Takao Yoshinaga

Recurrence and chaotic behavior resulting from nonlinear interaction between long and short waves

Long time asymptotic behavior resulting from nonlinear interaction between long and short waves is examined numerically by using the Fourier expansion method. A slightly modulated short wave is adopted as an initial condition. The results exhibit recurrence or chaotic motion, depending upon the magnitude of the control parameters involved in the governing equations. It is found that the chaotic motion is possible, even in a case for which only a single unstable mode exists in the Fourier modes.

Behavior of a Free Liquid Sheet Subject to a Temperature Difference between Both Surfaces

Behavior of a free viscous liquid sheet subject to a temperature difference between both surfaces is analytically examined by considering the thermocapillary effect. Under the long wave approximation, nonlinear evolution equations of the sheet thickness and velocity are derived for sufficiently small Prandtl number, while a nonlinear relation between the position of sheet centerline and the sheet thickness is obtained. It is shown that the surface profiles deviate from the symmetric (dilational) to the asymmetric with flat troughs and large crests as the temperature difference increases. It is also shown that there exist certain critical temperature difference ΔΘ c above which the sheet becomes linearly unstable. In the neighborhood of ΔΘ c , a weakly nonlinear equation of the sheet thickness is obtained and numerically solved for the instability. However, since ΔΘ c is estimated to be so large in both linear and nonlinear analyses, the sheet may be substantially stable as far as the small Prandtl number ...

Encapsulation and Disintegration of a Gas-Cored Annular Liquid Jet

Breakup and encapsulation phenomena are analytically investigated for a gas-cored compound liquid jet which consists of an inviscid and incompressible core gas and surrounding annular liquid. Applying the long wave approximation to both core and annular phases, a set of reduced nonlinear equations is derived for large deformations of the jet. Breakup of the jet is numerically examined in the reduced equations when the jet is semi-infinite and sinusoidal disturbances are fed at the end of the jet. It is found that there exit the most unstable frequencies of disturbances giving the shortest breakup time, which increase as the increase of input amplitudes and velocity ratios of the core to the annular phases, while increase or decrease depending upon the Weber numbers based on the annular phase. For small and medium Weber numbers, it is shown that the jet breaks up by pinching of the core phase and the capsule formation periods and sizes can be determined by the most unstable frequencies, which well agree with the results in the previous experiment and the existing phenomenological model. On the other hand, it is also shown for large Weber numbers that the jet breaks up by disintegration of the annular phase and fails to encapsulate the core gas.Copyright

Chaotic wave phenomena in a bubbly liquid based on the K-dV-Burgers model

Strong shock waves in a bubbly liquid are examined by using a simple numerical model based on the K-dV-Burgers equation. In this model, two kinds of coefficients of the equation are switched with each other depending upon the relative magnitude of the peak amplitude to a certain threshold. Irregular behavior is numerically found both in the oscillatory wave trains behind the shock front and in the evolution of the shock front itself. Since such irregularity is enhanced when the nonlinearity increases, the wave behavior is considered to be chaotic.

Chaotic phenomena on a coupled nonlinear oscillator based on the rollins-hunt's model

Based on the Rollins-Hunts model, chaotic phenomena in a driven coupled R-L-diode oscillator are examined numerically. It is found that a straightforward extension of this model to a system with two degrees of freedom is valid as far as the quasiperiodic route to chaos is concerned. However, this model is not sufficient to explain the intermittency and the quasiperiodic routes including the discontinuous (jump) bifurcations with hysteresis. Then it is shown that the additional nonlinearity due to variable capacitance of the diode is effective to explain the above phenomena. It is also shown that a two-dimensional discrete return map in which nonlinear terms are introduced in a characteristic form simulates systematically the numerical results. In particular, this map model can explain effectively the mechanisms which cause the intermittency and the cliscontinuous bifurcation.