We consider a mathematical structure of the mean field equation for nearly parallel vortex filament systems in the periodic broken path model. This system can be regarded as a three-dimensional extension of the point vortex system introduced by Onsager to investigate the 2D turbulence.
In this paper, we show the existence of a solution to the mean field equation of the system by analyzing the variational functional and reveal that this system is equipped with a dual variational structure as in the case of the point vortex system and that two mean field equations in terms of the stream function and the vorticity are derived from a Lagrangian. The mean field equation used in this paper is modified from that in our previous research by considering the boundary condition carefully, thus we get finer results.
Internal gravity waves propagate in a form of ‘beam’ from a wave source in the atmosphere and the ocean. The corresponding solution is an exact solution of the Euler equations. In the present study, we consider ‘triad resonance’ (3-wave interaction) among one beam and two plane waves. The triad resonance among three plane waves is well-known to occur, but their dynamics when one of them is a beam has not been elucidated so far. According to recent studies, occurrence of instability depends not only on their amplitudes but also on ‘width’ of the beam. We demonstrate this fact by numerical simulation of the Euler equations and clarify the effect of width on the stability of wave beam.
Stochastic synchronization, which is the coupling phenomena of synchronization and stochastic resonance, is considered to be related to formation of ordered structure, such as in the rhythm adjustment observed in non-linear systems including ocean system. To investigate chaos excitation and the relation of it to the stochastic synchronization in the oceanic double gyre, numerical simulations are conducted using 1.5 layer reduced gravity quasi-geostrophic model driven by seasonal changing forcing with red noise. Results show that by adding red noise to external forcing, synchronization (i.e., stochastic synchronization) occurs when the amplitude of external forcing is smaller than that in the case without noise, and the transition to chaos excitation occurs more rapidly when the amplitude of external forcing is larger, corresponding to the Curry-York model.
In our laboratory, in order to investigate the fundamental characteristics of radiation behind reflected air shock waves, shock tube experiments are performed systematically. The radiation behind the shock wave was observed by a high-speed video camera. The composed chemical species behind the shock waves were examined by using several kinds of narrow band-pass filters. Also, we analyzed the radiation spectra by using the fundamental radiation theory on a trial basis, and we compared qualitatively the theoretical results with the experimental ones. As the results, the experimental radiation intensity was increased with an increase in the incident shock Mach number for all the cases with the narrow band-pass filters such as atomic nitrogen and oxygen lines. The theoretical radiation spectra in the visible and the longer wavelength regions had several atomic nitrogen and oxygen lines. These theoretical atomic lines were much weaker than those spectra of the molecular band systems. The experimental results were extremely high compared qualitatively with the theoretical ones.
The free-molecular type LBM (FMT-LBM) is a new lattice Boltzmann model which can simulate supersonic flows described by the compressible Euler equations. FMT-LBM is superior to the existing LBM and other shock capturing schemes in the following three points: (I) advection term is linear, (II) supersonic flows and non-viscosity flows can be simulated, (III) small oscillations like sound waves can be captured with high resolution. We improve this scheme by using median filter, which is one of the image processing filters, to reduce peculiar numerical oscillations generated in expansion waves of high speed flows. Numerical results agree well with the corresponding theories and other numerical methods and show that this scheme can capture shock waves sharply like various shock capturing methods.
Asai et.al. have proposed the 3rd order 6 point scheme to compute advection transports. However, I can tell how long the time of the transportation has been performed through calculation. There is a tendency in the 3rd order 6-point scheme that the reproducibility of Gaussian and rectangular distribution will decline. From this, the calculation scheme based on the characteristic curve method has still got room for improvement. This paper introduces the development of the 5th order 6-point scheme for high-order accuracy computation scheme based on the characteristic curve method. As this scheme does not meet TVD conditions, it is newly developed for translation into the conservative form in order to apply the flux limiter and discriminator. It is defined as a 5th order conservative 6-point scheme. This proposed scheme is adapted and cleared flow problems. It is proved that the proposed scheme can be achieved excellent results from computer simulation.
In this article, we propose to use a new form of pressure Poisson equation (PPE) and pressure boundary conditions with the explicit Runge-Kutta (eRK) schemes for the incompressible unsteady flows. In the previous studies, the projection method of Chorin's type has been applied to the eRK schemes where the pressure is reconstructed from the scalar function at previous stages. We show that in the present form of PPE, the local acceleration terms are reconstructed from their previous stage values and thus reconstruction of pressure can be avoided. The proposed PPE method is applied to three third-order eRK schemes and the performance of the method is demonstrated for the benchmark problem.
Numerical simulation has been carried out for two-dimensional flow around two straight wing vertical axis wind turbines (SW-VAWT) with two blades. We divide the flow region into two parts so that two wind turbines can rotate independently in the simulation. Each part consists of two sub-regions; one sub-region rotates together with the wind turbine and the other is fixed in the external space. Every region has slender “overlapped area” and we use the overset grid system there. The Reynolds number is fixed to 2000 and a turbulence model is not used. In this study, the ratio of radius of the turbine to the distance is 1 to 2.8 and 1 to 3.2, and the flow is assumed to come parallel and perpendicular to two turbines. By changing the wind direction and the distance between turbines to analyze the interaction, we can estimate changes of torque coefficient and those of flow field quantitatively.
In this study, we investigate the flows around two S-shaped turbines rotating inversely by numerical simulation. In general, a rotational coordinate system is often used. When analyzing the flow around a rotating object, however, it is difficult to calculate with such coordinate system when two objects rotate in the reverse direction. Therefore, we use the overset grid that consists of two rotational coordinates for each turbine immersed in a steady coordinate to calculate such system of turbines. In this study, two-dimensional simulations for two turbines rotating inversely are performed, and the influence of interaction is investigated.
Patterns of convective flows produced by microorganisms swimming upward (namely, bioconvection) are investigated by numerical calculations of density model. The calculations suggests that there is a tendency for the aspect ratio of the convection cell to increase with Prandtl number. With respect to temporal change in bioconvection, the flow can be classified into three states (i.e. steady, unsteady, collapse). Comparing bioconvection to the bubble convection, another kind of particle-driven convection, there is similarity that steady-state and unsteady-state can be divided by Prandtl number, while difference is observed in the presence of the collapse pattern.
We focus on an elastic contact problem for indentation of a layer-substrate body. An elastic layer assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter and a spherical indenter. The analytical and exact solutions are obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presents not only the axial load but also the distribution of the dimensionless normal contact stress under cylindrical and spherical indentation, the distribution of the dimensionless normal displacement at the upper surface of the elastic layer and the stress singularity factor. Numerical results are given for several combinations of the ratio of shear modulus and Poisson’s ratios of the elastic layer and substrate, and the thickness of the elastic layer.
An analytical method using complex fractional moments (CFM) is applied for nonlinear systems under combined Gaussian and Poisson white noises. The CFM is a new kind of statistical moment, which is defined by extending the order of moments to a complex number, and is related to a Mellin transform of a probability density function (PDF). In order to find the PDF of the response of the system, first, we derive the governing equations of the response CFMs by applying a Mellin transform to the generalized Fokker-Planck-Kolmogorov equation. Since the governing equations are linear, they can be solved analytically to get the CFMs. Finally, the inverse Mellin transform to the CFMs yields the response PDF. The effectiveness of the present method is demonstrated by comparing analytical and Monte Carlo simulation results. The influence of parameters of the system and the excitation upon the accuracy of the present method is also discussed.
An approximate analytical method is proposed to estimate the statistical moments up to the 4th order of the response of a Duffing oscillator subjected to non-Gaussian random excitation. The non-Gaussian excitation is prescribed by a wide class of probability densities and the power spectrum with bandwidth parameter. The moment equations for the system response are derived from the equation of motion of the system and the stochastic differential equation governing the excitation. However, they are not closed due to the complexity of the diffusion coefficient of the stochastic differential equation for the excitation and the system nonlinearity. Therefore, applying the equivalent non-Gaussian excitation method and the equivalent linearization, a closed set of the moment equations are obtained approximately. In numerical examples, we analyze a Duffing oscillator under non-Gaussian excitation with various shapes of probability densities. the response moments obtained by the present method are compared with Monte Carlo simulation results.
This paper proposes an interaction model between particle-based free-surface flow and polygon-based rigid body dynamics. In our proposed model, we adopt a polygon wall boundary model to represent a rigid body in two-dimensional space. The polygon representation of rigid body is more flexible to express complicated-shaped rigid body compared with conventional particle-based representation. We formulate the model so that forces between fluid and rigid body are balanced on their interface. We employ polygon-based calculations of physical values for a rigid body, which only requires information of rigid body surfaces. A verification test for the proposed model is performed based on a free falling cylinder problem, and the result is compared with a theoretical solution in an equilibrium state of floating body.
This paper focuses on a weak coupling analysis system of 3-dimensional fluid-structure interaction problems. As the numerical discretization scheme, the stabilized incompressible smoothed particle hydrodynamics (ISPH) method is adopted for fluid dynamics involving free surface flow and the finite element method (FEM) is used for structural dynamics. To save cost in software developments maintenance, the open source software is utilized. Especially, a general-purpose finite element analysis system, named ADVENTURE_Solid, and a general-purpose coupling analysis platform, named REVOCAP_Coupler, are employed. Moreover, techniques of an interface marker on the fluid-structure boundary and a dummy mesh for a fluid analysis domain is adopted to solve the problem that the REVOCAP_Coupler performs to unify two or more grid-based method codes. To verify a developed system, the dam break problem with an elastic obstacle is demonstrated. Moreover, the effect of a relaxation parameter in the ISPH method is studied.
To investigate the internal flow of a coronary artery of the heart, we accomplished the simulation of the flow in the straight pipe with the effect of hyperelasticity previously and it was confirmed that it is necessary to take into account of the interactive effect between the fluid and vessel wall. In this research, the former method is extended to compute the flow in the branch pipe which is characteristic configuration of a coronary artery. From the simulation results, the situation of the internal flow and deformation of wall as well as the shear stress which change depending on the branch angle are obtained.
There are various types of sand dune on the earth. These shapes can be broadly classified by the complexity of the wind, the amount of sand and vegetation. We make a numerical model of sand dune with vegetation. The main processes are saltation, avalanche, saltation suppression effect and growth of vegetation. As a result of numerical simulation, a crescent shaped dune called as parabolic dune appeared. As it increased the amount of sand, transverse-like dunes with vegetation developed.