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dc.contributor.advisorTran, Chuong Van
dc.contributor.authorBlackbourn, Luke A. K.
dc.description.abstractIn this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes (2DNS), surface quasigeostrophic (SQG), alpha-turbulence and magnetohydrodynamic (MHD) equations. The main analytical focus is on the number of degrees of freedom of a given system, defined as the least value $N$ such that all $n$-dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract during the course of evolution. By equating $N$ with the number of active Fourier-space modes, that is the number of modes in the inertial range, and assuming power-law spectra in the inertial range, the scaling of $N$ with the Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum. This allows the recovery of analytic results that have until now only been derived phenomenologically, such as the $k$[superscript(-5/3)] energy spectrum in the energy inertial range in SQG turbulence. Phenomenologically I study the modal interactions that control the transfer of various conserved quantities. Among other results I show that in MHD dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralises the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. These theoretical results are backed up by high resolution numerical simulations, out of which have emerged some new results such as the suggestion that for alpha turbulence the generalised enstrophy spectra are not closely approximated by those that have been derived phenomenologically, and new theories may be needed in order to explain them.en_US
dc.publisherUniversity of St Andrews
dc.relationBlackbourn, L. A. K. & Tran C. V. (2011) Effects of friction on two-dimensional Navier-Stokes turbulence. Phys. Rev. E 84, 046322en_US
dc.relationBlackbourn, L. A. K. & Tran C. V. (2012) On energetics and inertial range scaling laws of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 703, 238-254en_US
dc.relationBlackbourn, L. A. K. & Tran C. V. (2013) Inertial-range dynamics and scaling laws of two-dimensional magnetohydrodynamic turbulence in the strong advection regime. Phys. Fluids, submitteden_US
dc.relationTran, C. V. & Blackbourn, L. (2009) Number of degrees of freedom of two-dimensional turbulence. Phys. Rev. E 79, 056308en_US
dc.relationTran, C. V. & Blackbourn, L. A. K. (2012) A dynamical systems approach to fluid turbulence. Fluid Dyn. Res. 44, 031417en_US
dc.relationTran, C. V. & Blackbourn, L. A. K. & Scott R. K. (2011) Number of degrees of freedom and energy spectrum of surface quasi-geostrophic turbulence. J. Fluid Mech. 684, 427-440en_US
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported
dc.subjectFluid dynamicsen_US
dc.subjectSurface quasigeostrophicen_US
dc.subjectEnergy cascadeen_US
dc.subject.lccFluid dynamics--Mathematical modelsen_US
dc.subject.lcshTurbulence--Mathematical modelsen_US
dc.subject.lcshNavier-Stokes equations--Numerical solutionsen_US
dc.subject.lcshMagnetohydrodynamics--Mathematical modelsen_US
dc.titleAn analytical, phenomenological and numerical study of geophysical and magnetohydrodynamic turbulence in two dimensionsen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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