A numerical investigation of the non-linear mechanics of wave disturbances in plane Poiseuille flows
By: by T.H. Gwain and W.H. Clark
Contributors: Clark, W. H.; Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1971
Place of publication: Monterey, California
Language: eng
Number of pages: 121
Subjects: Stability; Mathematical models; Fluid dynamics; Turbulence
Description: The response of a plane Poiseuille flow to disturbances of various initial wavenumbers and amplitudes is investigated by numerically integrating the equation of motion.  It is shown that for very low amplitude disturbances the numerical integration scheme yields results that are consistent with those predictable from linear theory.  It is also shown that because of non-linear interactions a growing unstable disturbance excites higher wavenumber modes which have the sam frequency, or phase velocity, as the primary mode.  For very low amplitude disturbances these spontaneously generated higher wavenumber modes have a strong resemblance to certain modes computed from the linear Orr-Sommerfeld equation.  In general it is found that the disturbance is dominated for a long time by the primary mode and that there is little alteration of the original parabolic mean velocity profile.  There is evidence of the existence of an energy equilibrium state which is common to all finite-amplitude disturbances despite their initial wavenumbers.  This equilibrium energy level is roughly 3-5% of the energy in the mean flow which is an order of magnitude higher than the equilibrium value predicted by existing non-linear theories. (Author)
Notes: Title from cover.

"2 September 1971"--Cover.

"NPS-57GN71091A"--Cover.

Author(s) key words: Hydrodynamic stability, finite-differences, turbulence, plane Poiseuille flow.

Includes bibliographical references (p. 39-40)

"Approved for public release; distribution unlimited"--Cover.

Technical report; 1971.

kmc/kmc 9/14/09.