Browsing Mathematics by Author "Gilbert, Andrew D."
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Accelerated diffusion in the centre of a vortex
Bajer, Konrad; Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 2001)The spiral windup and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turnover ... 
Critical layer and radiative instabilities in shallowwater shear flows
Riedinger, X; Gilbert, Andrew D. (Cambridge University Press, 20140623)In this study a linear stability analysis of shallowwater flows is undertaken for a representative Froude number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let ... 
Diffusion and the formation of vorticity staircases in randomly strained twodimensional vortices
Turner, M.R.; Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 2009)The spreading and diffusion of twodimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be ... 
Dissipative structures in a nonlinear dynamo
Gilbert, Andrew D.; Ponty, Y.; Zheligovsky, V. (Taylor & Francis, 20101202)This paper considers magnetic ﬁeld generation by a ﬂuid ﬂow in a system referred to as the Archontis dynamo: a steady nonlinear magnetohydrodynamic (MHD) state is driven by a prescribed body force. The ﬁeld and ﬂow become ... 
Dynamo action in the ABC flows using symmetries
Jones, Samuel Edward; Gilbert, Andrew D. (Taylor & Francis, 20130925)This paper concerns kinematic dynamo action by the 1:1:1 ABC flow, in the highly conducting limit of large magnetic Reynolds number Rm. The flow possesses 24 symmetries, with a symmetry group isomorphic to the group O24 ... 
Effective diffusion of scalar fields in a chaotic flow
Turner, M. R.; Gilbert, Andrew D.; Thuburn, John (American Institute of Physics, 2008)The advection of a tracer field in a fluid flow can create complex scalar structures and increase the effect of weak diffusion by orders of magnitude. One tool to quantify this is to measure the flux of scalar across contour ... 
The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source
Turner, M. R.; Thuburn, John; Gilbert, Andrew D. (American Institute of Physics, 2009)In this paper we examine the influence of periodic islands within a time periodic chaotic flow on the evolution of a scalar tracer. The passive scalar tracer is injected into the flow field by means of a steady source term. ... 
Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection
Ponty, Y.; Gilbert, Andrew D.; Soward, Andrew M. (Cambridge University Press, 2001)A numerical investigation is presented of kinematic dynamo action in a dynamically driven fluid flow. The model isolates basic dynamo processes relevant to field generation in the Solar tachocline. The horizontal plane ... 
Linear and nonlinear decay of cat's eyes in twodimensional vortices, and the link to Landau poles
Turner, M. R.; Gilbert, Andrew D. (Cambridge University Press, 2007)This paper considers the evolution of smooth, twodimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external ... 
Neutral modes of a twodimensional vortex and their link to persistent cat's eyes
Turner, M. R.; Gilbert, Andrew D.; Bassom, Andrew P. (American Institute of Physics, 2008)This paper considers the relaxation of a smooth twodimensional vortex to axisymmetry after the application of an instantaneous, weak external strain field. In this limit the disturbance decays exponentially in time at a ... 
Nonlinear dynamo action in rotating convection and shear
Zhang, Pu; Gilbert, Andrew D.; Zhang, Keke (Cambridge University Press, 2005)Magnetic field amplification by the motion of an electrically conducting fluid is studied, using a rotating planelayer geometry. The fluid flow is driven by convection, and by a moving bottom boundary, which leads to an ... 
Nonlinear equilibration of a dynamo in a smooth helical flow
Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1997)We investigate the nonlinear equilibration of magnetic fields in a smooth helical flow at large Reynolds number Re and magnetic Reynolds number Rm with Re >> Rm >> 1. We start with a smooth spiral Couette flow driven by ... 
On the form of the viscous term for two dimensional NavierStokes flows
Gilbert, Andrew D.; Riedinger, X; Thuburn, John (Oxford University Press, 20140227)The form of the viscous term is discussed for incompressible flow on a twodimensional curved surface S and for the shallow water equations. In the case of flow on a surface three versions are considered. These correspond ... 
The onset of thermal convection in Ekman–Couette shear flow with oblique rotation
Ponty, Y.; Gilbert, Andrew D.; Soward, Andrew M. (Cambridge University Press, 2003)The onset of convection of a Boussinesq fluid in a horizontal plane layer is studied. The system rotates with constant angular velocity Ω, which is inclined at an angle ϑ to the vertical. The layer is sheared by keeping ... 
Passive scalar decay in chaotic flows with boundaries
Zaggout, FA; Gilbert, Andrew D. (IOP Publishing for Japan Society of Fluid Mechanics, 20120229)This paper considers the longtime decay rate of a passive scalar in twodimensional flow. The focus is on the effects of boundary conditions for kinematically prescribed velocity fields with random or periodic time dependence. ... 
The spiral windup and dissipation of vorticity and a passive scalar in a strained planar vortex
Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1999)The response of a Gaussian vortex to a weak timedependent external strain field is studied numerically. The cases of an impulsive strain, an on–off step function, and a continuous random strain are considered. Transfers ... 
The spiral windup of vorticity in an inviscid planar vortex
Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1998)The relaxation of a smooth twodimensional vortex to axisymmetry, also known as `axisymmetrization', is studied asymptotically and numerically. The vortex is perturbed at t = 0 and differential rotation leads to the windup ... 
Spreading of twodimensional axisymmetric vortices exposed to a rotating strain ﬁeld
Turner, M.R.; Gilbert, Andrew D. (Cambridge University Press, 2009)This paper examines the evolution of an axisymmetric twodimensional vortex in a steadily rotating strain field and the dynamical interactions that can enhance vortex spreading through resonant behaviour. Starting with a ... 
Theory of ferromagnetic microswimmers
Gilbert, Andrew D.; Ogrin, Feodor Y.; Petrov, Peter G.; Winlove, C. Peter (Oxford University Press, 2011)This paper considers the dynamics of a microscale swimmer based on two magnetic beads that are elastically coupled together. A timevarying external magnetic field is imposed that has two principal effects: one is to exert ... 
Thresholds for the formation of satellites in twodimensional vortices
Turner, M. R.; Gilbert, Andrew D. (Cambridge University Press, 2008)This paper examines the evolution of a twodimensional vortex which initially consists of an axisymmetric monopole vortex with a perturbation of azimuthal wavenumber m = 2 added to it. If the perturbation is weak, then the ...