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Using a stereoscopic vision method, we have experimentally investigated the time evolution of a free thin disk motion with six degrees of freedom for the first time. It is found that, as the dimensionless moment of inertia I ‫ء‬ decreases, the trajectory of the disk transits from planar to nonplanar. New types of free falling motions were identified for small I ‫ء‬ values, including the spiral state and the transitional state. An extended Re− I ‫ء‬ phase diagram corresponding to different flow regimes was given. The underlying physics associated with the transition is found to be connected to the interactions between the moving object and induced vortices.Free body motions in fluids are ubiquitous in nature. Such phenomena, including rising bubbles, falling leaves, paper sheets, and dispersal of winged seeds, exhibit complicated dynamical behaviors. The related studies can be dated back to the work of Newton and Maxwell. Over the past half century, this classic topic has received renewed interests in a wide range of contexts including meteorology, 1,2 sedimentology, 3,4 biomechanics, 5 chemical engineering, 6 and unsteady flapping aerodynamics. 7 Due to interactions with the fluid flow, a free body does not generally select a rectilinear path. A variety of trajectories has been observed even for bodies with simple geometries, such as spheres and thin disks. Periodic oscillatory motion is the most common type and has been observed in flexible bodies such as bubbles, droplets, or solid bodies such as spheres, disks, or cones. For a free rising bubble in water, it is well known that its trajectory transits from zigzag to circular helix when the size exceeds a critical value. 8 However, for certain solid bodies, periodic oscillations are often observed to associate with planar motions. Field et al. 9 presented a phase diagram for thin disks based on the Reynolds number Re and dimensionless moment of inertia I ‫ء‬ . Steady falling, periodic oscillation, tumbling, and apparently chaotic motion were included in the phase diagram. These motions are similar to those found in the falling of two dimensional plates. [10][11][12][13][14] An earlier study by Willmarth et al. 15 observed that the fluttering of a free falling disk may not reside in a vertical plane. Recent experiments on freely rising cylinders 16 also reported helical trajectories. However, it is still unclear whether the nonplanar motion is caused by disturbances in experiments or intrinsically linked to the fluid-body interaction.In this letter, we report our experimental investigations of free falling thin circular disks in water. The unsteady wake structures were visualized with fluorescence dye and the body trajectories were measured with a stereoscopic vision method. Our results provide all the six degrees of freedom of falling thin disks over a wide range of the Reynolds number, Re= Ud / , and dimensionless moment of inertia,Here U is the averaged falling velocity over long distance, is the kinematic viscosity, h and d are thickness and diameter of the ...

In this paper, we present direct comparisons of experimental results on transition in wall-bounded flows obtained by flow visualizations, hot-film measurement, and particle-image velocimetry, along with a brief mention of relevant theoretical progresses, based on a critical review of about 120 selected publications. Despite somewhat different initial disturbance conditions used in experiments, the flow structures were found to be practically the same. The following observed flow structures are considered to be of fundamental importance in understanding transitional wall-bounded flows: the three-dimensional nonlinear wave packets called solitonlike coherent structures (SCSs) in boundary layer and pipe flows, the Λ-vortex, the secondary vortex loops, and the chain of ring vortices. The dynamic processes of the formation of these structures and transition as newly discovered by recent experiments include the following: (1) The sequential interaction processes between the Λ-vortex and the secondary vortex loops, which control the manner by which the chain of ring vortices is periodically introduced from the wall region into the outer region of the boundary layer. (2) The generation of high-frequency vortices, which is one of the key issues for understanding both transitional and developed turbulent boundary layers (as well as other flows), of which several explanations have been proposed but a particularly clear interpretation can be provided by the experimental discovery of secondary vortex loops. The ignorance of secondary vortex loops would make the dynamic processes and flow structures in a transitional boundary layer inconsistent with previous discoveries. (3) The dominant role of SCSs in all turbulent bursting, which is considered as the key mechanism of turbulent production in a low Reynolds-number turbulent boundary layer. Of direct relevance to bursting is the low-speed streaks, whose formation mechanism and link to the flow structures in wall-bounded flows can be answered more clearly than before in terms of the SCS dynamics. The observed SCSs and secondary vortex loops not only enable revisiting the classic story of wall-bounded flow transition, but also open a new avenue to reconstruct the possible universal scenario for wall-bounded flow transition.

The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.

Transition and turbulence production in a hypersonic boundary layer is investigated in the Mach 6 wind tunnel at Peking University, using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. Detailed analysis of the experimental observations is provided. It is found that, although the second mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves. Moreover, the second mode interacts strongly with low-frequency waves, which leads to immediate transition to turbulence.freestream velocity, m∕s u = velocity vector, m∕s u = x component of the velocity, m∕s v = y component of the velocity, m∕s w = z component of the velocity, m∕s x = streamwise coordinate along the cone's surface, mm y = coordinate normal to the cone's surface, mm z = transverse coordinate normal to the x-y plane, mm= viscous normal stress, Pa ρ = density, kg∕m 3 τ f = flow time scale, s τ p = particle relaxation time, s Φ = viscous dissipation function per unit volume, kg∕m · s 3 ω = vorticity, 1∕s