Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions

Abstract

The effect of scalar-field (temperature) boundary conditions on the inertial-convectiverange scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov n/3 prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertialconvective-range scaling exponents of the mixed, sixth-order, velocity-temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency -a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration -an effect that is notably less prominent in the other measures of internal intermittency.

Fluctuations of a passive scalar in a turbulent mixing layer

“…The scaling ranges are 120η < r < 280η and 100η < r < 200η for the streamwise and spanwise directions, respectively. Differently from the procedure used here, Lepore and Mydlarski [50] structure function because the statistic are not affected by intermittency and, at least in the homogeneous and isotropic case, are expected to scale according to the dimensional prediction [22,23]. In the present case dominated by mean shear, the dimensional prediction may be invalid.…”

“…In the spanwise direction, the range of scales with an approximately constant scaling exponent is even smaller. In order to identify scaling ranges for the analysis to follow, a procedure analogous to the one used by and Anselmet et al [49] and Lepore and Mydlarski [50] has been employed. The upper and lower bounds of the scaling range are defined by the locations at which the compensated second-order structure functions fall to 90% of their maximum value.…”

Péclet-number dependence of small-scale anisotropy of passive scalar fluctuations under a uniform mean gradient in isotropic turbulence

“…Accounting for this variation may be one of the key ingredients to suitably characterise different turbulently mixed states of a passive scalar. One successful example of this is found in the work by Lepore & Mydlarski (2012), who investigated higher-order scalar structure functions for two different scalar fields generated in two ways: heated cylinder and mandoline. They found that, although the scalar (temperature) is convected by an identical turbulent flow, the value of the thermal integral length scale differs between heated cylinder and mandoline, which results in the different values of the Péclet number based on this length scale.…”

“…They found that, although the scalar (temperature) is convected by an identical turbulent flow, the value of the thermal integral length scale differs between heated cylinder and mandoline, which results in the different values of the Péclet number based on this length scale. When plotted against the Péclet-number-compensated separation, which takes into account the variation of the thermal integral length scale, the higher-order scalar structure functions collapse at small scales for the two different scalar fields (Lepore & Mydlarski 2012).…”

Investigation of internal intermittency by way of higher-order spectral moments

“…Warhaft (2000) also confirmed that the intermittent behaviour of passive-scalar fields extends to scales larger than the dissipative ones, as is the case for velocity fields. Lepore & Mydlarski (2012) used the kurtosis of passive-scalar increments…”