Relating skewness and Fourier harmonics in low Reynolds number wake flow
Manthripragada, Krithsanvith
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https://hdl.handle.net/2142/124604
Description
Title
Relating skewness and Fourier harmonics in low Reynolds number wake flow
Author(s)
Manthripragada, Krithsanvith
Issue Date
2024-05-02
Director of Research (if dissertation) or Advisor (if thesis)
Saxton-Fox, Theresa
Department of Study
Mechanical Sci & Engineering
Discipline
Theoretical & Applied Mechans
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
fourier transforms
fourier series
Skewness
wake flows
Abstract
Simple, laminar wake flows require many Fourier modes to represent their dynamics, even though they are perfectly periodic with a single period. The spatial form of the Fourier modes alternate between having a maximum value in the center of the wake for odd harmonics and having a zero crossing in the center of the wake for even harmonics of the primary frequency. We demonstrate that the harmonic organization and the alternating shapes of the Fourier modes for simple wakes are direct results of the skewness of the wake, which changes sign at the center of the wake flow. Having a non-zero skewness guarantees that more than one Fourier mode is required to represent the dynamics, even for a perfectly periodic signal, and the spatial variation of the skewness explains the alternating structure of the Fourier modes’ shapes. We demonstrate these relationships through a one-dimensional analysis of how Fourier modes relate to skewness in a model problem and by examining the skewness and Fourier modes of a low Reynolds number flow past a flat plate at an angle of attack of 35 degrees.
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