Classical plume theory: 1937-2010 and beyond

Developing a theoretical description of turbulent plumes, the likes of which may be seen rising above industrial chimneys, is a daunting thought. Plumes are ubiquitous on a wide range of scales in both the natural and the man-made environments. Examples that immediately come to mind are the vapour plumes above industrial smoke stacks or the ash plumes forming particle-laden clouds above an erupting volcano. However, plumes also occur where they are less visually apparent, such as the rising stream of warmair above a domestic radiator, of oil from a subsea blowout or, at a larger scale, of air above the so-called urban heat island. In many instances, not only the plume itself is of interest but also its influence on the environment as a whole through the process of entrainment. Zeldovich (1937, The asymptotic laws of freely-ascending convective flows. Zh. Eksp. Teor. Fiz., 7, 1463-1465 (in Russian)), Batchelor (1954, Heat convection and buoyancy effects in fluids. Q. J. R. Meteor. Soc., 80, 339-358) and Morton et al. (1956, Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A, 234, 1-23) laid the foundations for classical plume theory, a theoretical description that is elegant in its simplicity and yet encapsulates the complex turbulent engulfment of ambient fluid into the plume. Testament to the insight and approach developed in these early models of plumes is that the essential theory remains unchanged and is widely applied today. We describe the foundations of plume theory and link the theoretical developments with the measurements made in experiments necessary to close these models before discussing some recent developments in plume theory, including an approach which generalizes results obtained separately for the Boussinesq and the non-Boussinesq plume cases. The theory presented - despite its simplicity - has been very successful at describing and explaining the behaviour of plumes across the wide range of scales they are observed. We present solutions to the coupled set of ordinary differential equations (the plume conservation equations) that Morton et al. (1956) derived from the Navier-Stokes equations which govern fluid motion. In order to describe and contrast the bulk behaviour of rising plumes from general area sources, we present closed-form solutions to the plume conservation equations that were achieved by solving for the variation with height of Morton's non-dimensional flux parameter Γ - this single flux parameter gives a unique representation of the behaviour of steady plumes and enables a characterization of the different types of plume. We discuss advantages of solutions in this form before describing extensions to plume theory and suggesting directions for new research. © 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

EEFIT mission to Haiti following the 12th January 2010 earthquake

The Mw= 7.2 Haiti earthquake of 12th January 2010 caused extensive damage to buildings and other infrastructure in the epicentral region in and around Port-au-Prince. The Earthquake Engineering Field Investigation Team (EEFIT), which is based in the United Kingdom, organised a field mission to Haiti with the authors as the team members. The paper presents the geotechnical findings of the team including those relating to soil liquefaction and lateral spreading and discusses the performance of buildings, including historic buildings, and bridges. Unprecedented use was made of damage assessments made from remote images (i. e. images taken from satellites and aircraft) when planning the post-earthquake relief effort in Haiti and a principal objective of the team was to evaluate the accuracy of such assessments. Accordingly, 142 buildings in Port-au-Prince were inspected in the field by the EEFIT team; damage assessments had previously been made using remote images for all these buildings. On the basis of this survey, the tendency of remote assessments to underestimate damage was confirmed; it was found that the underestimate applied to assessments based on oblique images using the relatively new technique of Pictometry, as well as those based on vertical images, although to a lesser degree. The paper also discusses the distribution of damage in Port-au-Prince, which was found to be strongly clustered in ways that appear not to have been completely explained. © 2012 Springer Science+Business Media B.V.