Show simple item record

dc.contributor.authorRasmussen, Henrik Obbekaer
dc.descriptionChapter five is excluded.
dc.description.abstractThis thesis concerns the theory of turbulence as well as that of wavelet transforms. The main contribution to the theory of turbulence is an extension of the von Karman-Howarth equation to turbulence that may be either two- or three-dimensional, and for which external forcing maintains the state of statistical equilibrium. The solution of this equation, for the range of separation where the contribution from viscous forces is negligible, yields the third-order structure function to all orders in the separation. For the case of three-dimensional turbulence, we obtain corrections, in the manner of Yakhot, to Kolmogorov's result from 1941. For the case of two-dimensional turbulence, we obtain novel predictions for the third-order structure function in the ranges dominated, respectively, by a downward enstrophy cascade and an upward energy cascade. Finally, we contribute to the theory of wavelet transforms by demonstrating the existence of a Gibbs phenomenon for the continuous wavelet transform; the overshoot of the reconstructed function, at points of discontinuity, is always smaller than the corresponding overshoot for the Fourier transform.
dc.description.sponsorshipThe work in this thesis was funded by the Carlsberg Foundation, the Science and Engineering Research Council of the UK, Schlumberger Research Cambridge, the Danish Research Academy.
dc.rightsAttribution 4.0 International (CC BY 4.0)
dc.subjectTwo-dimensional turbulence
dc.subjectThree-dimensional turbulence
dc.subjectHomogeneous isotropic turbulence
dc.subjectThird-order structure function
dc.subjectEnstrophy cascade
dc.subjectInverse energy cascade
dc.subjectReflectional symmetry
dc.subjectWavelet Gibbs Phenomenon
dc.subjectGibbs Phenomenon
dc.subjectvon Karman-Howarth equation
dc.subjectForced turbulence
dc.titleThe Statistical Theory of Stationary Turbulence
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentApplied Mathematics and Theoretical Physics
dc.contributor.orcidRasmussen, Henrik Obbekaer [0000-0001-8807-1273]
dc.publisher.collegeSt. Edmund's College
cam.supervisorMoffatt, Henry Keith

Files in this item


This item appears in the following Collection(s)

Show simple item record

Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's licence is described as Attribution 4.0 International (CC BY 4.0)