In asymptotic analysis of the hydrodynamic stability of shear flows, the viscous effects enter through the modified Tietjens Function, which is used in the graphical determination of the eigenvalues. For neutral normal modes the argument of this function is real, and values of the function have been calculated previously. For non-neutral normal modes the argument is complex; the present note gives the modified Tietjens Function for complex arguments. This function is particularly useful in investigating the behavior of lightly damped eigenmodes for shear flows of arbitrary velocity profile.
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Modified Tietjens Function for Asymptotic Analysis of Shear Flow Stability
A. K. M. F. Hussain,
A. K. M. F. Hussain
Mechanical Engineering Department, University of Houston, Houston, Texas
W. C. Reynolds
Mechanical Engineering Department, Stanford University, Stanford, Calif.
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Hussain, A. K. M. F., and Reynolds, W. C. (March 1, 1977). "Modified Tietjens Function for Asymptotic Analysis of Shear Flow Stability." ASME. J. Fluids Eng. March 1977; 99(1): 256–258. https://doi.org/10.1115/1.3448534
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