Welcome to the high-Reynolds-number fluid flow group page. We are a small group consisting of two members at present (although we have a number of alumni):

*Stephen J. Cowley**Philip A. Stewart*

This page is effectively a marker and rather out-of-date; it is still very much under construction. However, a number of people (including prospective students) have complained about the fact that we have no page! If you just want to read more WWW pages written by Stephen Cowley, then most of the Faculty of Mathematics pages (with the exception of the undergraduate pages) were initially written by him.

High-Reynolds-number fluid mechanics includes:

- the study of the drag, lift and/or heat-transfer properties of cars, ships, submarines, turbine blades and aircraft wings/fuselages,
- the forces experienced by buildings and other fixed structures (e.g. the legs of oil rigs), and
- the flow in the larger blood vessels.

One approach to understanding high-Reynolds-number flows is to construct asymptotic descriptions exploiting the inverse Reynolds number as a small parameter. Although systematic asymptotic analysis can sometimes be rather `elaborate', the resulting simplified equations capture essential physics, focus attention on key areas of the flow, and often have wide applicability (especially when combined with numerical solutions of the reduced equations).

**Separation.** When fluid flows rapidly past a rigid body, thin
layers of high vorticity develop adjacent to the body surface. These
`boundary layers' need not remain attached to the surface of the body - they
can *separate*. In aerodynamics this process is often referred to as
stall. A description of the start of three-dimensional unsteady separation
has been obtained. Interests include the relationship between separation and
(i) phenomena that arise in the interior of turbulent boundary layers, and
(ii) cavitation.

**Transition to Turbulence.** Transition to turbulence is important
because it can dramatically affect key properties of a flow, e.g. the drag on
a body. Studies have focussed:

- on the growth of nonlinear Tollmien-Schlichting waves in the context of `bypass' transition (this work is also related to unsteady separation);
- on the growth of oblique waves in temporally and spatially developing boundary layers and shear layers;
- on the `phase-locked' mechanism of instability (in conjunction with Xuesong Wu of Imperial College).

*Inter alia*, the relationship between a number of different asymptotic
approaches has been identified, and key assumptions highlighted. In addition:

- receptivity problems have been studied in order to examine how disturbances can enter boundary layers and influence transition to turbulence;
- similar asymptotic techniques have been used to study
vortex breakdown (a phenomenon which fixes inter-aircraft distances near
airports).

**Vortex Sheets.** Infinitely thin vortex sheets have been used for
many practical calculations, such as the behaviour of wakes behind aircraft
wings. However, because of Kelvin-Helmholtz instabilities, such models are
ill-posed, and are often only valid for a limited time due to the formation
of singularities. Such limitations apply even when there is a stable density
jump across the vortex sheet. Asymptotic solutions have given an important
insight into the nature of these ubiquitous singularities. Moreover, by
introducing various *regularisations* into the idealised vortex sheet
model, e.g. surface tension and/or viscosity, it should be possible to
understand analytically how vortex sheets roll-up in spirals. Since (i) the
thin shear layers that repeatedly form in high-Reynolds-number turbulent flow
will be subject to Kelvin-Helmholtz instability, and (ii) it has been argued
that spiral structures are generic features of turbulent flow, one of the
aims of this study is to provide an insight into a fundamental building block
of turbulence.

© Stephen J. Cowley, DAMTP, University of Cambridge.