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The structure of turbulent shear flow

The structure of turbulent shear flow
The structure of turbulent shear flow
A theoretical investigation is made of the mixing layer between
two streams. The work is divided into four sections. The first
involves the solution of the mean problem of laminar and turbulent
mixing. The equations of motion are written in terms of a
similarity variable. An eddy viscosity hypothesis is made to
describe the shear stresses. The similarity equations for both
laminar and turbulent problems are solved numerically by an
iterative schemeo
The second section examines the stability of the mixing layer.
The Orr-Sommerfeld equation of hydrodynamic stability is solved
numerically. Doth cases of spatial and temporal amplification
are examined. The shear layer is shown to be unstable to both
spatially and temporally growing disturbances at all Reynolds
numbers. A correction is made for the divergence of the mean
flow and leads to a value of critical Reynolds number of 12.3.
The third section presents a model for the turbulent mixing
layer. A set of partial differential equations describing the
flow are obtained. A Fourier transform technique is employed
to reduce this set to an ordinary differential equation for the
fluctuating flow field. The homogeneous form of this equation is
solved numerically. The resulting predictions of fluctuating
velocity, pressure and their correlations are compared with
measured values. The agreement is good in certain cases and this
serves as a guide to components of the flow governed by non-linear
processes.
The final section examines the non-linear growth of the mixing
layer through transition from laminar to turbulent flow. A set of
integral momentum and energy equations are written in terms of a
number of shape parameters of mean and fluctuating flow. The
amplitude of disturbances is shown to grow rapidly and reach a
limiting value. A sudden growth of the mixing layer thickness
through transition is also predicted. Comparison is made with
experimental results.
University of Southampton
Morris, Philip John
2d966f1e-22d5-4dff-abbe-547c3b8332b6
Morris, Philip John
2d966f1e-22d5-4dff-abbe-547c3b8332b6
Lilley, G.M.
cd839b0d-bb58-4e77-bf93-ac99f1a5e58d

Morris, Philip John (1971) The structure of turbulent shear flow. University of Southampton, Doctoral Thesis, 291pp.

Record type: Thesis (Doctoral)

Abstract

A theoretical investigation is made of the mixing layer between
two streams. The work is divided into four sections. The first
involves the solution of the mean problem of laminar and turbulent
mixing. The equations of motion are written in terms of a
similarity variable. An eddy viscosity hypothesis is made to
describe the shear stresses. The similarity equations for both
laminar and turbulent problems are solved numerically by an
iterative schemeo
The second section examines the stability of the mixing layer.
The Orr-Sommerfeld equation of hydrodynamic stability is solved
numerically. Doth cases of spatial and temporal amplification
are examined. The shear layer is shown to be unstable to both
spatially and temporally growing disturbances at all Reynolds
numbers. A correction is made for the divergence of the mean
flow and leads to a value of critical Reynolds number of 12.3.
The third section presents a model for the turbulent mixing
layer. A set of partial differential equations describing the
flow are obtained. A Fourier transform technique is employed
to reduce this set to an ordinary differential equation for the
fluctuating flow field. The homogeneous form of this equation is
solved numerically. The resulting predictions of fluctuating
velocity, pressure and their correlations are compared with
measured values. The agreement is good in certain cases and this
serves as a guide to components of the flow governed by non-linear
processes.
The final section examines the non-linear growth of the mixing
layer through transition from laminar to turbulent flow. A set of
integral momentum and energy equations are written in terms of a
number of shape parameters of mean and fluctuating flow. The
amplitude of disturbances is shown to grow rapidly and reach a
limiting value. A sudden growth of the mixing layer thickness
through transition is also predicted. Comparison is made with
experimental results.

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Published date: 1 August 1971

Identifiers

Local EPrints ID: 437400
URI: http://eprints.soton.ac.uk/id/eprint/437400
PURE UUID: f5c6a183-4909-4b82-8438-bde15cdf0555

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Date deposited: 29 Jan 2020 17:33
Last modified: 29 Jan 2020 17:33

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