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Generalised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models
(Department of Applied Mathematics and Theoretical Physics, University of CambridgeUniversity of CambridgeDepartment of Applied Mathematics and Theoretical PhysicsSt John's College, 2016-10-04)
In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application ...
On the orbital evolution of a pair of giant planets in mean motion resonance
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-07-04)
Pairs of extrasolar giant planets in a mean motion commensurability are common with 2:1 resonance occurring most frequently. Disc–planet interaction provides a mechanism for their origin. However, the time-scale on which ...
Spontaneous Wave Generation at Strongly Strained Density Fronts
(American Meteorological SocietyJournal of Physical Oceanography, 2016-06-23)
A simple analytical model is presented describing the spontaneous generation of inertia–gravity waves at density fronts subjected to strong horizontal strain rates. The model considers fronts of arbitrary horizontal and ...
An Analytic Solution for Gust-Aerofoil Interaction Noise Including Effects of Geometry
(Oxford University PressIMA Journal of Applied Mathematics, 2016)
An analytic solution is obtained for the sound generated by gust-aerofoil interaction for aerofoils with thickness, camber, and angle of attack. The model is based on the linearisation of the Euler equations about a steady ...
Particle organization after viscous sedimentation in tilted containers
(American Institute of PhysicsPhysics of Fluids, 2016-07-19)
A series of sedimentation experiments and numerical simulations have been conducted
to understand the factors that control the final angle of a static sediment
layer formed by quasi-monodisperse particles settling in an ...
Volume preservation by Runge–Kutta methods
(ElsevierApplied Numerical Mathematics, 2016-07-12)
It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge–Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and ...
Turbulent mixing, restratification, and phytoplankton growth at a submesoscale eddy
(WileyGeophysical Research Letters, 2016-05-13)
High-resolution large-eddy simulations are used to study the influence of submesoscale mixed layer instability and small-scale turbulence on phytoplankton growth in light-limited conditions. Four simulations are considered ...
Near-wall diffusion tensor of an axisymmetric colloidal particle
(American Institute of Physics PublishingThe Journal of Chemical Physics, 2016-07-21)
Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a ...
On the quadratic invariant of binary sextics
(Cambridge University PressMathematical Proceedings of the Cambridge Philosophical Society, 2016-07-28)
We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
Turbulent mixing due to the Holmboe wave instability at high Reynolds number
(Cambridge University PressJournal of Fluid Mechanics, 2016)
We consider numerically the transition to turbulence and associated mixing in stratified shear flows with initial velocity distribution $\bar U$(z, 0)e$_{x}$ = U$_{0}$e$_{x}$ tanh(z/d) and initial density distribution $\bar ...