General principles of pattern formation are introduced, such as the minimum energy principle, the minimum free energy principle and the minimum entropy production principle. In addition, two phenomena are explained, whose pattern formation principles are unknown, (i) thermal convection in a fluid with temperature-dependent viscosity and (ii) particle motions in a particle-liquid system under external horizontal vibration. Motivations of these researches are the interest in pattern formation mechanism.

View full abstract

Two-dimensional numerical simulations are performed to investigate the effect of weak acoustic excitation on the separated flow over an NACA0012 airfoil with the angle of attack a = 12°, at the Mach number M = 0.1 and at the low Reynolds numbers Re = 5 × 10⁴, 1 × 10⁵. The pressure amplitude of the induced acoustic wave is 0.05% of the static pressure at infinity. The results show that the acoustic waves with the appropriate frequencies make the time-averaged lift coefficient higher. This effective frequency range depends on the Reynolds number and its mean value St ≅ 0.023 √Re, which agrees with the experimental results of Zaman for an LRN- (1) -1007 airfoil. In the effective frequency range, the maximum vorticity in the laminar boundary layer of the airfoil becomes larger. On the other hand, there is no difference between the results of the two Reynolds numbers in the amplitudes of the lift coefficient variation due to the same excitation.

View full abstract

Dctailed flaw visualization is done to investigate the interaction of wig-tip vortex with a flat wall. The experiment is conducted by using a half-span wing model running through a square tunnel. The flow field induced by the tip vortex is visualized and analyzed by means of PIV as well as ahigh-speed video-camera system. The results demonstrate that the vortex close to the wall is not only convected in the lateral direction due to the image vortex but also away from the wall due to the secondary vortex generated through a vortex-surface interaction. It is also shown that the generation of secondary vortex occurs when the magnitude of wall pressure gradient induced by the tip vortex exceeds a critical value.

View full abstract

Large-scale horizontal mixing and transport barriers around the circumpolar vortex in the winter stratosphere are studied using a two-dimensional barotropic model on a spherical domain. A barotropically unstable jet is forced in order to obtain a fluctuating polar vortex. A flow with quasi-periodic time dependence and an aperiodic flow with similar behavior are investigated using several Lagrangian analyses.
Effective mixing inside and outside of the polar vortex is observed in the quasi-periodic flow. The process of the mixing is typical of chaotic mixing. The mixing regions are where the perturbations grow through barotropic instability. Poincare sections give accurate locations of chaotic mixing regions, and transport barriers are identified as the edges of invariant torus regimes. In addition to the transport barriers associated with strong potential vorticity gradients, another type of transport barrier exists, which is not related to the steep potential vorticity gradient.
The structure obtained in the aperiodic flow is relevant to that in quasi-periodic flow. The evolution of the correlation function is more typical of a chaotic zone. Chaotic mixing is also characterized by high values of Lyapunov exponents. Isolated regions are found near the center of the polar vortex, corresponding to the invariant tori in the Poincare sections of the quasi-periodic flow.

View full abstract

A possible circulation feature of thermal convection in the Martian lower atmosphere driven by radiative heating is investigated by the use of a two-dimensional anelastic model. Two cases of numerical simulations are performed; convection without dust and convection allowing dust injection from the surface by convective wind. The results of the simulations reveal that the thermal convection in the Martian lower atmosphere is km-size convection; the maximum vertical and horizontal scales of convective cells are 10 km and 5 km, respectively. In the case of dust-free condition, the values of both horizontal and vertical wind velocity often exceed 20 m see. The instantaneous maximum value of the surface stress associated with the km-size thermal convection reaches 0.04 Pa, which is equal to the threshold value to raise dust from the surface obtained experimentally. This result indicates that, the Martian general circulation models (GCMs), which have not been able to inject dust into the atmosphere, are now expected to simulate dust injection and the occurrence of global dust storm self-consistently by parameterizing the surface stress contribution associated with the km-size thermal convection. When dust is allowed to be injected into the atmosphere, dust spreads into the convective layer promptly and is well mixed within a few hours. After dust reaches the stratosphere, the depth of the convection layer becomes shallower and the intensity of convetive wind becomes smaller than those of the dust-free case. This is because the stratospheric temperature increases due to the absorption of solar radiation by dust.

View full abstract

Effects of temperature-dependence of viscosity on one-dimensional flows are analyzed. When hot fluid cooled as it flows, velocity-pressure characteristic curve represents negative inclination in certain region. In this negative differential resistance region, the pressure drop decreases with increased velocity. On two and three parallel channels model, negative differential resistance causes bifurcation of the solution. In this case, there are multiple steady flows with inhomogeneous velocity distribution besides homogeneous one. Stableness of some inhomogeneous flow and unstableness of homogeneous one are shown by numerical analyses. At last, the way of the bifurcation is described in a fixed law.

View full abstract

Two-dimensional thermal convection in a rapidly rotating cylindrical annulus is examined by the characteristics of topographic Rossby waves in order to understand the spiraling columnar convection appearing in rotating spherical systems. The top and the bottom boundaries of the annulus are inclined with respect to the rotation axis to model a spherical geometry. Through the topographic β effect of these boundaries, the rotation of the system affects two-dimensional columnar fluid motion.
The spiraling structure of critical convection obtained by linear stability analysis can be interpreted as the outward propagation of Rossby waves from the inner region, where convective motion is easily excited because of the small inclination of the boundaries. The flow pattern estimated with the dispersion relation well coincides with the structure of convection. The kinetic energy budget analysis shows that energy generated by buoyancy force in the inner region is transported by Rossby waves and dissipates in the whole region.
Mean flow generation by finite amplitude spiraling convection can be explained qualitatively by the properties of Rossby waves. Through the outward propagation of Rossby waves, whose momentum is in the prograde direction, prograde and retrograde mean flow is generated at the outer and the inner regions, respectively.

View full abstract