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Ibn Raḥīq is an 11th century scholar who compiled a book on popular astronomy. This work included a section in which he summarizes basic knowledge of the Milky Way as it was wide spread in the first centuries after the hejira. Ibn Raḥīq gives a comprehensive overview of the perception of the Milky Way that reaches from its use as a test for knowledge of the religious tradition and for agricultural purposes on the one hand to an exact astronomical description of its shape in the sky during the year and to theories of its nature and composition on the other hand. We use a comparison of his text to those of Ibn al-Haytham and others to investigate the role the Milky Way played in early Islamic civilization from its beginning until the 15th century.
We investigate the interaction of a downslope gravity current with an internal wave propagating along a two-layer density jump. Direct numerical simulations confirm earlier experimental findings of a reduced gravity current mass flux, as well as the partial removal of the gravity current head from its body by large-amplitude waves (Hogg et al., Environ. Fluid Mech., vol. 18 (2), 2018, pp. 383–394). The current is observed to split into an intrusion of diluted fluid that propagates along the interface and a hyperpycnal current that continues to move downslope. The simulations provide detailed quantitative information on the energy budget components and the mixing dynamics of the current–wave interaction, which demonstrates the existence of two distinct parameter regimes. Small-amplitude waves affect the current in a largely transient fashion, so that the post-interaction properties of the current approach those in the absence of a wave. Large-amplitude waves, on the other hand, perform a sufficiently large amount of work on the gravity current fluid so as to modify its properties over the long term. The ‘decapitation’ of the current by large waves, along with the associated formation of an upslope current, enhance both viscous dissipation and irreversible mixing, thereby strongly reducing the available potential energy of the flow.
Miscible liquids often come into contact with one another in natural and technological situations, commonly as a drop of one liquid present in a second, miscible liquid. The shape of a liquid droplet present in a miscible environment evolves spontaneously in time, in a distinctly different fashion than drops present in immiscible environments, which have been reported previously. We consider drops of two classical types, pendant and sessile, in building upon our prior work with miscible systems. Here we present experimental findings of the shape evolution of pendant drops along with an expanded study of the spreading of sessile drops in miscible environments. We develop scalings considering the diffusion of mass to group volumetric data of the evolving pendant drops and the diffusion of momentum to group leading-edge radial data of the spreading sessile drops. These treatments are effective in obtaining single responses for the measurements of each type of droplet, where the volume of a pendant drop diminishes exponentially in time and the leading-edge radius of a sessile drop grows following a power law of
at long times. A complementary numerical approach to compute the concentration and velocity fields of these systems using a simplified set of governing equations is paired with our experimental findings.