Thermo-diffusion impacts on the flow of an elastico-viscous fluid over an inclined heated plane with magnetized wall

The focus is in this article is to scrutinize the simultaneous significances of magnetic diffusion, thermo-diffusion and angular location on the hydromagnetic flow of an elastico-viscous fluid over an inclined heated plane with magnetized wall. The flow medium is considered to be uniformly permeable (Darcy-Brinkman porous medium) and the flow of the fluid is considerably affected due to the appearance of a strong magnetic field in the direction normal to the flow surface. The significances of Hall current, induced magnetic field and Coriolis force on flow nature is also included in the study. The leading non-dimensionalized equations are explored by regular perturbation analysis. Ultimately, the expressions for velocity field, induced magnetic field, temperature and concentration are obtained. We further derived the surface skin friction, surface current density, heat and mass fluxes. The computation of results is performed with the aid of Mathematica software and results are presented in graphical and tabular forms for distinct flow impacting parameters. Numerical simulation explores that mass diffusion factor brings growth in the fluid velocity, temperature and normal induced magnetic field while it reduces the main induced magnetic field. Magnetic diffusion develops the primary flow and primary induced magnetic field and lessens the normal flow and normal induced magnetic field. Inclination angle of the heated plane upgrades primary induced magnetic field while downgrading normal induced magnetic field.

Complex Vulnerabilities of the Water and Aquatic Carbon Cycles to Permafrost Thaw

The spatial distribution and depth of permafrost are changing in response to warming and landscape disturbance across northern Arctic and boreal regions. This alters the infiltration, flow, surface and subsurface distribution, and hydrologic connectivity of inland waters. Such changes in the water cycle consequently alter the source, transport, and biogeochemical cycling of aquatic carbon (C), its role in the production and emission of greenhouse gases, and C delivery to inland waters and the Arctic Ocean. Responses to permafrost thaw across heterogeneous boreal landscapes will be neither spatially uniform nor synchronous, thus giving rise to expressions of low to medium confidence in predicting hydrologic and aquatic C response despite very high confidence in projections of widespread near-surface permafrost disappearance as described in the 2019 Intergovernmental Panel on Climate Change Special Report on the Ocean and Cryosphere in a Changing Climate: Polar Regions. Here, we describe the state of the science regarding mechanisms and factors that influence aquatic C and hydrologic responses to permafrost thaw. Through synthesis of recent topical field and modeling studies and evaluation of influential landscape characteristics, we present a framework for assessing vulnerabilities of northern permafrost landscapes to specific modes of thaw affecting local to regional hydrology and aquatic C biogeochemistry and transport. Lastly, we discuss scaling challenges relevant to model prediction of these impacts in heterogeneous permafrost landscapes.

A Molecular Dynamics Investigation on Methane Flow and Water Droplets Sliding in Organic Shale Pores with Nano-structured Roughness

Roughness of surfaces significantly influences how methane and water flow in shale nanopores. We perform molecular dynamics simulations to investigate the influence of surface roughness on pore-scale transport of pure methane as well as of two-phase methane–water systems with the water sliding as droplets over the pore surface. For single-phase methane flow, surface roughness shows a limited influence on bulk methane density, while it significantly reduces the methane flow capacity. In methane–water systems, the mobility of water is a strong function of surface roughness including a clear transition between immobile and mobile water droplets. For cases with mobile water, droplet sliding speeds were correlated with pressure gradient and surface roughness. Sliding water droplets hardly deform, i.e., there is little difference between their advancing and receding contact angle with structured roughness.

Stepped Spillway Slope Effect on Air Entrainment and Inception Point Location

Spillway is a crucial hydraulic structure used to discharge excess water from the dam reservoir. Air entrainment is essential to prevent cavitation damage on the spillway, however, without air entrainment the risk of cavitation over the spillway increases. The most important parameter for the determination of air entrainment in stepped spillways is the inception point. The inception point is the location where the air starts to inter into the water flow surface over the spillway. It occurs when the turbulent boundary layer meets the free surface. The location of the inception point depends upon different parameters like flow rate, geometry, step size, and slope of the spillway. The main aim of this study was applying numerical simulation by using the realizable k-ϵ model and the volume of fluid (VOF) method to locate the location of the inception point. For this purpose, by using different stepped spillways with four different slopes (12.5°, 19°, 29°, and 35°) different flow rates were simulated, which gives the location of the inception point of different channel slopes of stepped spillways at different flow rates. The results demonstrated that the inception point location of mild slopes is farther from the crest of the spillway than the steep slope stepped spillway. Non-aerated flow zone length increases when the channel slope decreases from steep to mild slope.

A note on non-symmetric flow: surface shrinking in mutually orthogonal directions

In this note, we extend the problem treated in (Lok, Math Modelling Anal 24:617–634 (2019)) to the case of permeable surface which is shrinking in mutually orthogonal directions. Both numerical and asymptotic solutions are obtained for two important governing parameters, $$\gamma $$ γ the shrinking rate and S characterizing the fluid transfer through the boundary. In this problem, a restriction on S is required for a solution to exist. This contrasts with the problem in (Lok, Math Modelling Anal 24:617–634 (2019)) where no restriction on S is needed. Numerical solutions show that for a fixed value of S, two critical points $$\gamma _c$$ γ c are observed for $$S > 2$$ S > 2 . Conversely, two critical points $$S_c$$ S c are found for a given value of $$\gamma $$ γ when $$S > 2$$ S > 2 . A discussion on the nonexistence of solution for $$S = 2$$ S = 2 is given and asymptotic solutions for S large and $$(S-2)$$ ( S - 2 ) small are also presented.

Energy flow characteristics of friction-induced nonlinear vibrations in a water-lubricated bearing-shaft coupled system

Based on the energy flow theory of nonlinear dynamical system, the stabilities, bifurcations, possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper. It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-paramters. (a) Energy flow matrix has two negative and one positive energy flow factors, constructing an attractive local zero-energy flow surface, in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state, while forced vibrations by external forces show stable oscillations. (b) Energy flow matrix has one negative and two positive energy flow factors, spaning a divergence local zero-energy flow surface, so that the both free and forced vibrations are divergence oscillations with the system being unstable. (c) Energy flow matrix has a zero-energy flow factor and two opposite factors, which constructes a local zero-energy flow surface dividing the local phase space into stable, unstable and central subspace, and the simulation shows friction self-induced unstable vibrations for both free and forced cases. For a set of friction parameters, the system behaves a periodical oscillation, where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero. Numerical simulations have not found any possible chaotic motions of the system. It is discovered that the damping matrices of cases (a), (b) and (c) respectively have positive, negative and zero diagonal elements, resulting in the different dynamic behavour of system, which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications. Graphic Abstract

A retrospective of the work of Patience Cowie: the interaction of faults in space and time and their influences on subsurface fluid flow, surface processes and earthquakes

<p>Patience Cowie was a truly outstanding scientist whose research spanned several disciplines of structural geology and tectonics. She made a lasting contribution to every discipline she published in and as well as academic advances, produced significant impacts in the hydrocarbon industry and earthquake hazard assessment. Her research in fault mechanics and fault population was a genuine game-changer. The implications of her work for predicting fault patterns and linkage have been crucial for the interpretation of 3D seismic data, and for examining the interplay between faults and the basins they bound and sediments they host. More recently she explored relationships between fault geometry, slip rate and recurrence intervals along seismically active faults, with important implications for earthquake hazard assessment.</p><p>Patience’s drive to constrain physical explanations of the underlying dynamics of Earth processes meant her numerical modelling was always firmly grounded in field observations. Her models incorporated the effects of stress in time and space as fault system evolved, but always underpinned by geometric and kinematic observations in the field. She loved fieldwork and her joy at the beauty of geological structures was infectious and inspiring.  </p>

Subsidence of the lava flow formed during 2012-2013 Tolbachik fissure eruption: SAR data and thermal model

<p>During the Tolbachik fissure eruption which took place from November 27, 2012 to September 15, 2013 a lava flow of area about 45.8 km<sup>2</sup> and total lava volume ~0.6 km<sup>3</sup> was formed. We applied method of persistent scatterers to the satellite Sentinel-1A SAR images and estimated the rates of displacement of the lava field surface for 2017–2019. The surface mainly subsides along the satellite’s line-of-sight, with the exception of the periphery of the Toludski and Leningradski lava flows, where small uplifts are observed. Assuming that the displacements occur mainly along the vertical, the maximum average displacement rates for the snowless period of 2017–2019 were 285, 249, and 261 mm/year, respectively. On the Leningradski and Toludski lava flows the maximum subsidence was registered in areas with the maximum lava thickness.</p><p>To estimate the thermal subsidence of the lava surface we constructed a thermal model of lava cooling. It provides subsidence rate which are generally close to the real one over a significant part of the lava field, but in a number of areas of its central part, the real subsidence values are much higher than the thermal estimates. According to the thermal model when lava thickness exceeds 40 meters, even 5 years after eruption under the solidified surface there can be a hot, ductile layer, which temperature exceeds 2/3 of the melting one. Since on the Leningradski flow, the maximum subsidence is observed in the area of the fissure along which the eruption took place, one could assume that the retreat of lava down the fissure could contribute to the observed displacements of the flow surface. Subsidence can also be associated with compaction of rocks under the weight of the overlying strata. Migration of non-solidified lava under the solidified cover, also can contribute to the observed distribution of displacements - subsidence of the surface of the lava field in the upper part of the slope and a slight uplift at its periphery.</p><p>The work was supported partly by the mega-grant program of the Russian Federation Ministry of Science and Education under the project no. 14.W03.31.0033 and partly by the Interdisciplinary Scientific and Educational School of Moscow University «Fundamental and Applied Space Research».</p>