Self-similar spectra of a meandering scalar plume

The concentration of any plume rapidly decreases as it spreads due to diffusion. For instance, take a plume of contaminants released from a localized steady source into the atmosphere; typically, as the contaminant plume advects along the mean wind or streamwise in the (x) direction, it also spreads in both the vertical (z) and transverse (y) directions due to turbulent motions. As the plume spreads, the local concentration reduces, and if the contaminant is hazardous, then it is desired that the local concentration is within safe limits when it comes in contact with humans, livestock or plants. Ideally, the magnitude of concentration varies continuously, and the background turbulent flow imposes a range of time scales on to the scalar field. Likewise, the instantaneous spatial distribution of concentration also has a range of length scales. Thus, at a fixed location, although the concentration might be safe at a particular time instance, it may exceed the safe limit at another time. This phenomenon is widely studied; numerically and experimentally, mainly due to its practical importance. However, to date, there are very few reliable models for the concentration spectrum in the case of point-source plumes.

Recently, The University of Sydney researchers: Dr. Krishna Talluru and Dr. Kapil Chauhan, in collaboration with Dr. Jimmy Philip at The University of Melbourne, investigated the effect of source height and source distance on concentration spectra. Their focus was on time scales for concentration and the dependence of concentration on different time scales or frequency as characterized by the spectrum of concentration. Their work is published in the Journal of Fluid Mechanics.

In brief, the research team performed a range of experiments to measure instantaneous concentration in the vertical and transverse directions across the plume when the plume was released at different heights in the turbulent boundary layer (TBL) as well as at various upstream locations. The researchers carried out their experiments in the Boundary Layer Wind Tunnel (BLWT) at the University of Sydney.

The authors observed that the concentration spectra in a narrow meandering plume portrayed a self-similar behavior in both transverse (y) and vertical (z, i.e., wall-normal) directions. Also, the experimental data revealed self-similarity when the amplitude of concentration spectra was scaled by the local concentration variance whereas frequency was suitably scaled utilizing the integral length scale of the streamwise velocity or the boundary layer thickness and the source velocity as length and velocity scales, respectively. Furthermore, the obtained data revealed that at each frequency, the concentration energy distributed across the y and z directions was proportional to concentration variance at that location.

In summary, the study outlined an estimation approach based on the information of the spectrum at one location obtained from a point measurement and plume characteristics: such as the plume width and the variance distribution. The results reported were seen to be consistent with non-dimensional analysis performed by the researchers. Remarkably, in an interview with Advances in Engineering, Dr. Krishna Talluru pointed out that the observed self-similarity confirmed the possibility for one to measure the spectrum at one position in the plume and estimate the spectrum at any other position, given some averaged quantities; an interesting observation of much significance when it comes to practical applications.