Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer

Abstract

High-frequency fluctuations of temperature and of longitudinal and vertical velocity components have been measured with high-resolution probes in order to test the local-isotropy assumption. The simultaneous measurements of u’, w’, θ’ and the measurements in two space points with various separations in either the longitudinal or transverse directions were made in the large boundary layer (Rλ = 616) of the I.M.S.T. Air-Sea Interaction Simulation Tunnel. There is consistent evidence that the local-isotropy assumption is satisfied by the velocity field at all scales smaller than twenty times the Kolmogorov microscale (η ≈ 0.27 × 10−3 m), i.e. in the dissipative range of scales but not in the expected inertial subrange. The direct comparisons of the lateral and longitudinal temperature autocorrelation and structure functions show that the temperature field does not verify the isotropy assumption at all scales greater thanor equal to 37 and presumably at even smaller scales. This is confirmed by the study of the temperature-increment skewness and flatness factors. The spectral distribution -of the non-zero derivative skewness (S(θ) = +0.9) shows that it is essentially contributed by those scales for which the dynamic field satisfies isotropy.

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

“…Anisotropic turbulence evolving in a flat-plate boundary layer was detailed by Mestayer [14], confirming that local isotropy exists in the dissipative range of scales, typically smaller than 20 times the Kolmogorov microscale. Local isotropy at small scales is generally accepted at sufficiently high Reynolds number, provided that an inertial subrange separates the energetic scales from the dissipative ones.…”

Fronts in passive scalar turbulence

“…Predictions for the scaling of scalar gradient moments with the Péclet number are obtained by substituting r = η ∝ Pe −3/4 in the structure function expressions (5) and (7). It follows in particular that, in the presence of a large-scale gradient g, the skewness of the scalar gradient along this direction should decrease as Pe −1/2 .…”

“…Propagation phenomena of light beams and radio waves in the atmosphere are for example strongly influenced both by the magnitude and the spatial distribution of small-scale temperature gradients [2]. Their dynamical properties have been a subject of very accurate experimental investigations carried out in the last few years both in the atmosphere [2,3], in the ocean [4,5] and for laboratory turbulent flow [6][7][8][9]. A striking feature of all these situations is the presence of fronts (also called sheets or cliffs).…”

“…In particular, the probability density function (pdf) for the scalar derivatives along the direction of the large-scale scalar gradient are strongly skewed. Furthermore, the scalar gradient skewness (that should vanish for an isotropic field) is O(1), independently of the Péclet number [6][7][8][9]13,15]. This leads us to investigate scalar turbulence universality, i.e.…”

The inertial subrange in turbulent pipe flow: centreline

“…Yet, questions remain and laboratory experiments in a single facility in which the boundary conditions are well controlled are few. Using an inertial-subrange scaling that enables use of a linear ordinate, Saddoughi & Veeravalli (1994) were able to show that the inertial subrange and local isotropy do not necessarily coincide -see also Mestayer (1982). Of the two decades exhibiting a -5/3 slope on log-log axes, only the higher one had a spectral shear correlation coefficient approaching zero.…”