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The Statistical Theory of Stationary Turbulence 10.17863/CAM.41551 Rasmussen, Henrik Obbekaer 0000000188071273 Moffatt, Henry Keith This 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. University of Cambridge 1995-06-21 Thesis Doctoral Doctor of Philosophy (PhD) en The 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. https://www.repository.cam.ac.uk/handle/1810/294448 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/497c2c4c-41e9-4076-90b4-84acbe4f8dc8/download 74bf849fa8abe4108467fb958efac60a https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/478e4d0c-75e4-4c64-9e67-e64773ff7fcc/download 87eda9de84448d1f82354d60eee3eb5f https://creativecommons.org/licenses/by/4.0/ Two-dimensional turbulence Three-dimensional turbulence Homogeneous isotropic turbulence Third-order structure function Enstrophy cascade Inverse energy cascade Palinstrophy Reflectional symmetry Wavelet Gibbs Phenomenon Gibbs Phenomenon von Karman-Howarth equation Forced turbulence