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In this paper axisymmetric solutions of the Navier-Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in which the radial velocity along the axis is prescribed, and the other in which the radial velocity along the axis is obtained as an eigenvalue of the problem. The existence of these solutions are limited to a range of Reynolds numbers and the transition from one case to the other are discussed in detail.

A class of axisymmetric vortex solutions superposed upon radial stagnation flows is described. The new vortex solutions generalize the classical Burgers' vortex and Sullivan's vortex solutions in the presence of a volumetric line source at the symmetry axis, the former approaching the Burgers' vortex sheet when the source strength becomes very large. The stability of the generalized Burgers' vortex is studied. In a different manner from the classical solution, the generalized Burgers' vortices are found to be unstable for two-dimensional disturbances when the vortex Reynolds number is increased above a critical value, for a fixed strength of the volumetric source.

Diamond nanocrystals can harbor spin qubit sensors capable of probing the physical properties of biological systems with nanoscale spatial resolution. These diamond nanosensors can readily be delivered into intact cells and even living organisms. However, applications beyond current proof-of-principle experiments require a substantial increase in sensitivity, which is generally limited by surface-noise-induced spin dephasing and relaxation. In this work, we significantly reduce magnetic surface noise by engineering core-shell structures, which in combination with dynamical decoupling result in qubit coherence times (T2) ranging from 52us to 87us - a drastic improvement over the 1.1us to 35us seen in bare particles. This improvement in spin coherence, combined with an overall increase in particle fluorescence, corresponds to a two-order-of-magnitude reduction in integration time. Probing qubit dynamics at a single particle level, furthermore, reveals that the noise characteristics fundamentally change from a bath with spins that rearrange their spatial configuration during the course of an experiment to a more dilute static bath. The observed results shed light on the underlying mechanisms governing spin dephasing in diamond nanocrystals and offer an effective noise mitigation strategy based on engineered core-shell structures., Comment: Main text 10 pages 4 main figures and 10 extended data figures

A theoretical analysis is developed to investigate the effects of gas expansion due to heat release on unsteady diffusion flames evolving in a pipe flow in which the mixing of reactants is controlled by Taylor's dispersion processes thereby extending a previously developed theory based on the thermo-diffusive model. It is first shown that at times larger than radial diffusion times, the pressure gradient induced by the gas expansion is, in the first approximation, small in comparison with the prevailing pressure gradient driving the flow, indicating that corrections to the background velocity profile are small. The corrections to the velocity components along with the leading-order mixing variables such as the concentrations, temperature and density are solved for a Burke-Schumann flame. Due to the dependence of the effective Taylor diffusion coefficients on the gas density, quantitative and sometimes qualitative departures in predictions from the thermo-diffusive model are observed.

This paper investigates the steady axisymmetric structure of the cold boundary-layer flow surrounding fire whirls developing over localized fuel sources lying on a horizontal surface. The inviscid swirling motion found outside the boundary layer, driven by the entrainment of the buoyant turbulent plume of hot combustion products that develops above the fire, is described by an irrotational solution, obtained by combining Taylor's self-similar solution for the motion in the axial plane with the azimuthal motion induced by a line vortex of circulation $2 \pi \Gamma$. The development of the boundary layer from a prescribed radial location is determined by numerical integration for different swirl levels, measured by the value of the radial-to-azimuthal velocity ratio $\sigma$ at the initial radial location. As in the case $\sigma=0$, treated in the seminal boundary-layer analysis of Burggraf et al. (Phys. Fluids, 1971), the pressure gradient associated with the centripetal acceleration of the inviscid flow is seen to generate a pronounced radial inflow. Specific attention is given to the terminal shape of the boundary-layer velocity near the axis, which displays a three-layered structure that is described by matched asymptotic expansions. The resulting composite expansion, dependent on the level of ambient swirl through the parameter $\sigma$, is employed as boundary condition to describe the deflection of the boundary-layer flow near the axis to form a vertical swirl jet. Numerical solutions of the resulting non-slender collision region for different values of $\sigma$ are presented both for inviscid flow and for viscous flow with moderately large values of the controlling Reynolds number $\Gamma/\nu$. The velocity description provided is useful in mathematical formulations of localized fire-whirl flows, providing consistent boundary conditions accounting for the ambient swirl level.