Mathematical models for understanding phenomena: Vortex-induced vibrations

Abstract

This is a rather biased review paper emphasizing the importance of “understanding” of phenomena. This paper's purpose is to inspire young researchers to taste the real charms of research by observing the process of development of mathematical models of vortex-induced vibration phenomena of cylinders for understanding their essential mechanism. It first discusses the limitations of human abilities and important aspects of research. Then, it emphasizes the close relation between understanding and mathematical models, and five conditions for a desirable mathematical model: simplicity; inclusion of all essential properties; possession of physical meanings; wide scope of application; and possibility of development. It refers to Birkhoff's wake-oscillator (1953), Funakawa's early-wake model (1969), Nakamura's 2DOF flutter model (1970), the Hartlen-Currie model (1970), the Iwan-Blevins model (1974), Tamura's non-linear wake-oscillator model with a variable length (1979), and the Tamura–Shimada model (1987) for combined effects of vortex resonance and galloping. Some recent developments of the Tamura–Shimada model are also introduced. Then, it discusses the necessity of accurate experimental capture of early-wake behavior and the aerodynamic properties of a target cylinder in a given flow condition for further development of Tamura's model and the Tamura–Shimada model. Finally, the necessity for efforts to understand phenomena are emphasized.