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Title: The interaction between vorticity and internal gravity waves
Author: Griffiths, R. M.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 1999
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Our dissertation investigates the interaction between a localised region of vorticity and internal gravity waves, using only analytical methods. We aim to understand further the mechanism by which internal gravity waves radiate vorticity and to address the validity of applying an analogy of Lighthill's sound generation theory to the generation of internal gravity waves. We consider an initial value problem for a two-dimensional incompressible density-stratified fluid. The buoyancy frequency is taken to be constant and the Boussinesq approximation is imposed. To make the analysis as general as possible, and more importantly to assess the importance of nonlinear mechanisms in the generation of internal gravity waves, we include nonlinear terms in the equations of motion. To make further analytical progress we consider the case of a large internal Froude number Fr, which is more often realised in physical scenarios. We attempt solutions to the equations of motion via asymptotic expansions in the small parameter ε = 1/Fr2. We consider the main results of the dissertation to be twofold. First we see the appearance of distinct regions in space-time where different dominant balances occur in the equations of motion. In particular we have an inner region, a far field and a wave region, and we have been able to perform an asymptotic matching of the different solutions in these regions successfully. The magnitude of these regions is characterised by the small parameter ε. It is hoped that the existence of such regions could be confirmed experimentally. Such space-time regions do not occur in the linear analysis of this problem, but are only evident when nonlinear terms are retained in the equations of motion. The second part of our analysis that we consider to be important arises through the study of the dynamics of vorticity transfer in our problem. The introduction of stratification destroys conservation of vorticity; the non-conservation of vorticity is observed in the inner region and the far field.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available