Passive scalar statistics in high-Péclet-number grid turbulence

Abstract

The statistics of a turbulent passive scalar (temperature) and their Reynolds number dependence are studied in decaying grid turbulence for the Taylor-microscale Reynolds number, R λ , varying from 30 to 731 (21 6 P e λ 6 512). A principal objective is, using a single (and simple) flow, to bridge the gap between the existing passive gridgenerated low-Péclet-number laboratory experiments and those done at high Péclet number in the atmosphere and oceans. The turbulence is generated by means of an active grid and the passive temperature fluctuations are generated by a mean transverse temperature gradient, formed at the entrance to the wind tunnel plenum chamber by an array of differentially heated elements. A well-defined inertial-convective scaling range for the scalar with a slope, n θ , close to the Obukhov-Corrsin value of 5/3, is observed for all Reynolds numbers. This is in sharp contrast with the velocity field, in which a 5/3 slope is only approached at high R λ . The Obukhov-Corrsin constant, C θ , is estimated to be 0.45-0.55. Unlike the velocity spectrum, a bump occurs in the spectrum of the scalar at the dissipation scales, with increasing prominence as the Reynolds number is increased. A scaling range for the heat flux cospectrum was also observed, but with a slope around 2, less than the 7/3 expected from scaling theory. Transverse structure functions of temperature exist at the third and fifth orders, and, as for even-order structure functions, the width of their inertial subranges dilates with Reynolds number in a systematic way. As previously shown for shear flows, the existence of these odd-order structure functions is a violation of local isotropy for the scalar differences, as is the existence of non-zero values of the transverse temperature derivative skewness (of order unity) and hyperskewness (of order 100). The ratio of the temperature derivative standard deviation along and normal to the gradient is 1.2 ± 0.1, and is independent of Reynolds number. The refined similarity hypothesis for the passive scalar was found to hold for all R λ , which was not the case for the velocity field. The intermittency exponent for the scalar, µ θ , was found to be 0.25 ± 0.05 with a possible weak R λ dependence, unlike the velocity field, where µ was a strong function of Reynolds number. New, higher-Reynolds-number results for the velocity field, which smoothly follow the trends of Mydlarski & Warhaft (1996), are also presented.

Fronts in passive scalar turbulence

“…Contrary to the expected Pe −1/2 behavior, the skewness of the scalar derivative along the large-scale gradient ∂ θ ≡ g · ∇θ/|g| does not show any measurable dependence on the Péclet number [6][7][8][9]30]. The corresponding pdf P(∂ θ) is strongly asymmetric with a sharp maximum located at −g, signaling the mean gradient expulsion out of the plateaux regions.…”

“…[31,32] to analyze experimental and numerical turbulence data. The sine functions are in fact absent in the expansion (9), since the scalar field is statistically invariant under the transformation φ → −φ. Furthermore, as a result of their opposite symmetries with respect to the transformation r → −r (φ → φ + π), even and odd orders are expanded as…”

“…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.…”

Evolution of passive scalar statistics in a spatially developing turbulence

“…Some flows have shear (jets or wakes) and some are shear-free (grid turbulence). In most shear-free flows, a mean scalar gradient is imposed at the inlet [22][23][24][25][26], but there are also studies where the grid is heated [12,27,28]. It is important to stress that almost all of the previous studies on shear-free scalar turbulence are either experiments carried out rather far downstream of the grid, or periodic box direct numerical simulations with an imposed mean scalar gradient.…”