Redistribution Of Turbulent Kinetic Energy Research Articles

Turbulent kinetic energy redistribution in a gravity current interacting with an emergent cylinder

Gravity currents are flows driven by density gradients between two or more contacting fluids and play a key role in nature and industrial environments via global ocean circulations, climate variability and the distribution of airborne pollutants. In the present work, we study, experimentally, the changes induced by an emergent vertical PVC cylinder on the mean and turbulent flow fields of an unsteady bottom-generated lock release gravity current. Tests were carried out, with and without the cylinder, in refractive index matching conditions and instantaneous velocities were acquired with a Particle Image Velocimetry system. The mean velocity field, Reynolds stresses and terms of turbulent kinetic energy (TKE) budget for the currents head were presented and discussed. The results show that the adverse pressure gradient generated by the cylinder induces a uniform deceleration of the current head. Hence, there are no appreciable differences on the spatial distribution of the mean velocities in the current head, compared to the undisturbed current. On the other hand, the changes on the turbulent flow field are remarkable. The total diffusion of TKE decays in the inner part of the head while becoming stronger at the interface between the two fluids, as the current approaches the cylinder. This is associated to an increase of the diffusion term due to pressure fluctuations, that acts against diffusion due to velocity fluctuations and contributes to disrupt the transport of TKE from the interface between the fluids and the inner part of the current. As a result, in the presence of an obstacle, Reynolds stresses are suppressed in the inner part of the current head and enhanced at the interface.

A quantitative study on the turbulent kinetic energy redistribution in the near free-water-surface region of open channel flows

Open channel flows (OCFs) exhibit unique characteristics compared with other wall-bounded flows due to the presence of a free water surface. One of the well-known features is the turbulence kinetic energy (TKE) redistribution phenomenon in the near free-water-surface region. Unlike previous qualitative demonstrations, the present study aims providing a quantitative investigation of this phenomenon. Specifically designed super long domain direct numerical simulations (DNSs) of OCFs and closed channel flows (CCFs) are performed at three low-to-moderate friction Reynolds numbers (Reτ = 180–1000). The numerical configurations of the two flows (i.e., temporal and spatial resolution, domain size, Reynolds number, etc.) at identical Reτ are set to be the same, with the upper boundary being the only difference between them, to allow meaningful comparisons while super long domain sizes are adopted to facilitate fully spectral comparisons of the TKE features between the two flows. With such specifically designed DNS datasets, quantitative investigations of the TKE redistribution phenomenon in OCFs have been made. It is revealed that, as Reτ increases from 180 to 1000, the streamwise and spanwise TKE components of OCFs are higher than those of CCFs by 12%–23% and 28%–17%, respectively, while in the vertical direction OCFs are lower in TKE by 44%–31%. Overall, the TKE of OCFs is higher than that of CCFs by 3%–9% as Reτ increases from 180 to 1000. The comparison of OCFs and CCFs in pre-multiplied energy spectra reveals that VLSMs play a dominant role in the TKE redistribution phenomenon in OCFs.

Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers

Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to $Re_\tau =2000$ . Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant $\kappa =0.363$ occurs for OCF at $Re_\tau =2000$ , distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength $\lambda _x>3 h$ or spanwise wavelength $\lambda _z>0.5 h$ contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing $Re_\tau$ . In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.

Modulation of turbulence by saltating particles on erodible bed surface

Abstract

Effect of the nature of vitiated crossflow on the flow-field of a transverse reacting jet

The effect of the nature of vitiated crossflow on the structure and dynamics of non-reacting/reacting transverse jets is investigated. In this study, the vitiated crossflow is produced either by a low-swirl burner (LSB) that adds a swirling component to the crossflow or a bluff-body burner (BBB) that produces a uniform crossflow. The jet fluid is injected through a contoured injector, which provides a top-hat velocity profile. The swirling crossflow exhibits considerable swirl at the point of injection of the transverse jet. Two component high-repetition-rate PIV measurements demonstrate the influence of a vitiated crossflow generated by a low-swirl/bluff-body burner on the near-wake flow-field of the jet. Measurements at a plane below the injection location of the jet indicate that there is a continuous entrainment of PIV particles in case of swirling crossflow. The time-averaged flow-field shows that the velocity field for reacting/non-reacting jets in the LSB crossflow exhibits higher velocity gradients, in the measurement plane along jet cross section, as compared to BBB crossflow. It is found that the vorticity magnitude is lower in case of jets in the BBB crossflow and there is a delay in the formation of the wake vortex structure. The conditional turbulent statistics of the jet flow-field in the two crossflows shows that there is a higher degree of intermittency related to the wake vortex structure in case of a BBB crossflow, which results in a non-Gaussian distribution of the turbulent statistics. The wake Strouhal number calculation shows the influence of the nature of crossflow on the rate of wake vortex shedding. The wake Strouhal number for the jets in BBB crossflow is found to be lower than for the LSB crossflow. A decrease in the wake Strouhal number is observed with an increase in the nozzle separation distance. There is an increase in the dilatation rate owing to heat release which results in higher wake Strouhal number for reacting jets as compared to non-reacting jets. The POD analysis of the reacting and non-reacting jets shows the wake vortex structures to be the dominant flow structures in this study. There is a redistribution of turbulent kinetic energy from the shear layer to the coherent wake vortex structure with an increase in the nozzle separation distance. The wake structures in the near-wake region of jets in LSB crossflow are found to have a larger contribution to the kinetic energy as compared to jets in BBB crossflow.

Direct numerical simulation of turbulent flow in a spanwise rotating square duct at high rotation numbers

In this paper, direct numerical simulations have been performed to study the effects of Coriolis force on the turbulent flow field confined within a square duct subjected to spanwise system rotations at high rotation numbers. In response to the system rotation, secondary flows appear as large streamwise counter-rotating vortices, which interact intensely with the four boundary layers and have a significant impact on flow statistics, velocity spectra and coherent structures. It is observed that at sufficiently high rotation numbers, a Taylor–Proudman region appears and complete laminarization is almost reached near the top and side walls. The influence of large organized secondary flows on the production rate and re-distribution of turbulent kinetic energy has been investigated through a spectral analysis. It is observed that the Coriolis force dominates the transport of Reynolds stresses and turbulent kinetic energy, and forces the spectra of streamwise and vertical velocities to synchronize within a wide range of scales.

Coherent structures and their interactions in smooth open channel flows

The study presents experimental results of coherent structures and their interactions in a smooth open channel flow based on measurement of instantaneous two-dimensional velocity vectors with particle image velocimetry. The sampled data were analyzed through techniques of ensemble average, vortex extraction, and proper orthogonal decomposition (POD). Redistribution of turbulent kinetic energy is observed in the near-surface region. The spanwise vortices, which are closely related to hairpin vortices, exhibit a clear dependence on Reynolds number of the flow. Hairpin vortex packets and long streamwise vortices are identified as typical large-scale and super-scale coherent structures, respectively, and their interaction is revealed by examining the relationship between the population density of spanwise vortices and the coefficient functions of the first POD mode. Interactions between large-scale and super-scale structures have been recognized to support the hypothesis of closed-loop feedback cycle.

The URAPS closure for the normalized Reynolds stress

The Reynolds-averaged Navier–Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier–Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/ δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.

Energy cascade and spatial fluxes in wall turbulence

Real turbulent flows are difficult to classify as either spatially homogeneous or isotropic. Nonetheless these idealizations allow the identification of certain universal features associated with the small-scale motions almost invariably observed in a variety of different conditions. The single most significant aspect is a flux of energy through the spectrum of inertial scales related to the phenomenology commonly referred to as the Richardson cascade. Inhomogeneity, inherently present in near-wall turbulence, generates additional energy fluxes of a different nature, corresponding to the spatial redistribution of turbulent kinetic energy. Traditionally the spatial flux is associated with a single-point observable, namely the turbulent kinetic energy density. The flux through the scales is instead classically related to two-point statistics, given in terms of an energy spectrum or, equivalently, in terms of the second-order moment of the velocity increments. In the present paper, starting from a suitably generalized form of the classical Kolmogorov equation, a scale-by-scale balance for the turbulent fluctuations is evaluated by examining in detail how the energy associated with a specific scale of motion – hereafter called the scale energy – is transferred through the spectrum of scales and, simultaneously, how the same scale of motion exchanges energy with a properly defined spatial flux. The analysis is applied to a data set taken from a direct numerical simulation (DNS) of a low-Reynolds-number turbulent channel flow. The detailed scale-by-scale balance is applied to the different regions of the flow in the various ranges of scales, to understand how – i.e. through which mechanisms, at which scales and in which regions of the flow domain – turbulent fluctuations are generated and sustained. A complete and formally precise description of the dynamics of turbulence in the different regions of the channel flow is presented, providing rigorous support for previously proposed conceptual models.

Zone conditional assessment of flame-generated turbulence with DNS database of a turbulent premixed flame

Zone conditional two-fluid equations are derived and validated against a DNS database for a turbulent premixed flame. The conditional statistics of major flow variables are investigated to understand the mechanism of flame-generated turbulence. The flow field in the burned region shows substantially increased, highly anisotropic turbulence to conserve mass through a flamelet surface. The transverse component may be larger than the axial component for a distributed pdf of the flamelet orientation angle in the middle of the flame brush. The opposite occurs due to redistribution of turbulent kinetic energy and flamelet orientation mostly normal with respect to the mean flow at the end of the flame brush. The major source or sink terms of turbulent kinetic energy are the interfacial transfer by the mean reaction rate and the work terms induced by fluctuating pressure and velocity on the flame surface. Ad hoc modeling of some interfacial terms may be required for further application of the two-fluid model for modeling turbulence in turbulent premixed combustion simulations.

Large-eddy simulations of the wind-induced turbulent Ekman layer

At urbulent Ekman layer created by a steady wind near the water surface is investigated using the numerical method of large-eddy simulations. The classical case of a flow unaffected by density stratification and surface waves is revisited to understand the internal structure of the flow and implications of the traditional assumptions of constant effective viscosity and the ‘f -plane’ approximation. A series of numerical experiments reveals that the Ekman solution needs correcting even in this case. The examination of the effective viscosity hypothesis confirms its validity but shows that the viscosity varies strongly with depth. It increases in the subsurface layer of thickness about 1/4 the turbulent length scale and decreases below this level. A Bessel function solution is proposed that corresponds to the approximate effective viscosity profile and matches with the LES results. Strong flow dependence on the latitude and wind direction is detected and explained by the effects of redistribution of turbulent kinetic energy between the velocity components and modification of the vertical transfer of turbulent momentum. In this paper, we consider the classical problem of a turbulent flow generated near the ocean surface by a steady wind stress in the presence of Earth’s rotation. Interest in this flow goes back to Ekman’s landmark work published in 1905. (An interesting historical review of Fridtjof Nansen’s polar expedition and other events preceding Ekman’s paper is given by Walker (1991).) Ekman assumed a balance between the Coriolis force, viscous friction and the pressure gradient, adopted the approximation of constant vertical eddy viscosity Az ,a ndderived a solution now known as the ‘Ekman spiral’. In the case of a steady wind in the x-direction, the steady-state Ekman velocity profile in the open ocean is (for the northern hemisphere) u = V0 cos π + π D z

A model for the reduction of the turbulent energy redistribution by compressibility

Compressibility may strongly reduce the redistribution of turbulent kinetic energy. The question of how such effects can be taken into account in turbulence models is addressed here. First, a corresponding stochastic turbulence model is developed on the basis of a simplification of the generalized Langevin model for turbulent velocities. This model is then reduced to a deterministic model that extends existing methods by the consideration of structural compressibility effects. Combined with stochastic models for scalars, these velocity models may be used for compressible turbulent reacting flow simulations where the consideration of chemical reactions does not require approximations.

Dynamics and Energetics of Convective Plumes in the Atmospheric Surface Layer

Budgets of horizontal and vertical momentum and of turbulent kinetic energy in vertical direction within updrafts of convective plumes are evaluated, using experimental observations of velocities and temperatures and the corresponding pressure fluctuations calculated by a low-order dynamic model of plumes. The force balances revealed by the momentum budget study agree with the shape-preservation mechanisms for the plumes observed experimentally. The transport and redistribution of turbulent kinetic energy seen from the study of the budgets explain the relatively long lifetime of the convective plumes. Detailed pressure distributions within a convective plume and the role of the translation velocity in the development of the convective plume are discussed using the simulated flow fields.

Dynamic response of boundary-layer turbulence to oscillatory shear

The temporal response of a well-developed turbulent boundary layer to the superposition of oscillatory shear has been measured experimentally, over a wide range of frequencies. The response is primarily a periodic organization in magnitude of components of the turbulent velocity field at the forcing frequency. Oscillatory production of turbulence arises predominantly as a modulation of the mean production process in the parent boundary layer. Close to the wall, the relative phases of response of components of turbulent kinetic energy indicate that temporal redistribution of turbulent kinetic energy is driven by robust coherent motions of the underlying mean flow. The local directions of redistribution deduced from these measurements indicate a wall impingement (splatting) effect, consistent with characterizations from numerical simulation.

The Interaction between an Internal Gravity Wave and Turbulence in the Stably-Stratified Nocturnal Boundary Layer

Observations have been made of a stably-stratified nighttime boundary layer perturbed by Kelvin-Helmholtz internal waves with critical levels around 600 m. Significant turbulence intensities were measured although the time-mean gradient Richardson numbers were large and positive. It is shown by constructing energy budgets of wave and turbulent components separately that there is an essential flow of kinetic energy from wave to turbulence and that the mechanics of this exchange process depend upon the nonlinear character of the wave field. Turbulent energy budgets were followed through a wave cycle and revealed that turbulence production occurred during only one quarter of a wave period, the rest of the time being taken up by redistribution of turbulent kinetic energy (tke) among the three orthogonal components, relaxation under the effects of density stratification and dissipation. The principal path of energy dissipation is through conversion of vertical component tke to density fluctuations, which are in turn dissipated by molecular conductivity. Direct viscous dissipation of tke is negligible in comparison. This behavior is consistent with the quasi-two-dimensional character imposed on the turbulence by the strong stability and is clearly apparent in the behavior of the velocity and temperature spectra.