The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing t...The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).展开更多
The purpose of this paper is to analyze and visualize the exact invariant solution of the nonlinear simplified version of the shallow water equations which are being used to simulate equatorial atmospheric waves of pl...The purpose of this paper is to analyze and visualize the exact invariant solution of the nonlinear simplified version of the shallow water equations which are being used to simulate equatorial atmospheric waves of planetary scales. The method of obtaining the exact solution is based on the Lie group invariance principle. It is shown that the obtained invariant solution has a Fibonacci spiral-like form and has two parameters k and t<sub>0</sub>. We have defined a new model hypermarameter Δ<sub>k</sub>t = t – t<sub>0</sub>, where t is time. The question of particular interest is: can we tune the hypermarameter in order to match the exact solution to the actual Fibonacci spiral? It was discovered that the physically relevant part of the solution matches exactly the Fibonacci spiral.展开更多
This paper describes experimental and theoretical investigations of Tuned Liquid Damper (TLD) characteristics for suppressing the wave-excited structural vibration. The structural model for the experiments is scaled a...This paper describes experimental and theoretical investigations of Tuned Liquid Damper (TLD) characteristics for suppressing the wave-excited structural vibration. The structural model for the experiments is scaled according to a full size offshore platform by matching their dynamic properties. Rectangular TLDs of different sizes with partially filled liquid are examined. By observing the performance and behavior of TLDs through laboratory experiments, the Study investigates the influence of a number of parameters, including container size, container shape, frequency ratio, and incident wave characteristics. In an analytical study, a mathematical model that describes the nonlinear behavior of liquid in TLD and the interaction of TLD and structure is prerequisite. The validity of the model is evaluated and simulating results can reasonably match the corresponding experimental results.展开更多
文摘The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).
文摘The purpose of this paper is to analyze and visualize the exact invariant solution of the nonlinear simplified version of the shallow water equations which are being used to simulate equatorial atmospheric waves of planetary scales. The method of obtaining the exact solution is based on the Lie group invariance principle. It is shown that the obtained invariant solution has a Fibonacci spiral-like form and has two parameters k and t<sub>0</sub>. We have defined a new model hypermarameter Δ<sub>k</sub>t = t – t<sub>0</sub>, where t is time. The question of particular interest is: can we tune the hypermarameter in order to match the exact solution to the actual Fibonacci spiral? It was discovered that the physically relevant part of the solution matches exactly the Fibonacci spiral.
基金This research was financially supported partially by the National Science Foundation of Japan under grant No.10555173 This work was partially supported by the Scholarship from Japan Ministry of Education,Science and Culture.
文摘This paper describes experimental and theoretical investigations of Tuned Liquid Damper (TLD) characteristics for suppressing the wave-excited structural vibration. The structural model for the experiments is scaled according to a full size offshore platform by matching their dynamic properties. Rectangular TLDs of different sizes with partially filled liquid are examined. By observing the performance and behavior of TLDs through laboratory experiments, the Study investigates the influence of a number of parameters, including container size, container shape, frequency ratio, and incident wave characteristics. In an analytical study, a mathematical model that describes the nonlinear behavior of liquid in TLD and the interaction of TLD and structure is prerequisite. The validity of the model is evaluated and simulating results can reasonably match the corresponding experimental results.
