The use of efficient basis functions to model and represent flows with
internal sharp velocity gradients, such as shocks or eddy microfronts, are
investigated. This is achieved by analysing artificial data, observed atmospheric
turbulence data and by the use of a Burgers' equation based spectral
model. The concept of an efficient decomposition of a function into a basis
set is presented and alternative analysis methods are investigated. The
development of a spectral model using a generalized basis for the Burgers'
equation is presented and simulations are performed using a modified Walsh
basis and compared with the Fourier (trigonometric) basis and finite difference
techniques.
The wavelet transform is shown to be superior to the Fourier transform
or the windowed Fourier transform in terms of defining the predominant
scales in time series of turbulent shear flows and in 'zooming in' on local
coherent structures associated with sharp edges. Disadvantages are found
to be its inability to provide clear information on the scale of periodicity of
events. Artificial time series of varying amounts of noise added to structures
of different scales are analyzed using different wavelets to show that the
technique is robust and capable of detecting sharp edged coherent structures
such as those found in shear driven turbulence.
The Haar function is used as a wavelet to detect ubiquitous zones of
concentrated shear in turbulent flows sometimes referred to as microfronts.
The location and organization of these shear zones suggest that they may be
edges of larger scale eddies. A wavelet variance of the wavelet phase plane is
defined to detect and highlight events and obtain measures of predominant
scales of coherent structures. Wavelet skewness is computed as an indicator
of the systematic sign preference of the gradient of the transition zone. Inverse
wavelet transforms computed at the dilation corresponding to the peak
wavelet variance are computed and shown to contain a significant fraction of
the total energy contained in the record. The analysis of data and the numerical
simulation results are combined to propose that the sharp gradients
normally found in shear induced turbulence significantly affect the nature of
the turbulence and hence the choice of the basis set used for the simulation
of turbulence. / Graduation date: 1991
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/28735 |
| Date | 06 August 1990 |
| Creators | Gamage, Nimal K. K. |
| Contributors | Mahrt, Larry |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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