Experimental study of the structure of flow regions with negative turbulent kinetic energy production in confined three-dimensional shear flows with and without buoyancy

Abstract

Regions of negative turbulent kinetic energy ͑TKE͒ production are observed and studied in two different flows, namely in turbulent thermal Rayleigh-Bénard convection in a cubic cell, and in a mechanically agitated shear flow in absence of buoyancy, with a main focus on the small scale structure of the flow. The experimental investigation is performed using three-dimensional ͑3D͒ particle tracking velocimetry, which allows for measuring the three velocity components and the full tensor of velocity derivatives in a finite 3D volume. The capability to compute the TKE production term in its complete form P =−͗u i u j ͘S ij is crucial due to the three dimensionality of the flows. A comparative analysis of four different flow situations is performed in regions with positive and negative TKE production with and without buoyancy effects. In both, convective shear flow and shear flow without buoyancy, negative TKE production is associated with the unusual, more pronounced alignment of the velocity vector u with the first eigenvector 1 S of the mean rate-of-strain tensor, related to the stretching eigenvalue, ⌳ 1 S , in contrast to the positive TKE production associated with the alignment with the third eigenvector ͑i.e., related to the negative, compressing eigenvalue͒. In the negative TKE production region of convective flow we find ͑i͒ increased values for mean strain, ͑ii͒ increased values of the first contribution P ⌳ 1 in the eigenframe of the mean rate-of-strain tensor, and decreased values of the vertical contribution to the production term in a fixed frame of reference, ͑iii͒ stronger anisotropy of u, ͑iv͒ higher levels of fluctuating strain s 2 and enstrophy 2 , as well as ͑v͒ higher rates of their production, −s ij s jk s ki and i j s ij , compared to the respective values in positive TKE production region. In the shear flow without buoyancy, all the mentioned quantities are lower in the negative TKE production region than in the positive TKE production region. From this we conclude that the inverse energy transfer in the shear flow case without buoyancy is associated with depletion of the field of velocity derivatives. This does not occur in the cubic Rayleigh-Bénard convection cell. In this flow, buoyancy is observed to have an effect on three levels: the field of velocity derivatives, velocity fluctuations, and the mean flow field. It is inferred that buoyancy is able to maintain a region with the negative TKE production by acting on all these levels simultaneously.

Airside velocity measurements over the wind-sheared water surface using particle image velocimetry

“…Positive energy production represents the energy lost by the mean flow to the turbulence, whereas the negative energy production indicates the energy lost by the turbulence to the mean flow. A sustainable inverse energy transfer is possible only if any external force acts on both the field of fluctuating velocity and on the velocity derivative (Liberzon et al 2005). Therefore, the region of negative energy production may be governed by different physical mechanisms, which could be attributed due to the waveturbulence interaction in the near surface region.…”

Reynolds number dependence of relative dispersion statistics in isotropic turbulence

“…We can take some guidance on how best to achieve this compensation from simple stochastic models. 2,27 In the stochastic differential equation describing such models ͓e.g., Eq. ͑17͒ of Sawford et al 2 ͔, on inertial subrange scales the dissipation always occurs in the form 1/3 dt, and so if the dissipation is a function of time, we can simply change to a new "time" variable through the transformation d = 1/3 dt.…”

The Effects of Building Representation and Clustering in Large-Eddy Simulations of Flows in Urban Canopies

“…Higher values of the cosine indicate a better alignment. Indeed we make the same observation as Liberzon et al (2005) and note the strong alignment in the same region (475 m < x < 575 m). However, we also observe that, while strong global backscatter seems to start at a height of about 10 m in that area, the alignment is not very strong until a height of 25 m is reached.…”

“…10 is the relatively large area of global backscatter (negative shear production) indicating that the kinetic energy is being transferred from the turbulent motions to the mean flow. Global backscatter is not common and very particular flow conditions are needed to produce this transfer of energy (see Liberzon et al 2005 andChen et al 2006). Liberzon et al (2005) studied the occurrence of negative TKE production in a buoyant flow (Rayleigh-Bénard convection) and in a mechanical agitated neutral shear flow.…”

“…Global backscatter is not common and very particular flow conditions are needed to produce this transfer of energy (see Liberzon et al 2005 andChen et al 2006). Liberzon et al (2005) studied the occurrence of negative TKE production in a buoyant flow (Rayleigh-Bénard convection) and in a mechanical agitated neutral shear flow. They concluded that regions of negative shear production occur where the mean velocity vectorū is noticeably aligned with the first eigenvector of the strain rate tensor S i j = 0.5 ∂u i /∂ x j + ∂u j /∂ x i (corresponding to the largest positive eigenvalue, i.e.…”