# A. Jonathan MestelImperial College London | Imperial · Department of Mathematics

A. Jonathan Mestel

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48

Publications

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## Publications

Publications (48)

Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In the absence of a magnetic field, various well-known self-similar flows arise, generalising that of von Kármán. Magnetic field instabilities with the same similarity structure are s...

A similarity solution of a three-dimensional boundary layer is investigated. The outer flow is given by U = ( - xz, - yz, z2), corresponding to an axisymmetric poloidal circulation with constant potential vorticity. This flow is an exact solution of the Navier-Stokes. A wall is introduced at y = 0 along which a boundary layer develops towards x = 0...

Trapped modes of the Helmholtz equation are investigated in infinite, 2D acoustic waveguides with Neumann or Dirichlet walls. A robust boundary element scheme is used to study modes both inside and outside the continuous spectrum of propagating modes. An effective method for distinguishing between genuine trapped modes and spurious solutions induce...

Steady Boussinesq flow in a weakly curved channel driven by a horizontal temperature
gradient is considered. Linear variation in the transverse direction is assumed so that the problem reduces to a system of ordinary differential equations. A series expansion in G, a parameter proportional to the Grashof number and the square root of the curvature,...

Dynamo action is considered in a conducting cylindrical annulus surrounded by an insulator. The driving velocity field is assumed to be linear in the axial coordinate and to satisfy the incompressible Navier–Stokes equations. Such flows have recently been shown to exist with no forcing other than the similarity structure. Magnetic field instabiliti...

Steady incompressible flow down a slowly curving circular pipe is considered, analytically and numerically. Both real and complex solutions are investigated. Using high-order Hermite–Padé approximants, the Dean series solution is analytically continued outside its circle of convergence, where it predicts a complex solution branch for real positive...

Steady, incompressible flow down a slowly curving circular pipe is considered. Both real and complex solutions of the Dean equations are found by analytic continuation of a series expansion in the Dean number, K. Higher-order Hermite-Pade approximants are used and the results compared with direct computations using a spectral method. The two techni...

Motivated by numerous biological and industrial applications relating to bypasses, mixing and leakage, we consider low-Reynolds-number flow through a shunt between two channels. An analytical solution for the streamfunction is found by matching biorthogonal expansions of Papkovich–Fadle eigenfunctions in rectangular subregions. The general solution...

The ductus arteriosus is one of several shunts in the cardiovascular system. It is a small vessel connecting the aortic arch and pulmonary artery that allows blood to bypass the pulmonary circulation. It is open during foetal development because the foetal lungs cannot function and oxygenation of the blood occurs by exchange with the maternal blood...

We present a global-in-radius linear analysis of the axisymmetric magnetorotational instability (MRI) in a collisional magnetized
plasma with Braginskii viscosity. For a galactic angular velocity profile Ω we obtain analytic solutions for three magnetic
field orientations: purely azimuthal, purely vertical and slightly pitched (almost azimuthal). I...

Dynamo action is considered in a network of intertwined, helical pipes of rectangular cross-section. The flow in each pipe is driven solely by a pressure gradient and it is assumed that both the velocity and magnetic fields remain helically symmetric as the system evolves. The exact laminar solution is followed into the nonlinear regime. In a previ...

We present a global-in-radius linear analysis of the axisymmetric
magnetorotational instability (MRI) in a collisional magnetized plasma with
Braginskii viscosity. For a galactic angular velocity profile $\Omega$ we
obtain analytic solutions for three magnetic field orientations: purely
azimuthal, purely vertical and slightly pitched (almost azimut...

Adults and children can survive, and indeed thrive, with a small opening remaining in the ductus arteriosus. This is a shunt joining the aorta and pulmonary artery that forms during the fetal development in order to allow blood to bypass the lungs, and which normally closes soon after birth. Some patent ductus arteriosus cases appear asymptomatic s...

We consider the implosion of a hollow cylinder of ideal gas with non-zero electrical resistivity. It is shown that there exis self-similar solutions that collapse in a finite time for a range of power-law dependences of the resistivity on the plasm temperature, η∼Tδ. In contrast to the earlier work with zero resistivity, all field variables are fin...

We consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are...

The slow axisymmetric deformation of a conducting drop surrounded by a viscous insulating fluid subject to a uniform electric field is considered. Numerical computations, based on a boundary integral formulation, are used to follow the behavior of relatively inviscid and viscous drops right up to breakup. The type of breakup seen depends on the rat...

The time scales for the behavior of a conducting drop undergoing slow deformation in a uniform electric field are examined. Below the critical electric field strength, equilibrium shapes are possible and approached exponentially. At the critical value, the convergence behaves as t-1. Above (but still near) critical, there is a period of slow elonga...

We consider the slow deformation of a relatively inviscid conducting drop surrounded by a viscous insulating fluid subject to a uniform electric field. The general behaviour is to deform and elongate in the direction of the field. Detailed numerical computations, based on a boundary integral formulation, are presented. For fields below a critical v...

It has recently been shown that laminar, pressure-driven flow of a conducting fluid in a helical pipe can generate a dynamo. Geometrical constraints have hitherto required a relatively small Reynolds number, and a much larger magnetic Reynolds number, $R_m$. Here, a configuration with two interwoven helical pipes is considered which is shown to dri...

Steady, pressure-driven incompressible laminar flow of an electrically conducting fluid down a helically symmetric pipe is known to be capable of sustaining a dynamo at a fairly low hydrodynamic Reynolds number. The nonlinear time evolution of such a dynamo is investigated. Both the fluid motion and the magnetic field are assumed to be helically sy...

Steady, helically symmetric, pressure-driven flow of a fluid down a helical pipe is considered. Helical symmetry is a generalisation of axisymmetry, and the resulting motion has some similarity with Dean flow. It has been successfully used to model blood flow around three-dimensional arterial bends in the body. If the fluid is electrically conducti...

Steady incompressible laminar flow of an electrically conducting fluid down a helically symmetric pipe is investigated with regard to possible dynamo action. Both the fluid motion and the magnetic field are assumed to be helically symmetric, with the same pitch. Such a velocity field can be represented by its down-pipe component, v, and a streamfun...

The non-dissipative relativistic force-free condition should be a good approximation to describe the electromagnetic field
in much of the pulsar magnetosphere, but we may plausibly expect it to break down in singular domains. Self-consistent magnetospheric
solutions are found with field lines closing both at and within the light-cylinder. In genera...

Fully developed flows are often used to describe fluid motion in complex geometrical
systems, including the human macrocirculation. In fact they may frequently be quite
inappropriate even for geometrically simple pipes, owing to the unfeasibly large
viscous entry lengths required. Inviscid adjustment to changes in geometry, however,
occurs on t...

The equilibrium shapes of highly conducting, charged drops accelerating in an electric field are found. The maximum possible charge for a given field stength and surface tension is calculated. A spheroidal approximation often used for uncharged drops is generalized to include charge and is found to agree very well with the numerical solution when a...

The macrocirculation is modelled by incompressible Newtonian flow through a rigid network of pipes for which possible simplifications are discussed. The common assumptions of two-dimensionality or axisymmetry can be generalised to helical symmetry, and in the first part of the paper, the three-dimensionality of arterial bends is considered by varyi...

Independent high Reynolds number flows driven along two co‐axial circular cylinders merge at the abrupt termination of the inner cylinder. The viscous mixing downstream of the trailing edge is discussed. The upstream response in the annular gap is governed by an interaction between the shear layers at the outer wall and the inner boundary, w...

Two‐dimensional flow inside a closed, rigid container is driven by a spatially invariant source of vorticity. At high Reynold number an asymptotic structure with an inviscid core and boundary layers emerges. For an internal flow, the slip boundar velocity must in general decelerate in order to be periodic. Hence an adverse pressure gradient acts in...

The three dimensionally curved aortic arch is modeled as a portion of a helical pipe. Pulsatile blood flow therein is calculated assuming helical symmetry and an experimentally measured pressure pulse. Appropriate values for the Womersley and Reynolds numbers are taken from allometric scaling relations for a variety of body masses. The flow structu...

The high Reynolds number flow through a circular pipe divided along a diameter by a semi-infinite splitter plate is considered. Matched asymptotic expansions are used to analyse the developing flow, which is decomposed into four regions: a boundary layer of Blasius type growing along the plate, an inviscid core, a viscous layer close to the curved...

The polyelectrolyte layer coating mammalian cells, known as the
glycocalyx, is
important in communicating flow information to the cell. In this paper,
the layer is
modelled as a semi-infinite, doubly periodic array of parallel charged
cylinders. The
electric potential and ion distributions surrounding such an array are
found using
the Poisson–B...

The polyelectrolyte layer coating mammalian cells, known as the glycocalyx, may be important in communicating flow information to the cell. In this paper, the layer is modelled as a semi-infinite, doubly periodic array of parallel charged cylinders. The electric potential and ion distributions surrounding such an array are found using the linearize...

Fully developed flow in an infinite helically coiled pipe is studied,
motivated by
physiological applications. Most of the bends in the mammalian arterial
system curve
in a genuinely three-dimensional way, so that the arterial centreline has
not only
curvature but torsion and can be modelled by a helix. Flow in a helically
symmetric
pipe genera...

Fully developed flow in a helical pipe is investigated with a view
to modelling blood
flow around the commonly non-planar bends in the arterial system. Medical
research
suggests that the formation of atherosclerotic lesions is strongly correlated
with
regions of low wall shear and it has been suggested that the observed non-planar
geometry may...

When a pendant drop of weakly conducting fluid is raised to a high electric potential, it frequently adopts the shape of a Taylor cone from whose apex a thin, charged jet is emitted. Such a jet can display surprising longevity, but eventually breaks up into fine droplets, a fact utilized in electro-spraying devices. This paper examines the linear s...

Many electro-spraying devices raise to a high electric potential a pendant drop of weakly conducting fluid, which may adopt a conical shape from whose apex a thin, charged jet is emitted. Such a jet eventually breaks up into fine droplets, but often displays surprising longevity. This paper examines the stability of an incompressible cylindrical je...

This paper investigates the steady flow in a cone-jet at high Reynolds number, when circulation occurs within the drop while the jet is fed by a surface boundary layer. Two models of the phenomenon are presented, with very different similarity scalings. The first model is inviscid, using a crude momentum balance to approximate the layer. The cone a...

Magnéto-hydrodynamique. By BERTON. Masson, 1991. 253 pp. FF 330 - Volume 242 - A. J. Mestel

The penetration of a high-frequency alternating or rotating magnetic field into a conductor is considered. The magnetic Reynolds
number is assumed to be small. The standard high-frequency (or skin-depth) approximation is shown to be incorrect in the interior
of the conductor, leading to large relative errors. Two terms of the correct expansion are...

In steady, two-dimensional, inviscid flows it is well-known that, in the absence of rotational forcing, the vorticity is constant along streamlines. In a bounded domain the streamlines are necessarily closed. In some circumstances, investigated in this paper, this behaviour is exhbited also by forced viscous flows, when the variation of vorticity a...

In steady, two-dimensional, inertia-dominated flows it is well known that the vorticity is constant along the streamlines, which, in a bounded domain, are necessarily closed. For inviscid flows, the variation of vorticity across the streamlines is arbitrary, while for forced, weakly dissipitative flows, it is determined by the balance between visco...

When coils carrying high-frequency currents are placed in the neighbourhood of a stream of liquid metal (or other electrically conducting fluid), the magnetic pressure on the liquid surface causes a deflection of the stream. This effect is studied for a two-dimensional stream on the assumptions that the width of the stream is small compared with th...

The skin-depth solution for the penetration of an alternating magnetic field into a conductor breaks down in the vicinity of sharp corners, yet it is precisely such regions which are important in the study of liquid metal flows. This paper considers the behaviour of an alternating or rotating potential field diffusing into a two-dimensional wedge o...

The channel induction furnace is an electrically efficient device for the heating and stirring of liquid metals. In this paper an axisymmetric model for the channel flow is proposed, in which the fluid is confined to the inside of a torus. An exact solution for the magnetic field is found in terms of toroidal harmonic functions. Finite-difference m...

The process of levitation melting of metals is examined analytically and numerically for the case of axisymmetric toroidal high-frequency currents. The governing equations for the mean-velocity field and associated free-surface shape are derived under the assumption of low magnetic Reynolds number and the neglect of thermal effects. The form of the...

This paper is a summary of the Third Beer-Sheva Seminar on magnetohydrodynamic (MHD) flows and turbulence, held in Israel in March 1981 with 67 participants from 9 countries. Reviews and research papers were presented on fundamental MHD and turbulence studies, both theoretical and experimental, including two-phase phenomena, and on applications of...

The steady, pressure-driven flow of a conducting fluid down a helical pipe of rectangular cross-section is shown to drive a kinematic dynamo at moderate values of the magnetic Reynolds number, R m . The asymptotic structure of the growing modes is analysed as Rm → ∞. This is the first laminar, pressure-driven dynamo to be found.

## Projects

Project (1)