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We study the diffusive instability subject to a solid–liquid interface and a Kolmogorov flow using modal, non-modal analyses and energy analysis. It is found that the phase boundary has different effects on the threshold of diffusive convection for weak and strong salinity stratification. In the context of oceanography where the salinity Rayleigh number RS is very high, the ice–water interface has negligible influence on the onset of diffusive convection. In the presence of shear, the diffusive convection for RS < 106 tends to be inhibited and with the increase of shear intensity, the oscillatory, steady convective and Kelvin–Helmholtz instabilities will be successively dominant. For RS > 106, the shear has a destabilizing effect on the diffusive convection, due to the generation of thermohaline-sheared instability found by Radko (J. Fluid Mech., vol. 805, 2016, pp. 147–170). Non-modal analysis indicates that for realistic parameters of high-latitude oceans, with the transition of the ultimate energy source of instability from the density gradient to background current, the thermohaline-shear instability is expected to transition from oscillatory to steady instability. The initial transient amplification due to double diffusion has also been studied, which is due to the generation of overstable instability at the initial phase. For RS < 106, the optimal initial condition to achieve the maximum transient growth favours longitudinal rolls. For thermohaline-shear instability, however, it favours transverse rolls and specifically, in oscillatory thermohaline-shear instability, the transient amplification can be enhanced by the shear by one order of magnitude, thus having important influence on the stability of the system.
We study the two-dimensional Rayleigh–Bénard instability subject to the combined effects of a solid–liquid phase boundary and shear using linear stability theory and energy analysis. We consider two thermal states of the solid (isothermal and conducting), and two types of shear that can arise in different contexts. When the melting temperature is equal to that held at the top boundary, three instability modes can arise with the increase of Reynolds number Re that characterizes the shear intensity: a boundary mode, a mixed boundary–bulk mode and a bulk flow mode. When the melting temperature lies between the top and the bottom boundaries, the introduction of Couette flow, independent of its intensity, always leads to the mixed mode, whereas the instability with Poiseuille flow is dominated by the bulk flow mode once Re exceeds a critical value, below which the mixed mode dominates. The energy analysis suggests that there exist two mechanisms by which the shear flow affects the system: one is by inhibiting the upward heat flux and another is by absorbing energy from the perturbed hydrodynamic field. These two mechanisms can play totally different roles in different cases. Results in the high-Re regime indicate that, when Re exceeds its classical threshold, i.e. Re = 5772.2 for Poiseuille flow, the Tollmien–Schlichting instability will be dominant in the present system.
The high-altitude landscape of western Tibet is one of the most extreme environments in which humans have managed to introduce crop cultivation. To date, only sparse palaeoeconomic data have been reported from this region. The authors present archaeobotanical evidence from five sites (dating from the late first millennium BC and the early first millennium AD) located in the cold-arid landscape of western Tibet. The data indicate that barley was widely grown in this region by c. 400 BC but probably fulfilled differing roles within local ecological constraints on cultivation. Additionally, larger sites are characterised by more diverse crop assemblages than smaller sites, suggesting a role for social diversity in the development of high-altitude agriculture.
This study presents preliminary discoveries from Sding Chung cave, an early multi-burial cave site in the Himalayan highlands dating from 300BC–AD 300. Multiple human and animal bones within the cave provide unique evidence for understanding the diverse mortuary rituals and biocultural adaptations in this region.
Archaeological research demonstrates that an agropastoral economy was established in Tibet during the second millennium BC, aided by the cultivation of barley introduced from South-western Asia. The exact cultural contexts of the emergence and development of agropastoralism in Tibet, however, remain obscure. Recent excavations at the site of Bangga provide new evidence for settled agropastoralism in central Tibet, demonstrating a material divergence from earlier archaeological cultures, possibly corresponding to the intensification of agropastoralism in the first millennium BC. The authors’ results depict a more dynamic system of subsistence in the first millennium BC, as the populations moved readily between distinct economic modes and combined them in a variety of innovative ways.
Small, irregular terraces on hillslopes, or terracettes, are common landscape features throughout west central China. Despite their prevalence, there is limited understanding of the nature of these topographic features, the processes that form them, and the role humans played in their formation. We used an interdisciplinary approach to investigate the geology, ecology, and cultural history of terracette development within Jiuzhaigou National Park, Sichuan Province, China. Terracettes occur on south facing, 20° slopes at 2500 m elevation, which appears to coincide with places people historically preferred to build villages. Ethnographic interviews suggest that traditional swidden agricultural cycles removed tree roots, causing the loess sediments to lose cohesion, slump, and the terrace risers to retreat uphill over time. This evidence is supported by landslide debris at terracette faces. Archaeological analysis of terracette sites reveal remains of rammed spread soil structures, bones, stone tools, and ceramics dating from at least 2200 years before present within a distinct paleosol layer. Radiocarbon and optically stimulated luminescence dating of terracette sediments ranged in age from between 1500 and 2000 14C yr BP and between 16 and 0.30"ka, respectively. These multiple lines of evidence indicate a long history of human habitation within Jiuzhaigou National Park and taken together, suggest strong links between terracette formation and human-landuse interactions.
An edge-weighting problem of a graph G is an assignment of an integer weight to each edge e. Based on an edge-weighting problem, several types of vertex-coloring problems are put forward. A simple observation illuminates that the edge-weighting problem has a close relationship with special factors of the graphs. In this paper, we generalise several earlier results on the existence of factors with pre-specified degrees and hence investigate the edge-weighting problem — and in particular, we prove that every 4-colorable graph admits a vertex-coloring 4-edge-weighting.
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