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Title: Advection-diffusion of forced passive scalars
Author: Aston, J. R.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2007
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This thesis considers a forced passive scalar evolving through advection and diffusion in a large-scale flow evolving randomly in time. Recent theoretical work has provided predictions of many different aspects of the scalar field in such flows. The first part of this thesis reviews the previous theoretical work, which has used two different mathematical approaches, one using an ‘inertia tensor’ description of the structure of the scalar field and the other using a Fourier description. The second part of the thesis gives, for two-dimensional flows, the first extensive comparison between the theoretical predictions for the forced problem and full numerical simulations. The major predictions of the theory are verified, but some limitations and necessity clarifications are noted. Two points of interest are the probability density function (hereafter ‘pdf’) for the scalar field and the pdf for the scalar gradient. The theory underlying the predictions of exponential tails for the scalar pdf is examined and refined, allowing improved understanding of the range of values for which the exponential behaviour holds and of the form of the pdf for higher values. The effects of finite diffusivity and finite flow correlation time on the scalar gradient pdf are discussed. The third part of the thesis considers layerwise two-dimensional flows relevant to atmosphere and ocean. An extension is given of the ‘local’ theory to give a prediction for vertical wavenumber spectra. Full numerical simulations are used to examine the relevance of the local theories.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available