The properties of integral models for planar and axisymmetric unsteady jets

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Title: The properties of integral models for planar and axisymmetric unsteady jets
Authors: Craske, J
Item Type: Journal Article
Abstract: This article reviews and builds upon recent progress that has been made in understanding the mathematical properties of integral models for unsteady turbulent jets. The focus is on models that describe the evolution of the volume flux and the momentum flux in a jet, whose source conditions are time dependent. A generalized approach that postpones making assumptions about the ‘internal’ properties of the flow, such as the radial dependence of the longitudinal velocity profile, turbulent transport and pressure, allows one to understand how the resulting integral equations are affected by model-specific assumptions. Whereas the assumptions invoked in previous unsteady jet models have resulted in a parabolic system of equations, generalized equations that are derived from first principles have a hyperbolic character and statistical stability that depends sensitively on assumptions that are normally invoked a priori. Unsteady axisymmetric jets with Gaussian velocity profiles have special properties, including a tendency to remain straight-sided (conical) and marginal stability in response to source perturbations. A distinct difference between planar jets and axisymmetric jets is that the mean energy flux, which plays a leading-order role in determining the unsteady dynamics of jets, is significantly lower in planar jets. We hypothesize that in order to maintain marginal stability the turbulence and pressure fields in planar jets adjust themselves, relative to axisymmetric jets, to compensate for the lower mean energy flux.
Issue Date: 18-Oct-2016
Date of Acceptance: 11-Aug-2016
ISSN: 0272-4960
Publisher: Oxford University Press
Journal / Book Title: IMA Journal of Applied Mathematics
Copyright Statement: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: EPSRC
Keywords: Applied Mathematics
Publication Status: Published
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering

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