Title page for ETD etd-04072009-040910
|Type of Document
||Janajreh, Isam M.
||Quantification of linear and nonlinear energy transfer processes in a plane wake
||Master of Science
||Engineering Science and Mechanics
|Hajj, Muhammad R.
|Mook, Dean T.
|Ragab, Saad A.
|Tieleman, Henry W.
|Date of Defense
The transition to turbulence of plane wakes is characterized by the development of
the velocity-fluctuation field from a spectrum of weak random background noise in the
initial laminar wake to a nearly featureless broad spectrum of intense fluctuations within
the turbulent wake. This transition has also been described as a sequence of instabilities
and wave-wave interactions. In the initial small-amplitude stage,. a narrow, but
continuous, band of dominant instability modes centered near the most unstable mode,
known also as the fundamental mode, grow exponentially at rates that can be calculated
from the linearized Navier-Stokes equations. As these modes grow, the nonlinear terms
become more important and cannot be neglected anymore. The effect of these terms is
to introduce wave-wave interactions that lead to quadratic energy transfer between the
different spectral components of the velocity-fluctuation field. While the consequences
of these interactions, such as broadening of the power spectra, have been observed in
many experiments, the characteristics of these interactions have only been examined in
limited cases. Previous measurements of the auto-bispectrum showed that three-wave
interaction processes are important in the transitioning wake. However, quantification
of these processes can only be obtained from measurement of the nonlinear energy
transfer rates resulting from the nonlinear wave-wave interactions. Such quantification
is very important for understanding the effects of the different mechanisms involved in
the transition and final breakdown to turbulence. An understanding of these
mechanisms and their effects can then be used to control the transition by enhancing
certain mechanisms and reducing the role of others through external excitation. In this
work, quantitative estimates of the auto-bispectrum, linear and quadratic coupling
coefficients and the resulting energy transfer rates between the interacting waves at
different locations are presented in controlled and natural transitions of the plane wake.
The results show that, in both natural and controlled transitions, the underlying
nonlinear dynamics are similar. Basically, nonlinear interactions between the instability
modes result in energy transfer to harmonic bands as well as low-frequency difference
components. These components play an important role in the transfer of energy to the
sidebands and the valleys between the peaks. The results also show that, while
energy-transfer rates in natural transition are lower than in controlled transition, the
random nature of wave excitation in natural transition causes energy transfer to a band
of low-frequency components which leads to energy transfer to many sidebands and
results in a spectrum that differs dramatically from the one obtained in the controlled
case where two instabilities are excited.
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