New developments in field experiments in ASL: Kolmogorov 4/5 law and non-locality

    We report results of field and airborne experiments at large Reynolds numbers confirming the recently obtained equivalent form of the 4/5 Kolmogorov law (see Hosokawa, I. (2007) A Paradox concerning the Refined Similarity Hypothesis of Kolmogorov for Isotropic Turbulence, Prog. Theor. Phys., 118, 169–173). This and also exact purely kinematical relations demonstrate one of important aspects of non-locality of turbulent flows in the inertial range and stand in contradiction with the sweeping decorrelation hypothesis understood as statistical independence between large and small scales. The main point is that the 4/5 Komogorov law appears to be equivalent (roughly under the same assumptions) to the relation

                                                          <u₊²u_–>=<ε>r/30.                                           (1)         

    Here 2u₊=u₁(x+r)+u₁(x), 2u_–=u₁(x+r)–u₁(x); u₁(x) – is the longitudinal velocity component (in our case it will be just the streamwise velocity component) and <ε> – is the mean dissipation. Thus the relation (1) is a clear indication of absence of statistical independence between u₊ and u_–, i.e. between small and large scales.

    The experiments were performed with a measurement system, developed by the group of Prof. Tsinober, described in detail in our recent paper (Gulitski, G., Kholmyansky, M., Kinzelbach, W., Lüthi, B., Tsinober, A. and Yorish, S. (2007) Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 1. Facilities, methods and some general results, J. Fluid Mech., 589, 57–81) and consists of the multi-hot-wire probe connected to the anemometer channels, signal normalization device (sample-and-hold modules and anti-aliasing filters), data acquisition and calibration unit. The probe is built of five similar arrays. Each calibrated array allows obtaining three velocity components “at a point”. The differences between the properly chosen arrays give the tensor of the spatial velocity derivatives (without invoking of Taylor hypothesis); temporal derivatives can be obtained from the differences between the sequential samples. The Taylor micro-scale Reynolds numbers, Re_λ, for the experiments are shown in the table.

Experiment	102	SNM12	SNM11	Falcon	Jet
Reλ·10-3	10.7	5.9	3.4	1.6	0.05

Figure 1. Conventional 4/5 law (a). Verification of equation 1 (b).

    We exemplify the main results mentioned above in figure 1, showing the 4/5 law and its equivalent, as displayed by the relation (1), both normalized on <ε>r. It is seen that both hold for about 2.5 decades for the field experiments and more than for 3.5 decades in the airborne experiment. At Kfar Glikson measurement station, Israel, the measurements were performed from a mast of 10 m height (the corresponding data are marked “102”). At Sils-Maria, Switzerland (marked “SNM11” and “SNM12”) a lifting machine was used that allowed to reach various heights from about 1 m to 10 m. The airborne experiment (marked “Falcon”) was performed from the research aircraft of the DLR, Germany. “Jet” marks the experiment in a laboratory jet flow.

    Other related results will be given in the presentation.