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.

About the author

Krishna Talluru is a postdoctoral research fellow in the school of Aerospace, Mechanical and Mechatronic Engineering at the University of Sydney, Australia. He received his Bachelors degree in Mechanical Engineering in 2007 from the Indian Institute of Technology, Delhi, India. Later, he worked as a high school teacher before moving to Australia. He obtained his Ph.D. in 2014 from the University of Melbourne. He subsequently held postdoctoral positions at the University of Newcastle and the University of Sydney in Australia.

His research interests are turbulent boundary layers, scalar dispersion, wind engineering and buoyancy driven flows. His expertise is in experimental techniques that include hotwire anemometry, particle image velocimetry, pressure and load sensors, etc., and extracting flow physics using advanced signal and image processing methods.

About the author

Jimmy Philip is a senior lecturer in the Department of Mechanical Engineering at the University of Melbourne, Australia. He received his Bachelors and Masters degrees from the University of Pune and Indian Institute of Technology-Bombay, respectively, and his PhD from the faculty of Aerospace Engineering, Technion-Israel Institute of Technology. Subsequently, he was a post-doctoral researcher at LadHyX, Ecole Polytechnique, France and at the University of Melbourne. For about three years, he also worked as a Mechanical Engineer being a member of the Edison Engineering Development Program at the Global Research Center of the General Electric Company in India.

His research interests are shear flow instability, wall-bounded and free-shear turbulent flows including buoyancy effects, and entrainment mechanisms.

About the author

Kapil Chauhan is a lecturer in the School of Civil Engineering at the University of Sydney, Australia. He received his Bachelor’s degree in Mechanical Engineering from the Maharaja Sayajirao University, Baroda, India in 2000. Thereafter he obtained a Masters and PhD in Mechanical and Aerospace engineering from the Illinois Institute of Technology, Chicago in 2003 and 2007, respectively. His research interests are in turbulent wall-bounded flows, pollutant transport, urban heat islands, natural convection, and wind engineering. His expertise lies in measurement and experimental techniques, data-analysis and data-driven investigation of flow phenomena.


K. M. Talluru, Jimmy Philip, K. A. Chauhan. Self-similar spectra of point-source scalar plumes in a turbulent boundary layer. Journal of Fluid Mechanics (2019), volume 870, pages 698–717

Go To Journal of Fluid Mechanics (2019)

Check Also


Flow dynamics and heat transfer in partially porous microchannel heat sinks