Survey of nonlinear analysis methods in hydraulics

Research Project

Project/Area Number	02302064
Research Category	Grant-in-Aid for Co-operative Research (A)
Allocation Type	Single-year Grants
Research Field	Hydraulic engineering
Research Institution	Tokyo Institute of Technology
Principal Investigator	IKEDA S. Tokyo Institute of Technology, Dept. of Civil Eng., Professor, 工学部, 教授 (60016590)
Co-Investigator(Kenkyū-buntansha)	HOSODA T. Kyoto Univ., Dept. of Civil Eng., Research Associate, 工学部, 助手 (10165558) YAMASAKA M. Kanazawa Inst. of Tech., Dept. of Civil Eng., Assoc. Professor, 工学部, 助教授 (20174641) TSUJIMOTO T. Kanazawa Univ., Dept. of Civil Eng., Assoc. Professor, 工学部, 助教授 (20115885) KUROKI M. Hokkaido Univ., Dept. of Civil Eng., Assoc. Professor, 工学部, 助教授 (50002001) ISHIKAWA T. Tohoku Univ., Dept. of Civil Eng., Assoc. Professor, 工学部, 助教授 (50159696)
Project Period (FY)	1990 – 1991
Project Status	Completed (Fiscal Year 1991)
Budget Amount *help	¥1,300,000 (Direct Cost: ¥1,300,000) Fiscal Year 1991: ¥500,000 (Direct Cost: ¥500,000) Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Keywords	Nonlinear analysis / Fluid motion / Oscillation / Diffusion / Chaos / Numerical analysis / Boundary condition / 基線型 / 非線形解析 / 水理学
Research Abstract	Fluid motion is inherently nonlinear, and the nonlinearity appears in many phenomena. In the present study, various techniques to solve the nonlinear equations used are surveyed. They are as follows : (1) Various noninear oscillation systems were studied, in which nonlinear response, synchronization and subharmonic response were explained in detail. (2) The nonlinearlity which appears in diffusion process was summarized, in which various techniques to solve the diffusion equation were described, e. g. exact analytical solution, singular perturbation technique, approximate method to solve the boundary layer equation. (3) Nonlinearity also occurs for boundary conditions. As a typical example, finite amplitude wave (Stokes wave) was treated using perturbation technique. The nonlinearity which appears for the bottom concentration of suspended was described in this chapter. (4) Bifurcation and the associated phenomenon of chaos were also described in detail, and the theory was applied to Bernard cell and sloshing of liquid contained in tanks subject to oscillation. (5) Numerical method is now essential in solving the nonlinear equations. Modeling of turbulent flow, e. g. two-equation model, and techniques which are used in numerical computation are studied in this chapter. (6) The technique described in the above were applied to various flow field, e. g. galloping of elastic beam, sloshing subject to vertical oscillation, fall velocity of rigid body in turbulent flow, sediment transport, self-formed straight channels, river meandering, alternate bars and flood flows.