Mathematics Research Institute (MRI)
Welcome to the research outputs of the University of Exeter's Mathematics Research Institute, part of the College of Engineering, Mathematics and Physical Sciences
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Ribbon turbulence
(AIP, 2014)We investigate the nonlinear equilibration of a twolayer quasigeostrophic ow in a channel with an initial eastward baroclinically unstable jet in the upper layer, paying particular attention to the role of bottom ... 
Adaptive sliding mode observation in a network of dynamical systems
(Wiley Interscience, 20151226)This paper considers the problem of reconstructing state information in all the nodes of a complex network of dynamical systems. The individual nodes comprise a known linear part and unknown but bounded uncertainties in ... 
Superparameterisation of ocean deep convection
(University of Exeter, 20111201)Subgrid scale processes play an important role in ocean and climate modelling. Typical examples include clouds in atmospheric models, flows over restricted topographies or the resolution of con vective plumes in ocean ... 
Thresholds for the formation of satellites in twodimensional vortices
(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 ... 
Learning of spatio–temporal codes in a coupled oscillator system
(IEEE, 2009)In this paper, we consider a learning strategy that allows one to transmit information between two coupled phase oscillator systems (called teaching and learning systems) via frequency adaptation. The dynamics of these ... 
The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source
(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. ... 
The representation of snow in land surface schemes: results from PILPS 2(d)
(American Meteorological Society, 2001)Twentyone land surface schemes (LSSs) performed simulations forced by 18 yr of observed meteorological data from a grassland catchment at Valdai, Russia, as part of the Project for the Intercomparison of LandSurface ... 
Effects of frozen soil on soil temperature, spring infiltration, and runoff: results from the PILPS 2(d) experiment at Valdai, Russia
(American Meteorological Society, 20091218)The Project for Intercomparison of LandSurface Parameterization Schemes phase 2(d) experiment at Valdai, Russia, offers a unique opportunity to evaluate land surface schemes, especially snow and frozen soil parameterizations. ... 
Comparing the degree of land–atmosphere interaction in four atmospheric general circulation models
(American Meteorological Society, 2002)The strength of the coupling between the land and the atmosphere, which controls, for example, the degree to which precipitationinduced soil moisture anomalies affect the overlying atmosphere and thereby the subsequent ... 
GLACE: the global land–atmosphere coupling experiment. Part II: analysis
(American Meteorological Society, 2006)The 12 weather and climate models participating in the Global Land–Atmosphere Coupling Experiment (GLACE) show both a wide variation in the strength of land–atmosphere coupling and some intriguing commonalities. In this ... 
GLACE: the global land–atmosphere coupling experiment. Part I: overview
(American Meteorological Society, 2006)The Global Land–Atmosphere Coupling Experiment (GLACE) is a model intercomparison study focusing on a typically neglected yet critical element of numerical weather and climate modeling: land–atmosphere coupling strength, ... 
Climate–carbon cycle feedback analysis: results from the C4MIP model intercomparison
(American Meteorological Society, 2006)Eleven coupled climatecarbon cycle models used a common protocol to study the coupling between climate change and the carbon cycle. The models were forced by historical emissions and the Intergovernmental Panel on Climate ... 
In–out intermittency in partial differential equation and ordinary differential equation models
(American Institute of Physics, 2001)We find concrete evidence for a recently discovered form of intermittency, referred to as in–out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field ... 
On the geometry of orientationpreserving planar piecewise isometries
(Springer, 2002)Planar piecewise isometries (PWIs) are iterated mappings of subsets of the plane that preserve length (and hence angle and area) on each of a number of disjoint regions. They arise naturally in several applications and are ... 
Neutral modes of a twodimensional vortex and their link to persistent cat's eyes
(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 ... 
Effective diffusion of scalar fields in a chaotic flow
(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 ... 
Nonlinear equilibration of a dynamo in a smooth helical flow
(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 ... 
The spiral windup of vorticity in an inviscid planar vortex
(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 ... 
The spiral windup and dissipation of vorticity and a passive scalar in a strained planar vortex
(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 ... 
Accelerated diffusion in the centre of a vortex
(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 ...