Philosophiae Naturalis Principia Mathematica邦訳書の底本に関するノート

Large, distributed collections of miniaturized, wireless electronic devices1,2 may form the basis of future systems for environmental monitoring3, population surveillance4, disease management5 and other applications that demand coverage over expansive spatial scales. Aerial schemes to distribute the components for such networks are required, and—inspired by wind-dispersed seeds6—we examined passive structures designed for controlled, unpowered flight across natural environments or city settings. Techniques in mechanically guided assembly of three-dimensional (3D) mesostructures7–9 provide access to miniature, 3D fliers optimized for such purposes, in processes that align with the most sophisticated production techniques for electronic, optoelectronic, microfluidic and microelectromechanical technologies. Here we demonstrate a range of 3D macro-, meso- and microscale fliers produced in this manner, including those that incorporate active electronic and colorimetric payloads. Analytical, computational and experimental studies of the aerodynamics of high-performance structures of this type establish a set of fundamental considerations in bio-inspired design, with a focus on 3D fliers that exhibit controlled rotational kinematics and low terminal velocities. An approach that represents these complex 3D structures as discrete numbers of blades captures the essential physics in simple, analytical scaling forms, validated by computational and experimental results. Battery-free, wireless devices and colorimetric sensors for environmental measurements provide simple examples of a wide spectrum of applications of these unusual concepts. With a design inspired by wind-dispersed seeds, a series of three-dimensional passive fliers at the macro-, meso- and microscale are realized that can bear active electronic payloads.

Three-dimensional electronic microfliers inspired by wind-dispersed seeds.

The turbulent flow originating from the interaction between two parallel streams with different velocities is studied by means of direct numerical simulation. Rather than the more common temporal evolving layer, a spatially evolving configuration, with perturbed laminar inlet conditions is considered. The streamwise evolution and the self-similar state of turbulence statistics are reported and compared to results available in the literature. The characteristics of the transitional region agree with those observed in other simulations and experiments of mixing layers originating from laminar inlets. The present results indicate that the transitional region depends strongly on the inlet flow. Conversely, the self-similar state of turbulent kinetic energy and dissipation agrees quantitatively with those in a temporal mixing layer developing from turbulent initial conditions [M. M. Rogers and R. D. Moser, “Direct simulation of a self-similar turbulent mixing layer,” Phys. Fluids 6, 903 (1994)]. The statistical features of turbulence in the self-similar region have been analysed in terms of longitudinal velocity structure functions, and scaling exponents are estimated by applying the extended self-similarity concept. In the small scale range (60 400), the mean shear and large coherent structures result in a significant deviation from predictions based on homogeneous isotropic turbulence theory. In this second scaling range, the numerical values of the exponents agree quantitatively with those reported for a variety of other flows characterized by strong shear, such as boundary layers, as well as channel and wake flows.

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Statistics and scaling of turbulence in a spatially developing mixing layer at Reλ = 250

The early free fall stages of cones with a density ratio 1.18 and apex angles of $$30^{\circ }$$
 , $$45^{\circ }$$
 , $$60^{\circ }$$
 , and $$90^{\circ }$$
 were studied using a wireless 3-axis gyroscope and accelerometer to describe the cone 3D motions, while particle image velocimetry was used to capture the induced flow in the near wake. The Reynolds number based on the cones diameter and the velocity at which the cone reaches the first local velocity maximum is found to consistently set the limit between two distinctive states. Relatively rapid growth in the cone nutation and departure from the vertical axis is observed after this Re is reached. Sequences of vertical velocity, swirling strength, LES-decomposed velocity, and pressure fields show the formation and growth of a large and initially symmetric recirculation bubble at the cone base. Those also highlight the presence of a symmetric 3D vortex rollup dominating the near wake in the early stages of the fall. A shear layer develops at the edge of the wake and manifests in the periodic shedding of Kelvin–Helmholtz vortices that, due to the nature of the recirculation bubble, reorganize to constitute a part of the rollup. Later in the fall, the wake loses symmetry and shows high population of vortical structures leading to turbulence. The asymmetric wake leads to strong interactions between the flow field and the cone evidenced by the shedding of a part of the 3D large-scale vortex rollup. This shedding process along with the cone rotation around its own axis provides a possible explanation of the helical wake structure observed in other studies.

On the transient dynamics of the wake and trajectory of free falling cones with various apex angles

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.

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

This paper describes an experimental investigation of the dynamics of a freely falling thin circular disk in still water. The flow patterns of the disk zigzag motion are studied using dye visualization and particle image velocimetry. Time-resolved disk motions with six degrees of freedom are obtained with a stereoscopic vision method. The flow separation and vortex shedding are found to change with the Reynolds number, . At high Reynolds numbers a new dipole vortex is shed that is significantly different from Karman-type vortices. The vortical structures are mainly composed of leading-edge vortices, a counter-rotating vortex pair and secondary trailing-edge vortices. The amplitude of the horizontal oscillation is also dependent on the Reynolds number with a critical Reynolds number , where the oscillatory amplitude is proportional to for , but becomes invariant for . Three-dimensional dipolar vortices were also observed experimentally.

Experimental investigation of freely falling thin disks. Part 1. The flow structures and Reynolds number effects on the zigzag motion

The free-fall motion of a thin disk with small dimensionless moments of inertia (I < 10 3 ) was investigated experimentally. The transition from two-dimensional zigzag motion to three-dimensional spiral motion occurs due to the growth of three-dimensional disturbances. Oscillations in the direction normal to the zigzag plane increase with the development of this instability. At the same time, the oscillation of the nutation angle decreases to zero and the angle remains constant. The effects of initial conditions (release angle) were investigated. Two kinds of transition modes, zigzag‐spiral transition and zigzag‐spiral‐zigzag intermittence transition, were observed to be separated by a critical Reynolds number. In addition, the solution of the generalized Kirchhoff equations shows that the small I is responsible for the growth of disturbances in the third dimension (perpendicular to the planar motion).

Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral

We experimentally investigate the dynamics of surface waves excited by oscillations from a cylindrical sidewall. Particle-imaging-velocimetry measurements with fluorescent particles were used to determine the flow patterns near the sidewall of the cylindrical fluid container and to identify the locations of the evolving air–water interfaces. The high-frequency wall oscillations created four jets that originate at the cylindrical sidewall. Four vortex streets shed from the jets propagate from the sidewall to the centre of the container and subsequently excite a low-frequency gravity wave. The interaction between this gravitational surface wave and the high-frequency capillary waves was found to be responsible for creating droplet splash at the water surface. This phenomenon was first described as ‘Long-Xi’ or ‘dragon wash’ in ancient China. The physical processes for generating the droplet ejection, including the circular capillary waves, azimuthal waves, streaming jets and low-frequency gravity waves, are described in this paper.

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Experimental studies of surface waves inside a cylindrical container

We have conducted a detailed analysis of scaling for longitudinal and transverse velocity structure functions in a turbulent free shear flow. The free shear flow is generated via a mixing layer under varying conditions of upstream flow disturbances. Two velocity components are simultaneously measured with a pair of cross-wires at two spanwise locations, with varying positions of the second cross-wire, which allows us to study the statistics of two longitudinal and four transverse velocity increments. Spectra, probability density functions of the velocity increments, and scaling exponents are measured and discussed in relation to flow structures such as streamwise and spanwise vortices. Scaling exponents of the velocity structure functions are interpreted in the phenomenological framework of the hierarchical structure (HS) model of She & Leveque (Phys. Rev. Lett. vol. 72, 1994, p. 336). One HS parameter () related to the singularity index of the so-called most intermittent structures shows strong dependence on flow structures. The strongest intermittency occurs in the form of streamwise vortices. The results confirm that coherent small-scale flow structures are responsible for intermittency effects and anomalous scaling, and a complete set of measurements of longitudinal and transverse velocity variations are required to derive flow structural information.

Mingde Zhou

Papers

Experimental investigation of freely falling thin disks. Part 1. The flow structures and Reynolds number effects on the zigzag motion

Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral

Experimental studies of surface waves inside a cylindrical container

Hierarchical structures in a turbulent free shear flow

Hierarchical structures in a turbulent pipe flow