the largest magnitude transport terms, and the budget of turbulent kinetic energy is primarily driven by pressure gradient work and viscous dissipation. The results here differ from previous direct numerical simulation (DNS) studies, and should ultimately motivate additional research to aid the development of computational models which can better predict turbulent flame-flow dynamics in confined environments with mean pressure gradients.

A simplified semi-empirical model for long-range low-frequency noise propagation in the turbulent atmosphere

We present a semi-empirical long-range low-frequency acoustic propagation model, which accounts for atmospheric turbulence. Ostashev and Wilson’s scattering model is combined with a ray-theory based refraction model to account for turbulent scattering and refraction via a turbulent absorption coefficient. The coefficient is ascertained via integration of scattered energy. The model is formulated, calibrated, and validated via corresponding experiments conducted within the National Science Foundation Boundary Layer Wind Tunnel. The predictions of the newly proposed ‘bridging model’ match the wind tunnel experimental data with an average error of 11.9%. Example predictions are shown to quantify the effect of turbulent kinetic energy and turbulent integral length scale on long-range infrasound propagation. To demonstrate the approach, we present predictions of the propagation of noise from a tornado and a nonlinear wave.

Direct driving of simulated planetary jets by upscale energy transfer

Context. The precise mechanism that forms jets and large-scale vortices on the giant planets is unknown. An inverse cascade has been suggested by several studies. Alternatively, energy may be directly injected by small-scale convection. Aims. Our aim is to clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a system of rapidly rotating, deep, geostrophic spherical-shell convection. Methods. We analyze the nonlinear scale-to-scale transfer of kinetic energy in such simulations as a function of the azimuthal wave number, m. Results. We find that the main driving of the jets is associated with upscale transfer directly from the small convective scales to the jets. This transfer is very nonlocal in spectral space, bypassing large-scale structures. The jet formation is thus not driven by an inverse cascade. Instead, it is due to a direct driving by Reynolds stresses, statistical correlations of velocity components of the small-scale convective flows. Initial correlations are caused by the effect of uniform background rotation and shell geometry on the flows and provide a seed for the jets. While the jet growth suppresses convection, it increases the correlation of the convective flows, which further amplifies the jet growth until it is balanced by viscous dissipation. To a much smaller extent, energy is transferred upscale to large-scale vortices directly from the convective scales, mostly outside the tangent cylinder. There, large-scale vortices are not driven by an inverse cascade either. Inside the tangent cylinder, the transfer to large-scale vortices is even weaker, but more local in spectral space, leaving open the possibility of an inverse cascade as a driver of large-scale vortices. In addition, large-scale vortices receive kinetic energy from the jets via forward transfer. We therefore suggest a jet instability as an alternative formation mechanism of large-scale vortices. Finally, we find that the jet kinetic energy scales approximatively as ℓ−5, the same as for the so-called zonostrophic regime.

Flat bands arising from spin-orbit assisted orbital frustration

We present general design principles for engineering and discovering periodic systems with flat bands. Our paradigm exploits spin-orbit assisted orbital frustration on a lattice to produce band structures that contain multiplets of narrowly dispersing bands whose bandwidth is smaller than all other energy scales of the problem including the band gap surrounding the flat bands. We present a series of models in 1D and 2D on various lattices with different intracellular spin-orbit like potentials that hybridize the degrees of freedom in the unit cell. As an alternative to machine learning based exhaustive searches, these design principles and models can be used to search for flat band systems in a variety of physical settings and can be used to investigate the role of weakly dispersing highly orbitally frustrated degrees of freedom in systems where the interactions dominate over the kinetic energy scales of the system.

Generation of gravitational waves from freely decaying turbulence

We study the stochastic gravitational wave background (SGWB) produced by freely decaying vortical turbulence in the early Universe. We thoroughly investigate the time correlation of the velocity field, and hence of the anisotropic stresses producing the gravitational waves. With hydrodynamical simulations, we show that the unequal time correlation function (UETC) of the Fourier components of the velocity field is Gaussian in the time difference, as predicted by the “sweeping” decorrelation model. We introduce a decorrelation model that can be extended to wavelengths around the integral scale of the flow. Supplemented with the evolution laws of the kinetic energy and of the integral scale, this provides a new model UETC of the turbulent velocity field consistent with the simulations. We discuss the UETC as a positive definite kernel, and propose to use the Gibbs kernel for the velocity UETC as a natural way to ensure positive definiteness of the SGWB. The SGWB is given by a 4-dimensional integration of the resulting anisotropic stress UETC with the gravitational wave Green's function. We perform this integration using a Monte Carlo algorithm based on importance sampling, and find that the result matches that of the simulations. Furthermore, the SGWB obtained from the numerical integration and from the simulations show close agreement with a model in which the source is constant in time and abruptly turns off after a few eddy turnover times. Based on this assumption, we provide an approximate analytical form for the SGWB spectrum and its scaling with the initial kinetic energy and integral scale. Finally, we use our model and numerical integration algorithm to show that including an initial growth phase for the turbulent flow heavily influences the spectral shape of the SGWB. This highlights the importance of a complete understanding of the turbulence generation mechanism.

A prediction method for spatially decaying freestream turbulence

A simple set of equations, capable of quantifying and predicting the spatial decay of freestream turbulence (FST) is derived in the current study. The prediction equations are based on the inviscid estimate of the turbulent kinetic energy (TKE) dissipation rate. The new set of model equations includes the integral length scale and the turbulent kinetic energy as variables and is superior to the previous set of decay equations because, unlike those, they are not dependent on any physical grid parameters (b or M). This new set of equations, when compared and validated against 17 sets (2 active grids, 2 multi-scale grids, 9 square-cross-sectioned grids and 4 circular cross-sectioned grids) of previous, well-accepted, experimental data, including those relating to grid-generated turbulence and covering a wide range of turbulent Reynolds number (ReLu 0) (7.5 × 101 to 6.9 × 104), where Lu 0 is the initial integral length scale, showed very good agreement (within ±15%). This set of correlation equations can be used to estimate the local and/or initial turbulent kinetic energy and integral length scale (Lu ) in an FST flow and to locate the region within a flow domain where nearly-constant turbulence conditions are expected to prevail.

Control of plasmonic field enhancement by mode-mixing

We demonstrate experimentally that nanoscale control of plasmonic field enhancement becomes available by changing the polarization state of light. This is revealed by photoelectron emission from plasmonic nanorods illuminated with linearly and circularly polarized femtosecond laser pulses. Simulations show that the tunability of the field enhancement originates from the mode-mixing property of circularly polarized illumination, meaning simultaneous excitation of multiple plasmon modes of the nanostructures. Performing trajectory calculations of the photoemitted electrons, we prove that the kinetic energy scaling law remains the same irrespective to the polarization state.

Kinematics of sea star legged locomotion.

Sea stars have slower crawling and faster bouncing gaits. Both speed and oscillation amplitude increase during the transition from crawling to oscillating. In the bouncy gait, oscillating vertical velocities precede oscillating horizontal velocities by 90 deg, as reflected by clockwise circular hodographs. Potential energy precedes horizontal kinetic energy by 9.6 deg and so they are nearly in phase. These phase relationships resemble terrestrial running gaits, except that podia are always on the ground. Kinetic and potential energy scale with body mass as Mb 1.1, with the change in kinetic energy consistently two orders of magnitude less, indicating that efficient exchange is not feasible. Frequency of the bouncy gait scales with Mb-0.14, which is similar to continuously running vertebrates and indicates that gravitational forces are important. This scaling differs from the Hill model, in which scaling of muscle forces determine frequency. We propose a simple torque-stabilized inverted pendulum (TS-IP) model to conceptualize the dynamics of this gait. The TS-IP model incorporates mathematics equivalent to an angular spring, but implemented by a nearly constant upward force generated by the podia in each step. That upward force is just larger than the force required to sustain the underwater weight of the sea star. Even though the bouncy gait is the rapid gait for these sea stars, the pace of movement is still very slow. In fact, the observed Froude numbers (10-2 to 10-3) are much lower than those typical of vertebrate locomotion and are as low or lower than those reported for slow-walking fruit flies, which are the lowest values for pedestrian Froude numbers of which we are aware.

Magnetized decaying turbulence in the weakly compressible Taylor-Green vortex

Magnetohydrodynamic (MHD) turbulence affects both terrestrial and astrophysical plasmas. The properties of magnetized turbulence must be better understood to more accurately characterize these systems. This work presents ideal MHD simulations of the compressible Taylor-Green vortex under a range of initial subsonic Mach numbers and magnetic field strengths. We find that regardless of the initial field strength, the magnetic energy becomes dominant over the kinetic energy on all scales after at most several dynamical times. The spectral indices of the kinetic and magnetic energy spectra become shallower than k^{-5/3} over time and generally fluctuate. Using a shell-to-shell energy transfer analysis framework, we find that the magnetic fields facilitate a significant amount of the energy flux and that the kinetic energy cascade is suppressed. Moreover, we observe nonlocal energy transfer from the large-scale kinetic energy to intermediate and small-scale magnetic energy via magnetic tension. We conclude that even in intermittently or singularly driven weakly magnetized systems, the dynamical effects of magnetic fields cannot be neglected.

Abrasion regimes in fluvial bedrock incision

AbstractRiver incision into bedrock drives landscape evolution and couples surface changes to climate and tectonics in uplands. Mechanistic bedrock erosion modeling has focused on plucking—the hydraulic removal of large loosened rock fragments—and on abrasion—the slower fracturing-driven removal of rock due to impacts of transported sediment—which produces sand- or silt-sized fragments at the mineral grain scale (i.e., wear). An abrasion subregime (macro-abrasion) has been hypothesized to exist under high impact energies typical of cobble or boulder transport in mountain rivers, in which larger bedrock fragments can be generated. We conducted dry impact abrasion experiments across a wide range of impact energies and found that gravel-sized fragments were generated when the impact energy divided by squared impactor diameter exceeded 1 kJ/m2. However, the total abraded volume followed the same kinetic-energy scaling regardless of fragment size, holding over 13 orders of magnitude in impact energy and supporting a general abrasion law. Application to natural bedrock rivers shows that many of them likely can generate large fragments, especially in steep mountain streams and during large floods, transporting boulders in excess of 0.6 m diameter. In this regime, even single impacts can cause changes in riverbed topography that may drive morphodynamic feedbacks.

The scalar chemical potential in cosmological collider physics

Non-analyticity in co-moving momenta within the non-Gaussian bispectrum is a distinctive sign of on-shell particle production during inflation, presenting a unique opportunity for the “direct detection” of particles with masses as large as the inflationary Hubble scale (H). However, the strength of such non-analyticity ordinarily drops exponentially by a Boltzmann-like factor as masses exceed H. In this paper, we study an exception provided by a dimension-5 derivative coupling of the inflaton to heavy-particle currents, applying it specifically to the case of two real scalars. The operator has a “chemical potential” form, which harnesses the large kinetic energy scale of the inflaton, {overset{cdot }{phi}}_0^{1/2}approx 60H , to act as an efficient source of scalar particle production. Derivative couplings of inflaton ensure radiative stability of the slow-roll potential, which in turn maintains (approximate) scale-invariance of the inflationary correlations. We show that a signal not suffering Boltzmann suppression can be obtained in the bispectrum with strength fNL ∼ mathcal{O} (0.01–10) for an extended range of scalar masses lesssim {overset{cdot }{phi}}_0^{1/2} , potentially as high as 1015 GeV, within the sensitivity of upcoming LSS and more futuristic 21-cm experiments. The mechanism does not invoke any particular fine-tuning of parameters or breakdown of perturbation-theoretic control. The leading contribution appears at tree-level, which makes the calculation analytically tractable and removes the loop-suppression as compared to earlier chemical potential studies of non-zero spins. The steady particle production allows us to infer the effective mass of the heavy particles and the chemical potential from the variation in bispectrum oscillations as a function of co-moving momenta. Our analysis sets the stage for generalization to heavy bosons with non-zero spin.