Time-dependent Flow Model Research Articles

Time-dependent low-latitude core flow and geomagnetic field acceleration pulses

We present a new model of time-dependent flow at low latitudes in the Earth's core between 2000 and 2018, derived from magnetic field measurements made on board the {\it Swarm} and CHAMP satellites and at ground magnetic observatories. The model, called {\it CoreFlo-LL.1}, consists of a steady background flow without imposed symmetry plus a time-dependent flow that is dominated by geostrophic and quasi-geostrophic components but also allows weak departures from equatorial symmetry. We find that the equatorial region beneath the core-mantle boundary is a place of vigorous, localised, fluid motions; time-dependent flow focused at low latitudes close to the core surface is able to reproduce rapid field variations observed at non-polar latitudes at and above Earth's surface. Magnetic field acceleration pulses are produced by alternating bursts of non-zonal azimuthal flow acceleration in this region. Such acceleration sign changes can occur within a year or less, and when the structures involved are of large spatial scale they can give rise to geomagnetic jerks at the Earth's surface.

Time-dependent flow model of a generalized Burgers’ fluid with fractional derivatives through a cylindrical domain: An exact and numerical approach

Abstract Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers’ fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized G a , b , c ( . , t ) -functions. The corresponding results can be freely specified for the same results of Burgers’, Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest’s algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.

Non-linear time-dependent flow models of third grade fluids: A conditional symmetry approach

In this communication some non-linear flow problems dealing with the unsteady flow of a third grade fluid in porous half-space are analyzed. A new class of closed-form conditionally invariant solutions for these flow models are constructed by using the conditional or non-classical symmetry approach. All possible non-classical symmetries of the model equations are obtained and various new classically invariant solutions have been constructed. The solutions are valid for a half-space and also satisfy the physically relevant initial and the boundary conditions.

Combined global 2D–local 3D modeling of the industrial Czochralski silicon crystal growth process

A global, axisymmetric thermal model of a Czochralski furnace is coupled to an external, local, 3D, time-dependent flow model of the melt via the inclusion of turbulent heat fluxes, extracted from the 3D melt model, into the 2D furnace model. Boundary conditions of the 3D model are updated using results from the 2D model. In the 3D model the boundary layers are resolved by aggressive mesh refinement towards the walls, and the Large Eddy Simulation approach is used to model the turbulent flow in the melt volume on a relatively coarse mesh to minimize calculation times. It is shown that by using this approach it is possible to reproduce fairly good results from Direct Numerical Simulations obtained on much finer meshes, as well as experimental results for interface shape and oxygen concentration in the case of growth of silicon crystals with 210mm diameter for photovoltaics by the Czochralski method.

On the dynamics of current jets trapped to the flanks of mid-ocean ridges

[1] Time-mean abyssal current observations over the flanks of the East Pacific Rise (EPR) at 9–10°N and at the Juan de Fuca Ridge at 45°N document the occurrence of paired along-ridge current jets that are trapped to the ridge flanks and sheared across the ridge in an anticyclonic sense. A coincident feature, where local hydrothermal discharge effects are not in play, is the upward bowing of isopycnals over ridge crests and isopycnals plunging into ridge flanks. It would be tempting to explain the jets primarily as geostrophic responses to the doming/plunging isopycnal distribution, though that should lead to the question as to how the isopycnal perturbations originate. A numerical model of time-dependent flow on a cross-ridge (x–z) transect, forced in a way to be consistent with a yearlong, hourly sampled record of currents measured at the EPR ridge crest, is used to investigate some of the underlying physics. It will be shown that the jets can arise from oscillatory flows via eddy-momentum, eddy-heat, and eddy-salt fluxes that ultimately cause the isopycnals to dome over the ridge. As the probable offspring of velocity-velocity and velocity-density correlations that depend upon oscillatory motion, the jets are likely examples of stratified topographic flow rectification. An ancillary feature is a slight yearlong-averaged downward current O (0.1–0.5 mm/s) over the EPR ridge crest that crosses the time-mean, upward bowing isopycnals in a counter-intuitive vertical direction.

Natural systems evidence for the alteration of clay under alkaline conditions: An example from Searles Lake, California

Mudstones containing smectite have been altered under mildly alkaline conditions (9 < pH < 10) at Searles Lake, California over a 3 million-year time period. Published mineralogical investigations have shown that up to 70% of detrital clay may be replaced by authigenic minerals such as Fe-illite, analcime, and K-feldspar over timescales < 100 ka. This natural alteration has been simulated incorporating time-dependent boundary conditions of sedimentation and fluid composition, a Pitzer model for activities of aqueous species, and a coupled hydrogeological model for time-dependent flow in the sediment layers. Kinetic dissolution of detrital smectite under alkaline conditions was described using one of two models based on departure from thermodynamic equilibrium or by an empirical rate dependent upon aqueous Si concentrations. Secondary mineral growth was modelled with rates estimated using mineralogical data from the Searles Lake drillcore. The zonal pattern of smectite dissolution observed at Searles Lake was reproduced reasonably well by the ‘Cama TST’ model of montmorillonite dissolution; the other models strongly overestimated clay dissolution. However, the rate of primary montmorillonite dissolution was also a strong function of the assumed rate of growth of secondary minerals. The amount of K-feldspar growth was overestimated in each of the models, whereas analcime (comprising up to 10% of the Searles Lake drillcore composition in some zones) was absent from the results of all the model simulations. This assessment provides a test of the accuracy and reliability of published data in the application of models of smectite dissolution in the long-term and demonstrates that smectite will be reactive under mildly alkaline conditions under conditions of advective fluid transport.

Flow directions in gas assisted injection molding when cavities of square flat plates and pipes are involved 2. Development of time-dependent flow model

part of the paper. The predictions of the developed flow model were so quite consistent with the results of simulation that the proposed time-dependent flow model may be referred to describe very well the transient behavior of the move- ment of the interface of gas and melt-resin in the cavities. In addition, a timedependent model was also established and was used to compare with the results of Moldflow when cavities of pipes and runners were involved in configura- tion. It is amazing that the proposed developed model was ab le to predict exactly the cross-over between the trajectories of interface of upper and lower side, and it is also surprising to describe the time dependent behavior so well that the result of the predictions by the developed model were quite consistent to the results of simulation by Moldflow.

Basal melt at NorthGRIP modeled from borehole, ice-core and radio-echo sounder observations

AbstractFrom temperature measurements down through the 3001 m deep borehole at the North Greenland Icecore Project (NorthGRIP) drill site, it is now clear that the ice at the base, 3080 m below the surface, is at the pressure-melting point. This is supported by the measurements on the ice core where the annual-layer thicknesses show there is bottom melting at the site and upstream from the borehole. Surface velocity measurements, internal radio-echo layers, borehole and ice-core data are used to constrain a time-dependent flow model simulating flow along the north-northwest-trending ice-ridge flow-line, leading to the NorthGRIP site. Also time-dependent melt rates along the flowline are calculated with a heat-flow model. The results show the geothermal heat flow varies from 50 to 200 mW m–2 along the 100km section of the modeled flowline. The melt rate at the NorthGRIP site is 0.75 cm a–1, but the deep ice in the NorthGRIP core originated 50 km upstream and has experienced melt rates as high as 1.1 cm a–1.

A model for time-dependent flow in (giraffe jugular) veins: uniform tube properties

Computations are reported for a one-dimensional model of time-dependent flow in collapsible tubes representing long mammalian veins. The tubes are taken to have uniform intrinsic properties and we concentrate on the effect of longitudinal gravity. The main application is to the jugular vein of the upright giraffe, with given inflow rate from the head, a given pressure, slightly above the external, atmospheric pressure, at the downstream (vena caval) end, and a variety of initial conditions. We show that: (i) previously calculated steady flows are the long time limits of unsteady computations, although only after a considerable time in which slowly-decaying waves and elastic jumps propagate up and down, (ii) steady flows are indeed not found when the steady-flow analysis shown them not to exist, although the consequent unsteadiness is of such small amplitude as to be practically unimportant, (iii) the time taken for the flow to become steady when the neck is raised from the horizontal or the head-down position can be several seconds longer than the neck-raising time itself (3– 7 s ). We also find that roll-waves do not develop despite having been previously predicted for long collapsible tubes. Further application is made to the effect of postural changes on human neck and leg veins.

A time-dependent flow model for heavy metals in the Scheldt estuary

The main processes that determine the behaviour ofheavy metals in the Scheldt estuary are tidalhydrodynamics, sediment transport, and sorption ofheavy metals on suspended matter. The water qualitymodel WASP is applied to simulate the spatialdistribution of five heavy metals in the estuary,under average hydrodynamic and suspended sedimenttransport regimes. First, the hydrodynamical part ofthe model is constructed and the results are verifiedby comparison with measured water levels and flowvelocities. Secondly, a salt transport model is set upin order to evaluate the hydrodynamical dispersivemixing characteristics. Thirdly, a suspended sedimenttransport model is constructed and finally a transportmodel for heavy metals. The simulated distributions of the sorbedamounts of heavy metals, suspended sediment andsalinity in the estuary agree well with observations.The calculated profiles of dissolved and sorbedconcentrations of heavy metals in the water columnindicate an accumulation of heavy metals in the zoneof the turbidity maximum, while closer to the sea theconcentrations diminish due to mixing of the pollutedfluvial sediments with unpolluted marine sediments andbecause of sediment deposition in the estuary. It canbe concluded that only a small part of the heavymetals reaches the sea.

A Computational Approach to Controllability Issues for Flow-Related Models. (I): Pointwise Control of the Viscous Burgers Equation

We discuss the numerical solution of some controllability problems for time-dependent flow models. The emphasis is on algorithmic aspects, discretization issues, and memory-saving devices. In the first part of the article, we investigate the controllability of the viscous Burgers equation. In part two, we shall discuss the boundary controllability of a linear advection-diffusion equation and then the distributed controllability of the unsteady Stokes equations.

Numerical simulation of nocturnal drainage flow properties in a rugged canyon

A two-dimensional, time-dependent flow model coupled with a radiative transfer module has been applied to examine the characteristics of nocturnal flow in a steep canyon in the Rocky Mountains in Colorado. The effect of nighttime surface cooling on drainage flow is examined and compared with observations. In a complementary study, tracer data have been analyzed to estimate the mass flux from a tributary canyon and to examine processes of transport and diffusion. Simulations indicate that the strength and structure of the drainage wind are controlled mainly by terrain features, ambient wind conditions, and effective radiative cooling rates. The transport of tracer from a lower secondary vortex to an upper primary vortex is largely controlled by diffusional processes; removal of tracer from the canyon is controlled by the primary vortex and its interaction with the ambient wind. Differences between mass fluxes from model simulations and those calculated from experiments involve uncertainties in both the structure of the model and the analysis of data.

Parameterization of the pollutant transport and dispersion in urban street canyons

A two-dimensional, time-dependent flow model has been applied to the evaluation of pollutant dispersion properties in urban street canyons. The processes by which pollutants emitted at street level are transported and diffused from street canyons are examined to determine the exchange rates of pollutants between street canyons and the upper air under variable flow conditions and different aspect ratios (the ratio of the building height to the street width). The time constant, defined as the time required for the average pollutant concentration in the street canyon to be reduced to e−1, is parameterized as a function of canyon cross-sectional area, influx strength, Reynolds number, Peclet number, and aspect ratio. Time constants may be applied directly to urban air quality models for better estimation of emission rates.

Comparison of microphysics parameterizations in a three-dimensional dynamic cloud model

Abstract A three-dimensional, time-dependent flow model developed to simulate dynamics and cloud microphysics for warm-cloud processes is used to compare the moisture fields simulated with different cloud microphysics parameterization. Our parameterizations are based on detailed simulations of the physics of aerosols, clouds, and precipitation. The moisture content in the system is differentiated into water vapor, cloud water, and rain water. Advection and diffusion terms for momentum, potential temperature, and mixing ratios of water vapaor and cloud water are calculated by using finite-volume methods, while rain water mixing ratio fields are calculated by a Lagrangian method. The model simulations are examined through sensitivity analysis, interpreted in terms of the physical processes occurring, and are compared with simulations using parameterizations from the literature. Calculated precipitation totals are shown to vary by 10–30% among simulations with alternate parameterization.

Gas in globular clusters. II - Time-dependent flow models

view Abstract Citations (41) References (38) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gas in globular clusters. II. Time-dependent flow models. Vandenberg, D. A. ; Faulkner, D. J. Abstract A numerical method is described for solving the time-dependent flow equations of relevance to gas flows in globular clusters. This method involves a modification of Henyey's iteration technique as well as finite-difference approximations for mass, momentum, and energy conservation. As an initial application of the numerical method, a previous study is extended to low gas-input energies in order to determine the fate of gas in clusters of one million solar masses when radiative cooling prevents the occurrence of steady-state outflows. Evolutionary sequences of models are presented for selected values of a parameter corresponding to the energy of the gas ejected by a star itself, and the resulting unsteady winds are shown to be similar to those computed by Mathews and Baker (1971) for elliptical galaxies. The results indicate that accumulation of mostly neutral hydrogen may take place in a region of small dimensions near the center of the most tightly bound globular clusters. Publication: The Astrophysical Journal Pub Date: December 1977 DOI: 10.1086/155695 Bibcode: 1977ApJ...218..415V Keywords: Astronomical Models; Gas Flow; Globular Clusters; Interstellar Gas; Stellar Mass Ejection; Time Dependence; Boundary Value Problems; Dynamic Models; Finite Difference Theory; Hydrodynamic Equations; Iterative Solution; Radiant Cooling; Astrophysics full text sources ADS |

A physical model of time-dependent flow in the human air passages

A physical model of the time-dependent, homogenous, viscous and incompressible flow in the first twelve bronchial branches is described. The anatomical data given by Weibel (1963) are used. By means of these hypotheses we obtain the following equation: P alv( t) = k 1 V′ B ( t) + k 2 V B 2′( t), where k 1 and k 2 are constants which depend on bronchial geometry and P alv( t) and V B ( t) are the alveolar pressure and the mouth flow rate, respectively. Some results concerning laterobronchial pressure and velocities are given.

Determinants of maximal expiratory flow from the lungs.

Determinants of maximal expiratory flow from the lungs.