This article reviews recent developments of experimental and theoretical studies of standing surface waves excited by vertical periodic oscillation. Nonlinear phenomena in Faraday surface waves such as low-dimensional chaos of mode-competition, anomalous diffusion of floating particles on the surface, excitation of one-dimensional parametric solitary waves, two-dimensional pattern selection and associated spatiotemporal modulation have been found and investigated vigorously. Especially, spontaneous formation of various patterns on parametrically excited surface waves under different experimental conditions is explained and a theory based on Lyapunov functional method is applied to this problem.

View full abstract

It is commonly remarked that the theory of acoustics is based on an infinitesimal theory and the linear relation between sound pressure and particlevelocity is well understood for a description of sound propagation in a fluid. The relation does not hold when the amplitude of sound wave is increased to be finite. A brief survey on 'Nonlinear Acoustics' is presened here which forms a bridge between the linear acoustics and the theory of shock wave. Nonlinear acoustics is concerned with a study of the second order phenomena generated in sound beams due to the inherent nonlinearity of the medium. The main topics described here are waveform distortion, acoustic streaming, and acoustic radiation pressure. Other interests such as cavitation are included but not presented in this survey.

View full abstract

Large-scale frontlike structures, which are not expected from a simple wind-driven ocean circulation theory, can be found in basin-scale oceanic gyres. Recent works suggest that such a structure could be caused by nonlinear stationary Rossby wavelike disturbances superimposed on the wind-driven gyres. The present article gives a brief review on this problem, after outlinig a wind-driven ocean circulation therory (Svedrup theory) and nonlinear Rossby wave dynamics.

View full abstract

we give critical review on the present studies on fluidized beds which consists of fluid and solid mixtures. We have introduced a new algorithm to simulate fludized beds, which is a dynamical extension of the Stokesian dynamics method for the simulation of colloid. particles. From our simulation, We have found similarities between statistical steady states in fluidized beds and thermal equilbrium states in dense equilibrium liquids when we observe averaged quanties. On the other hand, the fluctuations in our simulation for fiuidized beds are as large as those observed in conventional fluid turbulences.

View full abstract

The long time motion of a linearly stratified inviscid non-diffusive fluid after the sudden discharge from a sink is studied theoretically. Both the line and the point sink flows are investigated. When the internal Froude number is small, the flow approaches the state of selective withdrawal. In this paper, we show in detail the asymptotic behaviour of internal waves which play an important role in establishing the selective withdrawal. Clear differences of the wave motion between the line and the point sink flows are also suggested.

View full abstract

Direct numerical simulation (DNS) of decaying isotropic turbulence with a passive scalar, say temperature, has been done on 128³-512³ grids of the Numerical Wind Tunnel at National Aerospace Laboratory. With the use of the alias-free Fourier spectral method, the solenoidal field decomposition of velocity was made to exactly satisfy the imcompressibility condition. The simulation covers the range of Taylor-microscale Reynolds number from about 90 to 160 for the fixed Prandtl number equal to 1. The universal spectral forms for velocity (noticed by She et al.) and temperature are verified, irrespective of Reynolds number. The fields of vorticity and temperature gradient are visualized to clarify their local structures such as “worms” and sheets, respectively. The statistics of velocity, its longitudinal and lateral gradients, temperature and its gradient are clarified at the fully-developed state. Particularly, temperature distributes in a non-Gaussian way, resembling “hard turbulence” in the Reyleigh-Benard flow. Finally, the multifractal nature of energy-dissipation in our DNS is discussed in comparison with existing theories.

View full abstract

A calculation code has been developed in order to simulate a spatially developing compressible round jet by solving the axisym metric and three-dimensional compressible Navier-Stokes equations. A fourth-order non-oscillatory scheme and Roe's approximate Riemann solver are used in space discretization, and the third-order Runge-Kutta scheme is utilized as time integration. This code has an advantage that it can be easily extended to any order of accuracy in space and time. The inflow and outflow boundary conditions are important in simulating spatially developing subsonic flow. Though several boundary conditions based on the characteristic method or the wave equation have been proposed, they are still incomplete to get accurate solutions. Here in this study a non-reflecting condition developed by Thompson is employed because of its simplicity without empirical parameters.
The present code is applied to study early stages of spatially developing round jet for two Mach numbers of 0.5 and 1.5. The characteristics of compressible round jet, including the effect of compressibility, are examined. In order to verify the numerical scheme and boundary conditions, calculations are first performed for axisymmetric flow, and then they are extended to three-dimensional jet. In both axisymmetric and three-dimentional calculations, the axial location at which vortex ring rolls up moves downstream as the Mach number increases. In the axisymmetric flow, two vortex rings generated one after the other by Kelvin-Helmholtz instability merge into a larger vortex ring, which is repeated in the downstream. In the three-dimensional flow, the subsonic jet develops three-dimensional rib structures after axisymmetric roll-up and pairing. On the other hand, in the supersonic jet the pairing is prevented by large axial vorticity, which enhances three-dimensionality of vortex. To the contrary, in both subsonic and supersonic jets, longitudinal vortices in the downstream slow down the growth rates of shear layer.

View full abstract