Numerical analysis of wind velocity effects on fire-wind enhancement

Variation in flow characteristics triggered through the fire-wind interface can potentially damage the buildings during bushfires. Fire-wind enhancement which is referred to as the increase of wind velocity, caused by the fire-wind interaction, is one of the destructive phenomena in this regard. In spite of the significance, the underlying mechanism contributing to this phenomenon is still not well understood. This study employs computational fluid dynamic (CFD) simulation to fundamentally investigate the effects of free-stream wind velocity on fire-wind enhancement through analyzing the momentum and buoyancy of fluid. Fire-wind interaction is shown to cause the generation of fire-induced longitudinal negative pressure gradient which results in fire-induced pressure and viscous forces in longitudinal direction. These forces are further found as the prime reason for the distortion of the wind velocity profile. A module is implemented to the FireFOAM solver to calculate and extract these forces quantitatively. The results reveal that under a constant fire intensity, the level of distortion and/or enhancement in the wind velocity profile comparatively reduces with the increase of free-stream wind velocity. A new non-dimensional group (modified Euler number) is introduced to take into account dominant fire-induced forces causing fire-wind enhancement. Richardson number and the modified Euler number are employed to determine the influence of free-stream wind velocity and longitudinal distance from the fire source on wind velocity enhancement. Large-eddy simulation (LES) results indicate that while the level of enhancement generally depends on both Richardson and the modified Euler number, the location of the maximum level of enhancement along the plume centreline coincides with the maximum value of modified Euler number under a constant free-stream wind velocity scenario.     

LES analysis of fire source aspect ratio effects on fire-wind enhancement

Enhancement of wind by bushfire, referred to as bushfire-wind enhancement phenomenon, causes damages to buildings located in bushfire-prone areas by increasing pressure load around the structures. This study focuses on the effects of point source aspect ratio (AR) on the wind enhanced by fire. FireFOAM solver of OpenFOAM platform is used to perform Large Eddy Simulation analysis for different fire source aspect ratios under two different fire source conditions: (i) identical fire intensity (fire heat release rate per unit area) and (ii) identical fire heat release rate conditions. Simulations were performed for three different fire source aspect ratios under these fire source boundary conditions. An appropriate normalization group based on fire source hydraulic diameter was introduced for fire-induced pressure gradient to explain the variation of wind enhancement with fire source aspect ratio. The results reveal that under a constant fire intensity condition, increasing the fire source aspect ratio causes a higher normalized fire-induced pressure gradient which leads to more intensified wind enhancement. In contrast, the increase of fire source aspect ratio while fire heat release rate is kept constant culminates in a reduction in the normalized fire-induced pressure gradient, reducing wind enhancement. Moreover, with the increase of the fire source aspect ratio, the area of counter-rotating vortices (CRV) where maximum wind enhancement occurs is expanded. The results also show that with the increase of fire source aspect ratio, the length of flame attachment to the ground immediately downstream of fire increases. In addition to the longitudinal wind enhancement, the effects of fire source aspect ratio on vertical velocity were also analyzed based on the Richardson number defined by hydraulic diameter and flow reference velocity. The effects of the aspect ratio on flame length were also studied. It was shown as a result of the increase of aspect ratio for one unit, flame length increases by approximately 14% and reduces by 7% under constant fire intensity and constant fire heat release rate condition, respectively.     

Drag and lift reduction of a 3D bluff-body using active vortex generators

In this study, a passive flow control experiment on a 3D bluff-body using vortex generators (VGs) is presented. The bluff-body is a modified Ahmed body (Ahmed in J Fluids Eng 105:429–434 1983) with a curved rear part, instead of a slanted one, so that the location of the flow separation is no longer forced by the geometry. The influence of a line of non-conventional trapezoïdal VGs on the aerodynamic forces (drag and lift) induced on the bluff-body is investigated. The high sensitivity to many geometric (angle between the trapezoïdal element and the wall, spanwise spacing between the VGs, longitudinal location on the curved surface) and physical (freestream velocity) parameters is clearly demonstrated. The maximum drag reduction is ?12%, while the maximum global lift reduction can reach more than ?60%, with a strong dependency on the freestream velocity. For some configurations, the lift on the rear axle of the model can be inverted (?104%). It is also shown that the VGs are still efficient even downstream of the natural separation line. Finally, a dynamic parameter is chosen and a new set-up with motorized vortex generators is proposed. Thanks to this active device. The optimal configurations depending on two parameters are found more easily, and a significant drag and lift reduction (up to ?14% drag reduction) can be reached for different freestream velocities. These results are then analyzed through wall pressure and velocity measurements in the near-wake of the bluff-body with and without control. It appears that the largest drag and lift reduction is clearly associated to a strong increase of the size of the recirculation bubble over the rear slant. Investigation of the velocity field in a cross-section downstream the model reveals that, in the same time, the intensity of the longitudinal trailing vortices is strongly reduced, suggesting that the drag reduction is due to the breakdown of the balance between the separation bubble and the longitudinal vortices. It demonstrates that for low aspect ratio 3D bluff-bodies, like road vehicles, the flow control strategy is much different from the one used on airfoils: an early separation of the boundary layer can lead to a significant drag reduction if the circulation of the trailing vortices is reduced.     

Large-eddy simulation of flow separation on an airfoil at a high angle of attack and Re = 105 using Cartesian grids

Incompressible flow separating from the upper surface of an airfoil at an 18° angle of attack and a Reynolds number of Re = 10⁵, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data.     

The effects of freestream turbulence on the drag coefficient of a sphere

The effects of freestream turbulence intensity and integral length scale as freestream turbulent parameters on the drag coefficient of a sphere were experimentally investigated in a closed circuit wind tunnel. The Reynolds number, Re = Ud/ν, was varied from 2.2 × 10⁴ to 8 × 10⁴ by using spheres with diameter d of 20, 51 and 102 mm in addition to altering the freestream velocity, U. The freestream turbulence intensity Tu and flow integral length scale Λ were manipulated by the utilization of orifice perforated plates. The proper combination of orifice perforated plate hole diameter, sphere size, and sphere location along the center line of the wind tunnel enabled the independent alterations of turbulence intensity and relative integral length scale (Λ/d) from 1.8% to 10.7% and from 0.1 to 2.6, respectively, at each studied Reynolds number. Results show that over the range of conditions studied, the drag always decreases with increasing Tu and, the critical Reynolds number at which the drag coefficient is dramatically reduced is decreased by increasing Tu. Most interestingly, the drag at any particular Re and Tu may be significantly lowered by reducing Λ/d; this is particularly the case at high Re and Tu.     

Effects of velocity fluctuations on heat transfer enhancement

The three-dimensional velocity fluctuation effects on heat transfer enhancement were experimentally investigated using a wind tunnel system and cylinders placed upstream of the test section in the wind tunnel. The cylinders with different diameters were used as turbulators to generate vortical flow motions with three-dimensional velocity fluctuations. A heated plate, part of the tunnel wall, was placed far downstream of the cylinders such that it was subjected mainly to flows with velocity fluctuations but with negligible steady vortical motions. These studies included three-component velocity measurements to characterize the near-wall and cross-section velocity fields and to obtain the turbulent kinetic energy. The temperatures were measured by thermocouples on the heated plate to obtain the convection heat transfer coefficients and the Nusselt numbers. Results indicate that the heat transfer was enhanced by the velocity fluctuations, which is attributed to the modification of boundary layer velocity profiles without the modification of boundary layer thickness. The resulting normalized Nusselt number was approximately a parabolic function of a dimensionless parameter, the product of Reynolds number and normalized turbulent kinetic energy.     

Hydrodynamics and dilution of an oil jet in crossflow: The role of small-scale motions from laboratory experiment and large eddy simulations

Experimental results were presented for the release of diesel oil from a one-inch (2.5 cm) vertical pipe in a crossflow at 0.27 m/s. The ratio of jet velocity to crossflow speed was 5.0 and the Reynolds number based on jet velocity and pipe diameter was $7.1\times {10}^3$. In the experiments, the plume shape was photographed, and the oil droplets were measured at two vertical locations on the center axis of the plume. Acoustic Doppler velocimetry (ADV) data was also obtained and compared to numerical predictions. The plume was simulated using large eddy simulation (LES), and the mixture multiphase model. The impact of the oil buoyancy was captured by adding a transport term to the volume fraction equation. Using the rise velocity based on d₅₀ (volume-median) droplet size in the lower part of the plume allowed us to capture the lower boundary of the plume, but the estimated upper boundary of the plume penetrated less into the crossflow as compared to the experimental findings. However, using the rise velocity of the d₅₀ at the upper part of the plume allowed one to estimate the upper boundary of the plume. As the droplets are too small to be resolved by the LES, we could not use a systematic approach to allow the multiphase plume to spread to mimic the observations. Based on the simulation results, the interaction between the jet and crossflow yielded small-sized flow structures near the upper boundary of the plume. The wake vortices initiated from the leeward side of the plume showed an alternating vorticity pattern in the wake. The shear layer vortices were induced by Kevin-Helmholtz instabilities mostly on the windward side of the plume. The formation of counter rotating vortex pair (CVP) altered greatly the hydrodynamics of the jet from that of a vertical jet to manifest flow reversals in all directions. The formation of CVP is likely to enhance the mixing of chemicals and droplets within the plume.     

Generation of coherent structures in supersonic flow past a finite-span flat plate

The formation of coherent structures on a flat plate in a supersonic flow is numerically investigated both in the case of strong shock incidence on the plate and in the problem of oncoming harmonic waves having an intensity of 1–5% of the freestream pressure P ₀. The same mechanism of the coherent structure formation is noticed in both nonstationary problems; it is due to the manifestation of the secondary instability generated in the gas flow owing to the influence of the vortices formed at the lateral edges of the plate. An analysis of the incident wave enhancement at the rear of the plate is made for different wave intensities and wavelength to plate width ratios. The flow patterns in the plate wake indicate the generation of an intense expansion wave in this region, which accelerates the gas flow to the freestream velocity.     

Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

Response of the Sphere Wake to Freestream Fluctuations

Direct numerical simulations have been used to investigate the response of the wake of a sphere to freestream fluctuations. This study has been motivated by the need to understand particle-induced turbulence enhancement in particulate flows. A sequence of simulations of flow past a sphere have been carried out where the frequency and amplitude of the freestream fluctuations and the flow Reynolds number has been varied systematically. It has been suggested that turbulence enhancement is primarily caused by vortex shedding from particles (Gore and Crowe, 1989; Hetsroni, 1989). Our simulations of the forced wake indicate that turbulence enhancement may be attributed to natural vortex shedding only when the freestream fluctuation level is low and the Reynolds number is greater than about 300. In addition to natural vortex shedding, the current simulations also suggest another mechanism for turbulence enhancement. It is found that in the presence of freestream fluctuations, the wake behaves like an oscillator and returns large amounts of kinetic energy to the surrounding fluid at resonance. This mechanism is not associated with natural vortex shedding and is therefore capable of enhancing freestream turbulence even at Reynolds numbers less than 300. Simulations also indicate that when the turbulence intensity of the carrier fluid is high, this resonance mechanism might be solely responsible for turbulence enhancement. Finally, our simulations also suggest a possible explanation for the correlation between turbulence enhancement and the ratio of the particle size to the size of energy containing eddies of turbulence found by Gore and Crowe (1989). Received 5 October 1999 and accepted 14 October 1999     

Smooth and rough turbulent boundary layers at high Reynolds number

A 2-D turbulent boundary layer experiment with zero pressure gradient (ZPG) has been carried out over a rough and a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effects of the upstream conditions and the Reynolds number on the downstream flow. For a given set of upstream conditions, such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m from the inlet of the wind tunnel to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R120,000, for which measurements of the mean velocity are reported. It is shown that by fixing the upstream conditions, the mean deficit profiles collapse with the freestream velocity, , but to different curves depending on the upstream conditions and surface roughness. Moreover, the effects of the upstream conditions, the Reynolds number, and roughness are completely removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits scaling, . Consequently, the true asymptotic profile in the turbulent boundary layer is found in ZPG flow regardless of the range of Reynolds number, surface conditions and initial conditions.     

The dispersal processes within the tide‐modulated Changjiang River plume,China

The dispersal processes of the tide‐modulated Changjiang River plume, China, are studied by using a three‐dimensional hydrodynamical module of the COHERENS (A COupled Hydrodynamical–Ecological model for REgional and Shelf Seas). The model is driven by the river discharge and the M₂ tidal constituent. Modelled results show: (1) the fresh water, which forms the Changjiang River plume expanding southeastwards, is discharged mostly into the North Channel, the North Passage, and the South Passage; (2) the larger horizontal gradient outside the North Channel and the North Passage forms a strong plume front; (3) the Changjiang River plume is homogeneous vertically, and dispersing gradually within the computational domain, with an averaged propagating rate of 3.38 km/day, while the plume front is surface‐to‐bottom type, and trapped between ?10 and ?18m isobaths; and (4) both the plume length and the plume front intensity vary periodically. The maximum plume length occurs about 2 h after low slack water and the minimum plume length during high slack water. The maximum plume front intensity occurs during high slack water and the minimum plume front intensity during low slack water. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical Analysis of the Impact of the Interior Nozzle Geometry on Low Mach Number Jet Acoustics

The flow and acoustic fields of subsonic turbulent hot jets exhausting from three divergent nozzles at a Mach number M=0.12 based on the nozzle exit velocity are conducted using a hybrid CFD-CAA method. The flow field is computed by highly resolved large-eddy simulations (LES) and the acoustic field is computed by solving the acoustic perturbation equations (APE) whose acoustic source terms are determined by the LES. The LES of the computational domain includes the interior of the nozzle geometry. Synthetic turbulence is prescribed at the inlet of the nozzle to mimic the exit conditions downstream of the last turbine stage. The LES is based on hierarchically refined Cartesian meshes, where the nozzle wall boundaries are resolved by a conservative cut-cell method. The APE solution is determined on a block structured mesh. Three nozzle geometries of increasing complexity are considered, i.e., the flow and acoustic fields of a clean geometry without any built-in components, a nozzle with a centerbody, and a nozzle with a centerbody plus struts are computed. Spectral distributions of the LES based turbulent fluctuated quantities inside the nozzle and further downstream are analyzed in detail. The noise sources in the near field are noticeably influenced by the nozzle built-in components. The centerbody nozzle increases the overall sound pressure level (OASPL) in the near field with respect to the clean nozzle and the centerbody-plus-strut nozzle reduces it compared to the centerbody nozzle due to the increased turbulent mixing. The centerbody perturbed nozzle configurations generate a remarkable spectral peak at S t=0.56 which also occurs in the APE findings in the near field region. This tone is generated by large scale vortical structures shed from the centerbody. The analysis of the individual noise sources shows that the entropy term possesses the highest acoustic contribution in the sideline direction whereas the vortex sound source dominates the downstream acoustics.     

Large Eddy Simulation of boundary layer transition over an isolated ramp-type micro roughness element

Boundary layer transition over an isolated surface roughness element is investigated by means of numerical simulation. Large Eddy Simulation (LES) flow-modeling approach is employed to study flow characteristics and transition phenomenon past a roughness element immersed within an incoming developing boundary layer, at a height-based Reynolds number of 1170. LES numerical results are compared to experimental data from literature showing the time-averaged velocity distribution, the velocity fluctuation statistics and the instantaneous flow topology.Despite slight difference in the intensity of streamwise velocity fluctuations, the present LES results and experimental data show very good agreement. The mean flow visualization shows streamwise counter-rotating vortices pairs formation downstream of the obstacle. The primary pair induces an upwash motion and a momentum deficit that creates a Kelvin-Helmholtz type flow instability. The instantaneous flow topology reveals the formation of coherent K-H vortices downstream that produce turbulent fluctuations in the wake of the roughness element. These vortices are streched and lifted up when moving downstream. The velocity fluctuations results show that the onset of the turbulence is dominated by the energy transfer of large-scale vortices.     

Flow structures and heat transfer on dimples in a staggered arrangement

Vortex structures and heat transfer enhancement mechanism of turbulent flow over a staggered array of dimples in a narrow channel have been investigated using Large Eddy Simulation (LES), Laser Doppler Velocimetry (LDV) and pressure measurements for Reynolds numbers Re_H = 6521 and Re_H = 13,042.The flow and temperature fields are calculated by LES using dynamic mixed model applied both for the velocity and temperature. Simulations have been validated with experimental data obtained for smooth and dimpled channels and empiric correlations. The flow structures determined by LES inside the dimple are chaotic and consist of small eddies with a broad range of scales where coherent structures are hardly to detect. Proper Orthogonal Decomposition (POD) method is applied on resolved LES fields of pressure and velocity to identify spatial–temporal structures hidden in the random fluctuations. For both Reynolds numbers it was found that the dimple package with a depth h to diameter D ratio of h/D = 0.26 provides the maximum thermo-hydraulic performance. The heat transfer rate could be enhanced up to 201% compared to a smooth channel.     

Slope effects on the fluid dynamics of a fire spreading across a fuel bed: PIV measurements and OH* chemiluminescence imaging

Slope is among the most influencing factor affecting the spread of wildfires. A contribution to the understanding of the fluid dynamics of a fire spreading in these terrain conditions is provided in the present paper. Coupled optical diagnostics are used to study the slope effects on the flow induced by a fire at laboratory scale. Optical diagnostics consist of particle image velocimetry, for investigating the 2D (vertical) velocity field of the reacting flow and chemiluminescence imaging, for visualizing the region of spontaneous emission of OH radical occurring during gaseous combustion processes. The coupling of these two techniques allows locating accurately the contour of the reaction zone within the computed velocity field. The series of experiments are performed across a bed of vegetative fuel, under both no-slope and 30° upslope conditions. The increase in the rate of fire spread with increasing slope is attributed to a significant change in fluid dynamics surrounding the flame. For horizontal fire spread, flame fronts exhibit quasi-vertical plume resulting in the buoyancy forces generated by the fire. These buoyancy effects induce an influx of ambient fresh air which is entrained laterally into the fire, equitably from both sides. For upward flame spread, the induced flow is strongly influenced by air entrainment on the burnt side of the fire and fire plume is tilted toward unburned vegetation. A particular attention is paid to the induced air flow ahead of the spreading flame. With increasing the slope angle beyond a threshold, highly dangerous conditions arise because this configuration induces wind blows away from the fire rather than toward it, suggesting the presence of convective heat transfers ahead of the fire front.     

Study of Density Effects in Turbulent Buoyant Jets Using Large-Eddy Simulation

Large-Eddy simulations (LES) of spatially evolving turbulent buoyant round jets have been carried out with two different density ratios. The numerical method used is based on a low-Mach-number version of the Navier–Stokes equations for weakly compressible flow using a second-order centre-difference scheme for spatial discretization in Cartesian coordinates and an Adams–Bashforth scheme for temporal discretization. The simulations reproduce the typical temporal and spatial development of turbulent buoyant jets. The near-field dynamic phenomenon of puffing associated with the formation of large vortex structures near the plume base with a varicose mode of instability and the far-field random motions of small-scale eddies are well captured. The pulsation frequencies of the buoyant plumes compare reasonably well with the experimental results of Cetegen (1997) under different density ratios, and the underlying mechanism of the pulsation instability is analysed by examining the vorticity transport equation where it is found that the baroclinic torque, buoyancy force and volumetric expansion are the dominant terms. The roll-up of the vortices is broken down by a secondary instability mechanism which leads to strong turbulent mixing and a subsequent jet spreading. The transition from laminar to turbulence occurs at around four diameters when random disturbances with a 5% level of forcing are imposed to a top-hat velocity profile at the inflow plane and the transition from jet-like to plume-like behaviour occurs further downstream. The energy-spectrum for the temperature fluctuations show both −5/3 and −3 power laws, characteristic of buoyancy-dominated flows. Comparisons are conducted between LES results and experimental measurements, and good agreement has been achieved for the mean and turbulence quantities. The decay of the centreline mean velocity is proportional to x ^−1/3 in the plume-like region consistent with the experimental observation, but is different from the x ⁻¹ law for a non-buoyant jet, where x is the streamwise location. The distributions of the mean velocity, temperature and their fluctuations in the near-field strongly depend upon the ratio of the ambient density to plume density ρ_a/ρ₀. The increase of ρ_a/ρ₀ under buoyancy forcing causes an increase in the self-similar turbulent intensities and turbulent fluxes and an increase in the spatial growth rate. Budgets of the mean momentum, energy, temperature variance and turbulent kinetic energy are analysed and it is found that the production of turbulence kinetic energy by buoyancy relative to the production by shear is increased with the increase of ρ_a/ρ₀. Received 16 June 2000 and accepted 26 June 2001     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Large-eddy simulation of a turbulent forced plume

This paper reports on an application of large-eddy simulation (LES) to a spatially-developing round turbulent buoyant jet. The numerical method used is based on a low-Mach-number version of the governing equations for compressible flow which can account for density variations. The second-order centre-difference scheme is used for spatial discretization and an Adams–Bashforth scheme for temporal discretization. Comparisons are made between LES results, experimental measurements and plume theory for the forced plume under moderate Reynolds number and good agreement has been achieved. It is found that the plume spreading and the centerline maximum mean velocity strongly depend on the forcing conditions imposed on the inflow plane. The helical mode of instability leads to a larger spreading rate as compared to an axisymmetric mode. The enhanced entrainment is directly related to the strong turbulent momentum and energy transports between the plume and surrounding fluid induced by vortex dynamics. The entrainment ratio is about 0.09 and falls into the range of experimentally determined values. Budgets of the mean momentum and energy equations are analyzed. It is found that the radial turbulent transport nearly balances the streamwise convection and the buoyancy force in the axial momentum equation. Also, the radial turbulent stress is balanced by the streamwise convection in the energy equation. The energy-spectrum for the axial velocity fluctuations shows a −5/3 power law of the Kolmogorov decay, while the power spectrum for the temperature fluctuations shows both −5/3 and −3 power laws in the inertial-convective and inertial-diffusive ranges, respectively.