Kinetic Energy Flux Research Articles

A Reduced Model for Salt-Finger Convection in the Small Diffusivity Ratio Limit

A simple model of nonlinear salt-finger convection in two dimensions is derived and studied. The model is valid in the limit of a small solute to heat diffusivity ratio and a large density ratio, which is relevant to both oceanographic and astrophysical applications. Two limits distinguished by the magnitude of the Schmidt number are found. For order one Schmidt numbers, appropriate for astrophysical applications, a modified Rayleigh–Bénard system with large-scale damping due to a stabilizing temperature is obtained. For large Schmidt numbers, appropriate for the oceanic setting, the model combines a prognostic equation for the solute field and a diagnostic equation for inertia-free momentum dynamics. Two distinct saturation regimes are identified for the second model: the weakly driven regime is characterized by a large-scale flow associated with a balance between advection and linear instability, while the strongly-driven regime produces multiscale structures, resulting in a balance between energy input through linear instability and energy transfer between scales. For both regimes, we analytically predict and numerically confirm the dependence of the kinetic energy and salinity fluxes on the ratio between solutal and thermal Rayleigh numbers. The spectra and probability density functions are also computed.

Experimental study of oscillating-grid turbulence interacting with a solid boundary

The interaction between oscillating-grid turbulence and a solid, impermeable boundary (positioned below, and aligned parallel to, the grid) is studied experimentally. Instantaneous velocity measurements, obtained using two-dimensional particle imaging velocimetry in the vertical plane through the centre of the (horizontal) grid, are used to study the effect of the boundary on the root-mean-square velocity components, the vertical flux of turbulent kinetic energy (TKE) and the terms in the Reynolds stress transport equation. Identified as a critical aspect of the interaction is the blocking of a vertical flux of TKE across the boundary-affected region. Terms of the Reynolds stress transport equations show that the blocking of this energy flux acts to increase the boundary-tangential turbulent velocity component, relative to the far-field trend, but not the boundary-normal velocity component. The results are compared with previous studies of the interaction between zero-mean-shear turbulence and a solid boundary. In particular, the data reported here are in support of viscous and ‘return-to-isotropy’ mechanisms governing the intercomponent energy transfer previously proposed, respectively, by Perot & Moin (J. Fluid Mech., vol. 295, 1995, pp. 199–227) and Walkeret al.(J. Fluid Mech., vol. 320, 1996, pp. 19–51), although we note that these mechanisms are not independent of the blocking of energy flux and draw parallels to the related model proposed by Magnaudet (J. Fluid Mech., vol. 484, 2003, pp. 167–196).

Higher-order turbulence statistics of wave–current flow over a submerged hemisphere

Higher-order turbulence characteristics such as turbulence production, turbulence kinetic energy flux, third order moments and velocity spectra associated with turbulent bursting events due to the influence of a submerged hemisphere under wave–current interactions are presented. The velocity components were measured using three dimensional (3D) 16 MHz micro-acoustic Doppler velocimetry (Micro-ADV). In the wave–current interactions, the contributions of turbulent bursting events such as ejections and sweeps significantly reduce in comparison to the current-only case. The distributions of the mean time intervals of ejection and sweeping events are found to alter due to the superposition of surface waves. Results also depict that the turbulence production in the wake region of the hemisphere reduces remarkably, due to the superposition of surface waves on the current. Further, spectral and co-spectral analysis demonstrates that there is a significant reduction of power spectral peak for both longitudinal and bottom-normal velocities upon superposition of surface waves, which signifies a remarkable change in energy distribution between different frequencies of waves.

Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

ABSTRACTIn this paper, we characterise the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence, restricted in a vertical plane, under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k−3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k−3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano–Obukhov scaling that transitions from a shallow k−11/5 form at large scales, to a steeper approximate k−3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterised by an approximate k−1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k−2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k−1.6 power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale-dependent nature of the corresponding flux.

Comparison of synthetic jet actuators based on sharp-edged and round-edged nozzles

Axisymmetric synthetic jet actuators based on a loudspeaker and on two types of flanged nozzles were tested and compared experimentally. The first type of the nozzle was a sharp-edged circular hole. The second one had a special design with fillets at inner and outer nozzle exit and with a small step in the middle of the nozzle. The function of the step was to prevent the flow reattachment during the extrusion stroke. The actuators with the two types of nozzles were operated at resonance and were compared first qualitatively using a simple phase locked flow visualization. Then the hot-wire anemometer was used to measure velocity distributions along nozzle axis and velocity profiles at the nozzle exit. Comparison of the nozzles was based on evaluation of the characteristic velocity and integral quantities (volumetric, momentum, and kinetic energy fluxes). It was found out that these quantities, which were evaluated at the nozzle exit, differ substantially for both nozzles. On the other hand the velocity flow field in farther distances from the nozzle exit area did not exhibit such prominent differences.

Устойчивый алгоритм согласования потоков импульса и кинетической энергии при перестройке сетки

Устойчивый алгоритм согласования потоков импульса и кинетической энергии при перестройке сетки

Modeling RF waves in spatially dispersive inhomogeneus plasma using an iterative wavelet spectral method

The wave equation for a spatially dispersive inhomogeneous magnetized plasma is given by an integro-differential equation. The effects caused by spatial dispersion in the directions perpendicular and parallel to the magnetic field are quite different. In this study, we show how to solve the wave equation using a newly developed iterative wavelet spectral method for two cases. In the first case, the method is applied to a propagating kinetic Alfven wave in the perpendicular direction and solved to all orders in FLR. To conserve the kinetic energy flux, first order corrections in equilibrium gradients are used in the dielectric response tensor. In the second case, we verify the method for a fast wave minority heating scenario and study the up- and downshift in the parallel wave number.

Measurements of suspended sediment transport and turbulent coherent structures induced by breaking waves using two-phase volumetric three-component velocimetry

Sediment suspension and transport under plunging regular waves was investigated in a laboratory surf zone using the volumetric three-component velocimetry technique. The two-phase flow measurements captured the motions of sediment particles simultaneously with the three-component, three-dimensional velocity fields of turbulent coherent structures (large eddies) induced by plunging breakers. Sediment particles were separated from fluid tracers based on a combination of particle spot size and brightness in the two-phase flow images. The interactions between the large eddies and bottom sediment were investigated in the outer surf zone. The measured data showed that breaker vortices impinging on the bottom was the primary mechanism that lifted sediment particles into suspension. High suspended sediment concentrations were found in the wall-jet region where the impinging flow was deflected outward and upward. Sediment particles were also trapped by counter-rotating vortices behind the down flow. Suspended sediment concentrations were significantly lower in the impingement zone where the fluid velocities were downward, even though the turbulent kinetic energy in the down flow was very high. Suspended sediment concentration was well correlated with vertical velocity and apparent shear stresses in the deflected flow, and with vorticity magnitude in the counter-rotating vortices. A linear relationship was found between net sediment flux and net turbulent kinetic energy flux over one wave cycle. It was found that a strong deflected flow in front of the impingement zone enhanced onshore sediment transport compared to a more symmetrical flow pattern, while counter-rotating vortices kept sediment particles in suspension for transport offshore after flow reversal. Onshore sediment transport was observed in less than 20% of the breaking waves. In most wave cycles, net sediment flux was directed offshore due to advection by predominantly offshore flow velocities.

Source spectra of the gravity waves obtained from momentum flux and kinetic energy over Indian region: Comparison between observations and model results

Using 8 years (May 2006 to March 2014) of high resolution and high accuracy GPS radiosonde observations available from a tropical station Gadanki (13.5°N, 79.2°E), India, we have investigated the climatology of gravity wave energy and zonal momentum fluxes in the lower stratosphere. We also obtained best fit spectrum model for the gravity waves (GWs) for this tropical station. In general, strong annual variation in the energy and momentum flux with maximum during Indian summer monsoon is observed in the lower stratospheric region (18–25km). By considering different source spectra, we have applied Gravitywave Regional or Global RAy Tracer (GROGRAT) model run on monthly basis using the source spectrum values at different altitudes on the ERA-Interim background fields to obtain the kinetic energy and zonal momentum fluxes for each of the spectra considered. These simulated fluxes are compared with the observed fluxes to arrive at the best fit spectrum model. It is found that the spectrum which represents the convection transient mountain mechanism that is purely anti-symmetric and anisotropic in nature is the best fit model for Gadanki location. This information would be useful in parameterization of the GWs in numerical models over Indian region.

Partitioning of integrated energy fluxes in four tail reconnection events observed by Cluster

AbstractWe present the partitioning of integrated energy flux from four tail reconnection events observed by Cluster, focusing on the relative contributions of Poynting flux, electron, H+ and O+ enthalpy, and kinetic energy flux in the tailward and earthward directions in order to study temporal and spatial features of each event. We further subdivide the Poynting flux into three frequency bands to examine the possible structures and waves that contribute most significantly to the total Poynting flux from the reconnection region. Our results indicate that H+ enthalpy flux is often dominant, but O+ enthalpy, electron enthalpy, Poynting flux, and H+ kinetic energy flux can contribute significant or greater total energy flux depending on spacecraft location with respect the current sheet, flow direction, temporal scale, and local conditions. We observe integrated H+ enthalpy fluxes that differ by factors of 3–4 between satellites, even over ion inertial length scales. We observe strong differences in behavior between H+ and O+ enthalpy fluxes in all events, highlighting the importance of species‐specific energization mechanisms. We find tailward‐earthward asymmetry in H+ enthalpy flux, possibly indicative of the influence of the closed earthward boundary of the magnetotail system. Frequency filtering of the Poynting flux shows that current sheet surface waves and structures on the timescale of current sheet flapping contribute significantly, while large‐scale structure contributions are relatively small. We observe that the direction and behavior of the Poynting flux differs between bands, indicating that the observed flux originates from multiple distinct sources or processes.

Three-dimensional diastolic blood flow in the left ventricle

Three-dimensional blood flow in a human left ventricle is studied via a computational analysis with magnetic resonance imaging of the cardiac motion. Formation, growth and decay of vortices during the myocardial dilation are analyzed with flow patterns on various diametric planes. They are dominated by momentum transfer during flow acceleration and deceleration through the mitral orifice. The posterior and anterior vortices form an asymmetric annular vortex at the mitral orifice, providing a smooth transition for the rapid inflow to the ventricle. The development of core vortex accommodates momentum for deceleration and for acceleration at end diastolic atrial contraction. The rate of energy dissipation and that of work done by viscous stresses are small; they are approximately balanced with each other. The kinetic energy flux and the rate of work done by pressure delivered to blood from ventricular dilation is well balanced by the total energy influx at the mitral orifice and the rate change of kinetic energy in the ventricle.

Effects of Geostrophic Kinetic Energy on the Distribution of Mesopelagic Fish Larvae in the Southern Gulf of California in Summer/Fall Stratified Seasons.

Effects of geostrophic kinetic energy flux on the three-dimensional distribution of fish larvae of mesopelagic species (Vinciguerria lucetia, Diogenichthys laternatus, Benthosema panamense and Triphoturus mexicanus) in the southern Gulf of California during summer and fall seasons of stronger stratification were analyzed. The greatest larval abundance was found at sampling stations in geostrophic kinetic energy-poor areas (<7.5 J/m3), where the distribution of the dominant species tended to be stratified. Larvae of V. lucetia (average abundance of 318 larvae/10m2) and B. panamense (174 larvae/10m2) were mostly located in and above the pycnocline (typically ~ 40 m depth). In contrast, larvae of D. laternatus (60 larvae/10m2) were mainly located in and below the pycnocline. On the other hand, in sampling stations from geostrophic kinetic energy-rich areas (> 21 J/m3), where mesoscale eddies were present, the larvae of the dominant species had low abundance and were spread more evenly through the water column, in spite of the water column stratification. For example, in a cyclonic eddy, V. lucetia larvae (34 larvae/10m2) extended their distribution to, at least, the limit of sampling 200 m depth below the pycnocline, while D. laternatus larvae (29 larvae/10m2) were found right up to the surface, both probably as a consequence mixing and secondary circulation in the eddy. Results showed that the level of the geostrophic kinetic energy flux affects the abundance and the three-dimensional distribution of mesopelagic fish larvae during the seasons of stronger stratification, indicating that areas with low geostrophic kinetic energy may be advantageous for feeding and development of mesopelagic fish larvae because of greater water column stability.

Conceptual duct shape design for horizontal-axis hydrokinetic turbines

In the present paper, conceptual duct shape design for kinetic energy extraction with hydrokinetic turbines is discussed. The goal is to nd a single-passage axisymmetric geometry that holds stable flow with maximum kinetic energy ux at duct throat. For nding the optimum duct shape, the fluid flow was numerically simulated in a wedge shaped space with Flow-Simulation Software. In a multi-stage conceptual design, tabulated con gurations were employed to study each geometrical characteristic separately. These include curvature of pro le camber, trailing edge shape, pro le tip shape, and duct exit cross sectional area. The revolved pro le of each duct consists of a well constrained composite curve with few degrees of freedom. The Sketcher environment of SolidWorks Software provides a feasible method of rebuilding constrained curves. Duct shape optimization was performed based on successive flow simulation and approximation of optimum geometric dimension at optimum flow condition. The drag coecients were compared with available experiments. Based on the numerical simulations with needle shaped leading edge, the duct throat velocity can be increased. Inversely, the flow blockage can reduce the kinetic energy flux at duct throat. The optimum duct shape has shown the greatest frictional drag coecient and the minimum flow separation.

Extending the diabatic surface layer wind shear profile for offshore wind energy

In this research the diabatic surface layer wind shear model is extended for offshore wind energy purposes to higher altitudes based on Gryning's wind profile and the resistance functions proposed by Byun. The wind profile is in theory applicable up to the boundary layer height, which is parametrized with the Rossby-Montgommery equation. The coefficient c of the Rossby-Montgommery equation is found to be stability dependent with decreasing values up to 0.04 for stable conditions and increasing values up to 0.17 for unstable conditions. The proposed shear profile has been validated with 1 year of offshore observation data, and a significant improvement in accuracy is found compared to traditional surface layer shear profiles or power laws. The influence of adopting this extended shear profile for wind energy is analysed in terms of the kinetic energy flux and blade root fatigue loads experienced by a wind turbine. It is found that, especially for stable conditions, results deviate significantly compared to using the traditional surface layer shear profile. The kinetic energy flux decreases by up to 15%.

Study of a collocated Lagrange‐remap scheme for multi‐material flows adapted to HPC

SummaryThis paper describes a collocated numerical scheme for multi‐material compressible Euler equations, which attempts to suit to parallel computing constraints. Its main features are conservativity of mass, momentum, total energy and entropy production, and second order in time and space. In the context of a Eulerian Lagrange‐remap scheme on planar geometry and for rectangular meshes, we propose and compare remapping schemes using a finite volume framework. We consider directional splitting or fully multi‐dimensional remaps, and we focus on a definition of the so‐called corner fluxes. We also address the issue of the internal energy behavior when using a conservative total energy remap. It can be perturbed by the duality between kinetic energy obtained through the conservative momentum remap or implicitly through the total energy remap. Therefore, we propose a kinetic energy flux that improves the internal energy remap results in this context. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Mean kinetic energy transport and event classification in a model wind turbine array versus an array of porous disks: Energy budget and octant analysis

An array of model turbines with rotors is compared experimentally to an array of model turbines with stationary porous disks. The main discrepancy in the mean velocity components between the two cases is found in the out-of-plane component while the fluctuations of the out-of-plane component are found to play a dramatically different role in the vertical flux of mean kinetic energy. The study has wide implications on the use of the actuator disk model as a parametrization for a rotor in computational work.

Long-Term Variability of the Wind Field over the Indian Ocean Based on ERA-Interim Reanalysis

A detailed study of long-term variability of winds using 30 years of data from the European Centre for Medium-range Weather Forecasts global reanalysis (ERA-Interim) over the Indian Ocean has been carried out by partitioning the Indian Ocean into six zones based on local wind extrema. The trend of mean annual wind speed averaged over each zone shows a significant increase in the equatorial region, the Southern Ocean, and the southern part of the trade winds. This indicates that the Southern Ocean winds and the southeast trade winds are becoming stronger. However, the trend for the Bay of Bengal is negative, which might be caused by a weakening of the monsoon winds and northeast trade winds. Maximum interannual variability occurs in the Arabian Sea due to monsoon activity; a minimum is observed in the subtropical region because of the divergence of winds. Wind speed variations in all zones are weakly correlated with the Dipole Mode Index (DMI). However, the equatorial Indian Ocean, the southern part of the trade winds, and subtropical zones show a relatively strong positive correlation with the Southern Oscillation Index (SOI), indicating that the SOI has a zonal influence on wind speed in the Indian Ocean. Monsoon winds have a decreasing trend in the northern Indian Ocean, indicating monsoon weakening, and an increasing trend in the equatorial region because of enhancement of the westerlies. The negative trend observed during the non-monsoon period could be a result of weakening of the northeast trade winds over the past few decades. The mean flux of kinetic energy of wind (FKEW) reaches a minimum of about 100 W m−2 in the equatorial region and a maximum of about 1500 W m−2 in the Southern Ocean. The seasonal variability of FKEW is large, about 1600 W m−2, along the coast of Somalia in the northern Indian Ocean. The maximum monthly variability of the FKEW field averaged over each zone occurs during boreal summer. During the onset and withdrawal of monsoon, FKEW is as low as 50 W m−2. The Southern Ocean has a large variation of about 1280 W m−2 because of strong westerlies throughout the year.

Shear-driven instabilities and shocks in the atmospheres of hot Jupiters

General circulation models of the atmosphere of hot Jupiters have shown the existence of a supersonic eastward equatorial jet. In this paper, we investigate the effects of compressibility on the atmospheric dynamics by solving the standard Euler equations. This is done by means of a series of simulations performed in the framework of the equatorial beta-plane approximation using the finite volume shock-capturing code RAMSES. At low resolution, we recover the classical results described in the literature: we find a strong and steady supersonic equatorial jet of a few km/s that displays no signature of shocks. We next show that the jet zonal velocity depends significantly on the grid meridional resolution. When that resolution is fine enough to properly resolve the jet, the latter is subject to a Kelvin-Helmholtz instability. The jet zonal mean velocity displays regular oscillations with a typical timescale of few days and a significant amplitude of about 15% of the jet velocity. We also find compelling evidence for the development of a vertical shear instability at pressure levels of a few bars. It seems to be responsible for an increased downward kinetic energy flux, significantly affecting the temperature of the deep atmosphere, and appears to act as a form of drag on the equatorial jet. This instability also creates velocity fluctuations that propagate upward and steepen into weak shocks at pressure levels of a few mbars. We conclude that hot Jupiter equatorial jets are potentially unstable to both a barotropic Kelvin-Helmholtz instability and a vertical shear instability. Upon confirmation using more realistic models, both instabilities could result in significant time variability of the atmospheric winds, may provide a small scale dissipation mechanism in the flow, and might have consequences for the internal evolution of hot Jupiters.

The cross-scale physical-space transfer of kinetic energy in turbulent premixed flames

Multi-scale interactions and kinetic-energy transfer between turbulence and flames are fundamental to understanding and modeling premixed turbulent reacting flows. In order to investigate these phenomena, direct numerical simulations of a turbulent premixed flame are analyzed in this study. The results reveal a flux of kinetic energy that involves a cross-scale transfer through the turbulence cascade and whose prevailing direction in the flame brush is from subgrid to resolved scales. The root cause of this reversal in energy transfer, termed subgrid-scale (SGS) backscatter, is the effect of thermal expansion in the subgrid scales, by which small amounts of enthalpy created by combustion heat release are transformed into small-scale kinetic energy by means of the SGS pressure-gradient velocity correlation. The resulting overload of SGS kinetic energy is transferred to the resolved scales through SGS backscatter. This cross-scale flux of energy, along with a larger one that relies on large-scale quantities only and does not involve the energy cascade, describes the transformation of combustion heat release into kinetic energy in the turbulent premixed flame. Based on scaling analyses, it is theorized that the contribution of the cross-scale flux to the total kinetic-energy augmentation vanishes in combustion regimes in which the flame-transit time is too short to allow for activation of the non-linear convective mechanisms of the energy cascade.

Monsoon low-level jet over the gateway of Indian summer monsoon: a comparative study for two distinct monsoon years

High-resolution radiosonde measurements are used to study the characteristics and dynamics of monsoon low-level jet at the monsoon onset region of Cochin (10.04 $$^\circ$$ N; 76.32 $$^\circ$$ E) in India under two contrasting monsoon years, 2013 and 2015. The core speed and core height of the low-level jet is significantly higher during the strong monsoon year of 2013 than for the monsoon-deficient year of 2015. The average core heights for these years are seen to exist at 2.03 and 2.20 km, respectively. The low-level jet-modulated parameters such as moisture flux, momentum flux and kinetic energy flux show higher values during monsoon of 2013 as compared to 2015. Among the monsoon low-level jet parameters, the moisture flux has the strongest influence on the observed rainfall over Cochin. Also, an exponential function is seen to best explain the moisture flux–rainfall relationship. The weakening of monsoon during 2015 is attributed most likely to an eastward shift of the core convective activity from the Indian subcontinent as revealed from satellite observation of the upper tropospheric humidity. A close association is seen between the rainfall over Cochin and the convective activity over the Indian subcontinent. Observational studies such as this, which links monsoon rainfall, monsoon low-level jet parameters and convective activity, are expected to enhance the understanding of monsoon processes in general and subsequently improve the forecasting skill of models.