Imperial College London

Dr Maarten van Reeuwijk

Faculty of EngineeringDepartment of Civil and Environmental Engineering

Reader in Environmental Fluid Mechanics



+44 (0)20 7594 6059m.vanreeuwijk Website




Miss Rebecca Naessens +44 (0)20 7594 5990




331Skempton BuildingSouth Kensington Campus






BibTex format

author = {Craske, J and Salizzoni, P and van, Reeuwijk M},
doi = {10.1017/jfm.2017.259},
journal = {Journal of Fluid Mechanics},
pages = {774--790},
title = {The turbulent Prandtl number in a pure plume is 3/5},
url = {},
volume = {822},
year = {2017}

RIS format (EndNote, RefMan)

AB - We derive a new expression for the entrainment coefficient in a turbulent plume usingan equation for the squared mean buoyancy. Consistency of the resulting expressionwith previous relations for the entrainment coefficient implies that the turbulent Prandtlnumber in a pure plume is equal to 3/5 when the mean profiles of velocity and buoyancyhave a Gaussian form of equal width. Entrainment can be understood in terms of thevolume flux, the production of turbulence kinetic energy or the production of scalarvariance for either active or passive variables. The equivalence of these points of viewindicates how the entrainment coefficient and the turbulent Prandtl and Schmidt numbersdepend on the Richardson number of the flow, the ambient stratification and the relativewidths of the velocity and scalar profiles. The general framework is valid for self-similarplumes, which are characterised by a power-law scaling. For jets and pure plumes it isshown that the derived relations are in reasonably good agreement with results fromdirect numerical simulations and experiments.
AU - Craske,J
AU - Salizzoni,P
AU - van,Reeuwijk M
DO - 10.1017/jfm.2017.259
EP - 790
PY - 2017///
SN - 1469-7645
SP - 774
TI - The turbulent Prandtl number in a pure plume is 3/5
T2 - Journal of Fluid Mechanics
UR -
UR -
VL - 822
ER -