A study of large-scale atmospheric turbulent kinetic energy in wave-number frequency space

Tellus ◽  
1969 ◽  
Vol 21 (6) ◽  
pp. 760-788 ◽  
Author(s):  
Larry L. Wendell
2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.


2007 ◽  
Vol 129 (7) ◽  
pp. 842-851 ◽  
Author(s):  
Uri Vandsburger ◽  
Yiqing Yuan

A new self-excited jet methodology was developed for the mixing enhancement of jet fluid with its surrounding, quiescent, stagnant, or coflowing fluid. The nozzles, of a square or rectangular cross section, featured two flexible side walls that could go into aerodynamically-induced vibration. The mixing of nozzle fluid was measured using planar laser-induced fluorescence (PLIF) from acetone seeded into the nozzle fluid. Overall, the self-excited jet showed enhanced mixing with the ambient fluid; for example, at 390Hz excitation a mixing rate enhancement of 400% at x∕D=4 and 200% at x∕D=20 over the unexcited jet. The mixing rate was sensitive to the excitation frequency, increasing by 60% with the frequency changing from 200 to 390Hz (corresponding to a Strouhal number from 0.052 to 0.1). It was also observed that the mixing rate increased with the coflow velocity. To explain the observed mixing enhancement, the flow field was studied in detail using four-element hot wire probes. This led to the observation of two pairs of counter rotating large-scale streamwise vortices as the dominant structures in the excited flow. Shedding right from the nozzle exit, these inviscid vortices provided a rapid transport of the momentum and mass between the jet and the surrounding fluid at a length scale comparable to half-nozzle diameter. Moreover, the excited jet gained as much as six times the turbulent kinetic energy at the nozzle exit over the unexcited jet. Most of the turbulent kinetic energy is concentrated within five diameters from the nozzle exit, distributed across the entire jet width, explaining the increased mixing in the near field.


2017 ◽  
Vol 3 (2) ◽  
Author(s):  
M. Benz ◽  
T. Schulenberg

A new numerical model for stratified two-phase flows with wavy interface is derived in this study. Assuming an equilibrium condition between turbulent kinetic energy, potential energy, and surface energy, the turbulent length scale in the inner region of a two-layer turbulence approach can be described by a statistical model to account for the influence of the waves. The average wave number, which is an input parameter to this model, is taken from wave spectra. They can be predicted from a Boltzmann statistic of turbulent kinetic energy. The new turbulence model is compared with the two-phase k–ϵ turbulence model. Time-averaged flow properties calculated by the new approach, such as velocity, turbulence, and void profiles, are shown to be in good agreement with experimental data.


2015 ◽  
Vol 62 (3-4) ◽  
pp. 77-99 ◽  
Author(s):  
Donatella Termini

AbstractLaboratory experiments in a straight flume were carried out to examine the evolution of large-scale horizontal turbulent structures under flat-bed and deformed-bed conditions. In this paper, the horizontal turbulence of flow under these conditions is analyzed and compared. The conditioned quadrant method is applied to verify the occurrence of turbulent events. The distributions of horizontal Reynolds shear stress and turbulent kinetic energy are also presented and discussed. Results show the occurrence of an “initial” sequence of horizontal vortices whose average spatial length scales with the channel width. Under deformed-bed conditions, this spatial length does not change.


Author(s):  
B. Hu ◽  
S. Banerjee ◽  
K. Liu ◽  
D. Rajamohan ◽  
J. M. Deur ◽  
...  

We performed Large Eddy Simulation (LES) of a turbulent non-reacting n-Heptane spray jet, referred to as Spray H in the Engine Combustion Network (ECN), and executed a data analysis focused on key LES metrics such as fraction of resolved turbulent kinetic energy and similarity index. In the simulation, we used the dynamic structure model for the sub-grid stress, and the Lagrangian-based spray-parcel models coupled with the blob-injection model. The finest mesh-cell size used was characterized by an Adaptive Mesh Refinement (AMR) cell size of 0.0625 mm. To obtain ensemble statistics, we performed 28 numerical realizations of the simulation. Demonstrated by the comparison with experimental data in a previous study [7], this LES has accurately predicted global quantities, such as liquid and vapor penetrations. The analysis in this work shows that 14 realizations of LES are sufficient to provide a reasonable representation of the average flow behavior that is benchmarked against the 28-realization ensemble. With the current mesh, numerical schemes, and sub-grid scale turbulence model, more than 95% of the turbulent kinetic energy is directly resolved in the flow regions of interest. The large-scale flow structures inferred from a statistical analysis reveal a region of disorganized flow around the peripheral region of the spray jet, which appears to be linked to the entrainment process.


2009 ◽  
Vol 633 ◽  
pp. 191-231 ◽  
Author(s):  
MARCO SIMIANO ◽  
D. LAKEHAL ◽  
M. LANCE ◽  
G. YADIGAROGLU

The detailed investigation of an unstable meandering bubble plume created in a 2-m-diameter vessel with a water depth of 1.5 m is reported for void fractions up to 4% and bubble size of the order of 2.5 mm. Simultaneous particle image velocity (PIV) measurements of bubble and liquid velocities and video recordings of the projection of the plume on two vertical perpendicular planes were produced in order to characterize the state of the plume by the location of its centreline and its equivalent diameter. The data were conditionally ensemble averaged using only PIV sets corresponding to plume states in a range as narrow as possible, separating the small-scale fluctuations of the flow from the large-scale motions, namely plume meandering and instantaneous cross-sectional area fluctuations. Meandering produces an apparent spreading of the average plume velocity and void fraction profiles that were shown to remain self-similar in the instantaneous plume cross-section. Differences between the true local time-average relative velocities and the difference of the averaged phase velocities were measured; the complex variation of the relative velocity was explained by the effects of passing vortices and by the fact that the bubbles do not reach an equilibrium velocity as they migrate radially, producing momentum exchanges between high- and low-velocity regions. Local entrainment effects decrease with larger plume diameters, contradicting the classical dependence of entrainment on the time-averaged plume diameter. Small plume diameters tend to trigger ‘entrainment eddies’ that promote the inward-flow motion. The global turbulent kinetic energy was found to be dominated by the vertical stresses. Conditional averages according to the plume diameter showed that the large-scale motions did not affect the instantaneous turbulent kinetic energy distribution in the plume, suggesting that large scales and small scales are not correlated. With conditional averaging, meandering was a minor effect on the global kinetic energy and the Reynolds stresses. In contrast, plume diameter fluctuations produce a substantial effect on these quantities.


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