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151 records · Page 9

Dynamics of two fluids under periodic acceleration

The evolution of the interface between two fluids confined in a rectangular cavity is investigated numerically to predict its transient behavior. These computations address mixing characteristics of fluids under microgravity conditions, particularly g-jitter conditions resulting from aircraft vibration or crew motion, and have applications in solution crystal growth. The two-dimensional formulation employs the Boussinesq approximation and treats the mixing of two fluids as an initial value problem with a prescribed concentration field. For fluid mixing of practical applications inside a cavity, it is shown that nonlinear convective transport can dominate over both viscous and molecular diffusion. However, viscous diffusion can become important for low Reynolds number or certain cavity sizes. A stacking phenomenon is shown to occur for aspect ratios (Ar) approximately between 5 to 10. For aspect ratios in the neighborhood of 0.1 to 0.2, inner cells evolve at the interface with increasing time. For a square cavity of Ar = 1, chaotic mixing of the fluid appears to occur for a Stokes-Reynolds number greater than about 5.

Duval, Walter M. B.↗

SPARROW: Steam Propelled Autonomous Retrieval Robot for Ocean Worlds

The Steam Propelled Autonomous Retrieval Robot (SPARROW) for Ocean Worlds was a Phase I mission concept study funded under the NASA NIAC program. This report represents the findings of that study and recommendations for future work. SPARROW, envisioned as a soccer ball-sized payload to a primary lander mission, is a propulsively hopping robot for the exploration of Europa's rugged, icy surface. A multi-thruster, passively gimballed robot within a protective, spherical shell, SPARROW is able to freely rotate, self-right, and tumble over chaotic terrains. Europa's abundant surface ice would be harvested as an in situ propellant source. The principal objective of SPARROW is to increase the science return of a Europa landed asset by enabling access to distal, spatially distributed geologic units. The design of mobility systems for Europa is challenging, due in part to its almost entirely unconstrained surface topography and strength. Images returned by Voyager and Galileo yielded resolutions on the order of hundreds of meters per pixel, with localized regions reaching 6 meters per pixel—still far larger than a typical rover. A key benefit of SPARROW's hopping, impact-tolerant design, is that it eliminates the need for a priori information regarding terrain topography and surface strength; no surface reaction forces are required for motion. In this context, SPARROW is believed to be entirely terrain agnostic. In this report we detail the results of three study objectives: i) to quantify the energy required to collect surface ice, change its phase, and maintain propellant temperature, ii) to identify control and estimation strategies that enable SPARROW to successfully reach, and return from, regions of scientific interest, and iii) to characterize the impact of SPARROW's range on likely science return. Five water-based propellant architectures are presented alongside their mass, power, and volume requirements. Monte Carlo simulations of SPARROW hopping and tumbling over 1 km of glacial ice are summarized, characterizing SPARROW's sensitivity to uncertainty in: initial pose, thrust profile, and vehicle-terrain interaction. A science traceability matrix is presented, which details the effect of sortie range on three science goals: constraining Europa's evolutionary morphology, assessing sub-surface ocean habitability, and searching for life and/or biosignatures.

Autonomous↗

SPARROW: A Steam Propelled Autonomous Retrieval Robot for Ocean Worlds

This paper presents the results of a NIAC Phase I study into the use of a propulsively hopping robot for the exploration of Europa’s rugged, icy surface. Named the“Steam Propelled Retrieval Robot for Ocean Worlds,” SPARROW is a multi-thruster robot passively gimballed within a protective, spherical shell, which enables it to freely rotate, self-right, and tumble over chaotic terrains. SPARROW is envisioned as a soccerball-sized payload to a primary lander mission. Europa’s abundant surface ice would be harvested as an in situ propellant source. The principal objective of SPARROW would be to increase the science return of a Europa landed asset by enabling access to distal, spatially distributed geologic units. The design of mobility systems for Europa is challenging, due in part to its almost entirely unconstrained surface topography and strength. Images returned by Voyager and Galileo yielded resolutions on the order of hundreds of meters per pixel, with localized regions reaching 6 meters per pixel—still far larger than a typical rover. A key benefit of SPARROW’s hopping, impact-tolerant design, is that it eliminates the need for a piori information on the terrain topography and surface strength; no surface reaction forces are required for motion. In this context, SPARROW is entirely terrain agnostic. In this paper we detail the results of three study objectives: i) to quantify the energy required to collect surface ice, change its phase, and maintain propellant temperature, ii) to identify control and estimation strategies that enable SPARROW to successfully reach, and return from, regions of scientific interest, and iii) to characterize the impact of SPARROW’s range on likely science return. Five water-based propellant architectures are presented alongside their mass, power, and volume requirements. Monte Carlo simulations of SPARROW hopping and tumbling over 1 km of glacial ice are summarized, characterizing SPARROW’s sensitivity to uncertainty in: initial conditions, thrust control, and cage-terrain interaction. Finally, a science traceability matrix is presented, which details the effect of sortie range on three science goals: constraining Europa’s evolutionary morphology, assessing sub-surface ocean habitability, and searching for life and/or biosignatures.

Phillips, Cynthia↗

Transport barriers to self-propelled particles in fluid flows

Here, we present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble Bacillus subtilis bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into xy space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Transient Mixing Driven by Buoyancy Flows

Mixing driven by buoyancy-induced flows is of particular interest to microgravity processes, as the body force that governs the intensity of flow fields can be directly controlled. We consider a model experimental system to explore the dynamics of mixing which employs two miscible liquids inside a cavity separated initially by a divider. The two liquids are oriented vertically inside a rectangular cavity with constant width and height, and varying depths to span the range of a Hele-Shaw cell to a 3-[) configuration. The two miscible liquids can be sufficiently diluted and died, for example water and deuterium oxide, such that a distinct interface exists across the divider. The transient mixing characteristic of the two fluids is addressed by following the Lagrangian history of the interface for various aspect ratios in the z-plane (depth variation) as well as a range of pulling velocities of the divider. The mixing characteristics of the two fluids are quantified from measurement of the length stretch of the interface and its flow field using respectively image processing techniques and Particle Imaging Velocimetry. Scaling analysis shows that the length stretch depends on four governing parameters, namely the Grashof number (Gr), Schmidt number (Sc), aspect ratio (Ar), and Reynolds number (Re). Variation of the Schmidt number is taken into account through thermophysical property variation. Thus our problem reduces to a codimension three bifurcation in parametric space for Gr, Ar, and Re. Our experimental results show that for Gr on the order of 106 and a nominal cavity aspect ratio Ar = 0.2, the net effect of removal of the divider and the overwhelming buoyancy force causes an overturning motion which stretches and folds the interface to produce ml internal breakwave. The structure of the breakwave is similar to the ubiquitous Rayleigh-Taylor instability morphology. The breakwave is dissipated either through internal or wall collision depending on the impulsive velocity of the divider as prescribed by the Reynolds number. The decay of the collision event occurs through sloshing oscillations over a short time scale. The two fluids then become stably stratified with a diffusive band at the interface indicating local mass transport. The local bifurcation of the internal breakwave is investigated as a function of aspect ratio. Results show that for narrow cavities on the order of 2mm (Ar = 0.04) folding does not occur, the interface only stretches. As the cavity size increases folding occurs through a supercritical bifurcation. Insight into the mechanism of folding is obtained from measurement of the flow field which shows that in the neighborhood of the folding event, there exists hyperbolic points caused by multiple vortex interactions. The global length stretch of the interface as a function of time is nearly Gaussian; calculations of finite-time Liapunov exponents as well as construction of horseshoe maps indicate the likelihood of a chaotic transient.

W.M.B. Duval↗

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. Finally, in all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗