In this section
@article{Craske:2015:10.1017/jfm.2014.669,
author = {Craske, J and van, Reeuwijk M},
doi = {10.1017/jfm.2014.669},
journal = {Journal of Fluid Mechanics},
pages = {538--566},
title = {Energy dispersion in turbulent jets. Part 2. A robust model for unsteady jets},
url = {http://dx.doi.org/10.1017/jfm.2014.669},
volume = {763},
year = {2015}
}
TY - JOUR
AB - In this paper we develop an integral model for an unsteady turbulent jet that incorporates longitudinal dispersion of two distinct types. The model accounts for the difference in the rate at which momentum and energy are advected (type I dispersion) and for the local deformation of velocity profiles that occurs in the vicinity of a sudden change in the momentum flux (type II dispersion). We adapt the description of dispersion in pipe flow by Taylor (Proc. R. Soc. Lond. A, vol. 219, 1953, pp. 186–203) to develop a dispersion closure for the longitudinal transportation of energy in unsteady jets. We compare our model’s predictions to results from direct numerical simulation and find a good agreement. The model described in this paper is robust and can be solved numerically using a simple central differencing scheme. Using the assumption that the longitudinal velocity profile in a jet has an approximately Gaussian form, we show that unsteady jets remain approximately straight-sided when their source area is fixed. Straight-sidedness provides an algebraic means of reducing the order of the governing equations and leads to a simple advection–dispersion relation. The physical process responsible for straight-sidedness is type I dispersion, which, in addition to determining the local response of the area of the jet, determines the growth rate of source perturbations. In this regard the Gaussian profile has the special feature of ensuring straight-sidedness and being insensitive to source perturbations. Profiles that are more peaked than the Gaussian profile attenuate perturbations and, following an increase (decrease) in the source momentum flux, lead to a local decrease (increase) in the area of the jet. Conversely, profiles that are flatter than the Gaussian amplify perturbations and lead to a local increase (decrease) in the area of the jet.
AU - Craske,J
AU - van,Reeuwijk M
DO - 10.1017/jfm.2014.669
EP - 566
PY - 2015///
SN - 0022-1120
SP - 538
TI - Energy dispersion in turbulent jets. Part 2. A robust model for unsteady jets
T2 - Journal of Fluid Mechanics
UR - http://dx.doi.org/10.1017/jfm.2014.669
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000351862000012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR - http://hdl.handle.net/10044/1/18946
VL - 763
ER -