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The drag coefficient ( C D ) of a sphere freely rolling without slipping on a rough plane is presented in this study. Increasing panel roughness has been found to increase C D , although lubrication theory predicts that the larger gap imposed by the rougher panel should yield a smaller drag. We propose that this increase in drag is due to the effects of rolling resistance, which increases with panel roughness. The total drag on a sphere is decomposed into fluid drag and drag due to rolling resistance, where the fluid drag is predicted using a combined analytical–numerical approach. It is shown that rolling resistance can be modeled as a resistive torque opposing the sphere motion, generated by the offset contact normal force from the sphere center plane. This coefficient of rolling resistance ( μ r ) can be predicted using the root mean square roughness ( R q ) of the panel. Additionally, μ r is observed to increase with sphere down-slope velocity and an empirical relationship between μ r , R q , and non-dimensional velocity ( U ∗ ) is given. A comparison of the drag predicted by the proposed model with measured data indicates good agreement for all the four panels considered. Consistent with previous literature, a non-linear relationship between μ r , R q , and U ∗ is proposed. Although increasing panel roughness leads to a smaller fluid drag due to the larger gap imposed by rougher panels, the drag due to rolling resistance increases more rapidly. This leads to an increase in total drag with increase in the panel roughness. Additionally, increasing panel roughness is observed to have a significant effect on the sphere wake, leading to irregular wake shedding and increase in the Strouhal number. [ABSTRACT FROM AUTHOR]

An experimental study was conducted on head-on collisions of Re = 2000 and 4000 vortex rings upon air–water interfaces to study the vortex dynamics and the effects of different vortex ring Reynolds numbers on the key vortex flow mechanisms. Unfiltered tap water was used where surface contaminants were present; hence, the interfacial stress levels are lower but not entirely zero like an idealized free surface. Results demonstrate that the vortex dynamics involve first, the resulting secondary and tertiary vortex rings transitioning into wavy states, before their upper loops disconnect/reconnect to the interface to form U-shaped vortex loops along the inner and outer peripheries of the primary vortex ring, respectively, in an alternating pattern. Second, tertiary vortex loops entangle around the primary vortex ring to produce counter-rotating vortex pairs that reorganize themselves along the primary vortex ring outer periphery, between the primary vortex ring and secondary vortex loops, as well as hairpin-like structures that aid ejection of primary vortex ring momentum. Third, secondary vortex loops rotate toward the collision axis before their lower segments are entrained by the primary vortex ring. A higher Reynolds number primary vortex ring would confer additional flow changes, such as a higher wave number for the secondary and tertiary vortex rings/loops, pairings of secondary vortex loops "side-arms" that reduce their instances by about half and formations of Tsai–Widnall–Moore–Saffman instabilities induced by flow perturbations. Finally, vortex flow models proposed to explain the flow mechanism at different flow stages are found to be in good agreements with the experimental visualizations. [ABSTRACT FROM AUTHOR]

Most variational principles in classical mechanics are based on the principle of least action, which is only a stationary principle. In contrast, Gauss' principle of least constraint is a true minimum principle. In this paper, we apply Gauss' principle to the mechanics of incompressible flows, thereby discovering the fundamental quantity that Nature minimizes in most flows encountered in everyday life. We show that the magnitude of the pressure gradient over the domain is minimum at every instant of time. We call it the principle of minimum pressure gradient (PMPG). It turns a fluid mechanics problem into a minimization one. We demonstrate this intriguing property by solving four classical problems in fluid mechanics using the PMPG without resorting to Navier–Stokes' equation. In some cases, the PMPG minimization approach is not any more efficient than solving Navier–Stokes'. However, in other cases, it is more insightful and efficient. In fact, the inviscid version of the PMPG allowed solving the long-standing problem of the aerohydrodynamic lift over smooth cylindrical shapes where Euler's equation fails to provide a unique answer. The PMPG transcends Navier–Stokes' equations in its applicability to non-Newtonian fluids with arbitrary constitutive relations and fluids subject to arbitrary forcing (e.g., electromagnetic). [ABSTRACT FROM AUTHOR]

Lie derivative is an important concept in differential geometry. From the perspective of theoretical fluid dynamics, the present paper evaluates and interprets the Lie derivatives of the fundamental surface physical quantities (including skin friction, surface vorticity, and surface pressure) with respect to a characteristic velocity field in near-wall incompressible viscous flows. It is found that the Lie derivatives are directly associated with the boundary enstrophy flux, an orthogonal pair of skin friction and surface vorticity, and an orthogonal pair of surface enstrophy gradient and its conjugate vector, while components of the Lie derivatives in skin-friction-surface-vorticity orthogonal frame are related to four on-wall coupling scalar quantities (associated with the skin friction divergence and the surface vorticity divergence). The derived theoretical results are first evaluated in a laminar oblique Hiemenz flow and a turbulent channel flow. Then, features of the Lie derivatives are explored in a typical skin friction structure generated by a complex separated flow over a hill model. The present exposition provides a unique perspective of the Lie derivatives to the boundary vorticity dynamics and near-wall flow physics. [ABSTRACT FROM AUTHOR]

Turbulence near a free surface is of multi-layered nature and of fundamental significance in understanding vast marine and ocean processes. Direct numerical simulation of an open channel with the free surface modeled by a free-slip boundary is performed. Complex multi-layered turbulence (i.e., the blockage layer, the slip layer, and the Kolmogorov layer) under the free surface are first identified based on predefined anisotropy indices. Later on, statistical features of the anisotropic turbulence inside the three turbulence layers are presented. Most importantly, considering the drastic variation of both velocity and vorticity in near-surface layers, we revisit the complex multi-layered turbulence by the velocity–vorticity correlation structure (VVCS) method [Chen et al., J. Fluid Mech. 742, 291–307 (2014)]. It is found that the VVCS can physically depict evolution of the hairpin vortex inside the channel, including generation in the bottom wall region, expansion in the bulk flow, process of getting flattened in the blockage layer, and then distortion and breakdown in the slip layer and the Kolmogorov layer. Specifically, the correlation structures VVCS11 for streamwise velocity and streamwise vorticity reflect how the hairpin legs are spatially distributed, while the correlation structures VVCS13 for streamwise velocity and spanwise vorticity describe the evolution of the hairpin vortex head. In the end, a cradle-like structure model is proposed based on the VVCS results and the vortex ring collision model is introduced to improve the understanding of the multi-layered turbulence under free surface. Hopefully, this research can be of value in future turbulence modeling work on free surface flows. [ABSTRACT FROM AUTHOR]

From the Navier–Stokes–Korteweg equations, the exact relations between the fundamental surface physical quantities for the two-phase viscous flow with the diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux, and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for the analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme, focusing on the spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure, and enstrophy flux at the interface and the wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall. [ABSTRACT FROM AUTHOR]

This paper presents a concise derivation of the temporal-spatial evolution equation of the wall-normal enstrophy flux on a no-slip flat wall. Each contribution to the evolution is explicitly expressed using the two fundamental surface quantities: skin friction (or equivalently surface vorticity) and surface pressure which are coupled through the boundary enstrophy flux (BEF). The newly derived relation is then used to explore, in a preliminary manner, the physical features of surface quantities and their dynamical roles in wall-bounded laminar and turbulent flows. It is confirmed that the BEF usually changes its sign near the separation and attachment lines in the skin friction field. For the simulated incompressible turbulent channel flow at R e τ = 180 , violent variations of different terms in the derived formulation are observed in the regions below the strong wall-normal velocity events (SWNVEs) when compared to other common regions. Near the SWNVEs, the evolution of the wall-normal enstrophy flux is found to be dominated by the wall-normal diffusion of the vortex stretching term which is relatively weak or negligible for laminar flows. Combined with our previous research results, it is conjectured that the strong interaction between the quasi-streamwise vortex and the channel wall intensifies the temporal-spatial evolution of the wall-normal enstrophy flux on the wall, which accounts for the highly intermittent feature of the viscous sublayer. [ABSTRACT FROM AUTHOR]

We study the capillary-driven breakup of a slender drop suspended in a quiescent viscous fluid using direct numerical simulation. We focus on a parametric space comprising viscosity ratio and Ohnesorge number. While the large Ohnesorge number approximation of the problem has received experimental and theoretical attention over the years, the influence of inertia—at small Ohnesorge number—on the behavior of the slender drop is not well studied. We first validate our simulation results with previous experimental results at large viscosity ratios. We then consider the drop suspended in a quiescent fluid and systematically study the capillary-driven breakup of the drop at different Ohnesorge numbers and viscosity ratios. Our simulations reveal that the slender drop breaks up under all conditions, but the instability is transitional for some viscosity ratios. By considering both inertial and viscous effects in the ambient surrounding fluid, we show how the structure of the flow field is modified upon the introduction of inertia and how the viscosity of the surrounding fluid aids in vorticity diffusion. Finally, we extend the stability diagram for drops, which classifies them into asymptotically unstable and asymptotically stable states in a parametric space comprising viscosity ratio and Ohnesorge number. We finely probe the stability diagram and present a stability curve in the parametric space of viscosity ratio and Ohnesorge number. [ABSTRACT FROM AUTHOR]

The zero-frequency linear plasma response to static applied non-axisymmetric fields is calculated using a resistive two-fluid model in diverted, toroidal geometry. Within this model, the effects on the plasma response of resistivity, rotation, differential ion and electron velocity, and dissipation are explored. Rotation is generally found to inhibit the formation of islands in the plasma, in qualitative agreement with theoretical results. When two-fluid effects are included, it is found that the penetration of the non-axisymmetric fields is generally greatest when the part of the electron rotation perpendicular to the equilibrium magnetic field is small at the mode-rational surface. Strong rotation shear in the edge is found to enhance the plasma response there. The entire plasma, including the separatrix and scrape-off layer, is included in the computational domain. [ABSTRACT FROM AUTHOR]

Circuit depth reduction is of critical importance for quantum chemistry simulations on current and near term quantum computers. This issue is tackled by introducing a chemically aware strategy for the unitary coupled cluster ansatz. The objective is to use the chemical description of a system to aid in the synthesis of a quantum circuit. We combine this approach with two flavors of symmetry verification for the reduction of experimental noise. These methods enable the use of Quantinuum's System Model H1 ion trap quantum computer for a 6-qubit quantum subspace expansion calculation. We present (i) calculations to obtain methane's optical spectra; (ii) an atmospheric gas reaction simulation involving [ C H 3 ⋅ —H—OH]‡. Using our chemically aware unitary coupled cluster state-preparation strategy in tandem with state of the art symmetry verification methods, we improve device yield for CH4 at 6 qubits. This is demonstrated by a 90% improvement in two-qubit gate count and a reduction in relative error to 0.2% for electronic energy calculated on System Model H1. [ABSTRACT FROM AUTHOR]