Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the interaction between velocity increment and energy dissipation in the turbulent cascade
243
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We adress the problem of interactions between the longitudinal velocity increment and the energy dissipation rate in fully developed turbulence. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows for a precise characterization of the joint statistical properties of velocity increment and energy dissipation. In particular, it is possible to determine the differential equation that governs the evolution along scales of the joint probability density of these two quantities. The properties of this equation provide interesting new insights into the coupling between energy dissipation and velocity incrementas leading to small scale intermittency.
rate research
Read More
We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R_lambda, of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R_lambda, this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.
An experiment was performed using SPIV in the LMFL boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy, $varepsilon = 2 u langle s_{ij}s_{ij} rangle$ where $s_{ij}$ is the fluctuating strain-rate and $langle~rangle$ denotes ensemble averages. Also measured were all the moments of the full average deformation rate tensor, as well as all of the first, second and third fluctuating velocity moments except those involving pressure. The Reynolds number was $Re_theta = 7500$ or $Re_tau = 2300$. The results are presented in three separate papers. This first paper (Part I) presents the measured average dissipation, $varepsilon$ and the derivative moments comprising it. It compares the results to the earlier measurements of cite{balint91,honkan97} at lower Reynolds numbers and a new results from a plane channel flow DNS at comparable Reynolds number. It then uses the results to extend and evaluate the theoretical predictions of cite{george97b,wosnik00} for all quantities in the overlap region. Of special interest is the prediction that $varepsilon^+ propto {y^+}^{-1}$ for streamwise homogeneous flows and a nearly indistinguishable power law, $varepsilon propto {y^+}^{gamma-1}$, for boundary layers. In spite of the modest Reynolds number, the predictions seem to be correct. It also predicts and confirms that the transport moment contribution to the energy balance in the overlap region, $partial langle - pv /rho - q^2 v/2 rangle/ partial y$ behaves similarly. An immediate consequence is that the usual eddy viscosity model for these terms cannot be correct. The second paper, Part II, examines in detail the statistical character of the velocity derivatives. The details of the SPIV methodology is in Part III, since it will primarily be of interest to experimentalists.
In three dimensional turbulence there is on average a cascade of kinetic energy from the largest to the smallest scales of the flow. While the dominant idea is that the cascade occurs through the physical process of vortex stretching, evidence for this is debated. In the framework of the Karman-Howarth equation for the two point turbulent kinetic energy, we derive a new result for the average flux of kinetic energy between two points in the flow that reveals the role of vortex stretching. However, the result shows that vortex stretching is in fact not the main contributor to the average energy cascade; the main contributor is the self-amplification of the strain-rate field. We emphasize the need to correctly distinguish and not conflate the roles of vortex stretching and strain-self amplification in order to correctly understand the physics of the cascade, and also resolve a paradox regarding the differing role of vortex stretching on the mechanisms of the energy cascade and energy dissipation rate. Direct numerical simulations are used to confirm the results, as well as provide further results and insights on vortex stretching and strain-self amplification at different scales in the flow. Interestingly, the results imply that while vortex stretching plays a sub-leading role in the average cascade, it may play a leading order role during large fluctuations of the energy cascade about its average behavior.
An original experimental setup has been elaborated in order to get a better view of turbulent flows in a von Karman geometry. The availability of a very fast camera allowed to follow in time the evolution of the flows. A surprising finding is that the development of smaller whorls ceases earlier than expected and the aspect of the flows remains the same above Reynolds number of a few thousand. This fact provides an explanation of the constancy of the reduced dissipation in the same range without the need of singularity. Its cause could be in relation with the same type of behavior observed in a rotating frame.
Features of the turbulent cascade are investigated for various datasets from three different turbulent flows. The analysis is focused on the question as to whether developed turbulent flows show universal small scale features. To answer this question, 2-point statistics and joint multi-scale statistics of longitudinal velocity increments are analysed. Evidence of the Markov property for the turbulent cascade is shown, which corresponds to a 3-point closure that reduces the joint multi-scale statistics to simple conditional probability density functions (cPDF). The cPDF are described by the Fokker-Planck equation in scale and its Kramers-Moyal coefficients (KMCs). KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker-Planck equation for each dataset. The knowledge of these stochastic cascade equations enables to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. IFT is taken as a new tool to prove the optimal functional form of the Fokker-Planck equations and subsequently to investigate the question of universality of small scale turbulence. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multi-scale cascade, with other words their own stochastic fingerprint.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
