Multilayer Flows Research Articles

Characterization of water bursting and discharge into underground mines with multilayered groundwater flow systems in the North China coal basin

A conceptual framework for characterization of water bursting and discharge into underground mines with multilayered groundwater flow systems is presented, based on the features of the site conditions and analyses of the water bursting and mine inundation events of the North China coal basin. Comprehensive analyses of the hydrogeological conditions for establishment of the three-dimensional groundwater flow systems of the North China coal basin revealed different vertical hydraulic connection paths or channels. These connections include karst collapse columns, fault or fracture zones, buried weathering zones, and fracture networks in aquitards, within the multilayered groundwater flow systems. Also examined, was the effect of the primary features of the flow system and those different connection paths on water bursting and discharge into the underground coal mines. It was demonstrated that appropriately identifying and adequately understanding the three-dimensional multilayered groundwater flow systems and those various vertical hydraulic connection mechanisms are critical for appropriately preventing water bursting hazards and predicting water discharge into underground mines. A valuable guideline is presented on characterization of water bursting and discharge into underground mines with multilayered groundwater flow systems.

Observations on the characteristics of tides in the Bab el Mandab Strait

While well known for its multilayered exchange flow, the Bab el Mandab Strait is also of interest as a transitional region between two distinctly different tidal regimes: the Gulf of Aden, where tides are mixed and have a range in excess of 2 m, and the Red Sea, where tidal fluctuations are principally semidiurnal and their range is generally less than 1 m. Observations collected in the strait indicate that dominant constituents for both elevations and currents are the K1 and M2. The vertical structure of the tidal currents differs between semidiurnal and diurnal constituents and depends on the location and stratification. The major part of the tidal signal is barotropic, but energetic baroclinic currents mainly of the diurnal period are observed near Perim Narrows and the Hanish Sill during winter months. The relationship between the barotropic currents and surface tides near Perim is fairly well explained by a simple momentum balance. To first order, a balance exists between local acceleration and the elevation gradient in the along‐strait direction, while in the cross‐strait direction, a balance between local acceleration, Coriolis term, and elevation gradient is observed. At the same location the barotropic transport fluctuations reach amplitudes of 1.6 Sv. The K1 and M2 barotropic energy fluxes are small and are directed into the strait at Perim Narrows and the Hanish Sill for the M2 constituent and into the strait near Perim and out of the strait near Hanish for the K1 constituent.

Numerical solution of duct flows of multiple visco-plastic fluids

We consider numerical solution of duct flows of multiple visco-plastic fluids using both regularisation techniques and the augmented Lagrangian method. Using single fluid test problems, we demonstrate that there are certain classes of problems for which the augmented Lagrangian method is superior. These problems include those of determining the critical Bingham numbers and pressure gradients for which the flow stops, i.e. the yield limit. We then apply this method to two practical problems involving multiple fluids in ducts: multi-layer lubrication flows and counter-current exchange flows. Again we demonstrate the effectiveness of the augmented Lagrangian method for this type of problem.

Prospect hunting below Deccan basalt: imaging challenges and solutions

Thick Mesozoic sediments under the basalt cover of the Deccan traps along the northwest coast of India are considered to be potential targets for hydrocarbon exploration together with the Indus basin of Pakistan. Sub-basalt seismic imaging is difficult in these formations, as the Deccan traps are composed of multilayered lava flows. Seismic imaging issues associated with high velocity basalt include: 1. Multiples generated in interbedded units of basalt and between the top of the basalt and the sea floor. 2. Energy scattering from and absorption by heterogeneities. 3. Wave mode conversion at the top of the basalt. Radon-based analysis can solve some of the difficulties related to multiples. The use of low frequency sources and multicomponent technology are other methods commonly suggested to improve sub-basalt imaging. The Deccan basalt area is very heterogeneous and has not been mapped effectively by high resolution seismic. At present, only standard streamer data are available in this area. Model-based imaging together with other methods can improve the sub-basalt image and add confidence in the reservoir modelling. Imaging challenges in this setting are discussed using examples from the Kutch basin on the northwest coast of India, where the primary reservoir (Bhuj formation) is overlain by thick basalt.

Nonlinear stability of a visco-plastically lubricated viscous shear flow

A common problem in multi-layer shear flows, especially from the perspective of process engineering, is the occurrence of interfacial instabilities. Here we show how multi-layer duct flows can in fact be made nonlinearly stable, by using a suitable lubricating fluid. First we show how interfacial instabilities may be eliminated through the introduction of a yield stress fluid as the lubricant and by preserving an unyielded layer adjacent to the interface. Second we show how to treat the nonlinear stability of a two-layer flow, allowing finite motion of the domains. We focus on the simplest practically interesting case of visco-plastically lubricated viscous shear flow: a core–annular pipe flow consisting of a central core of Newtonian fluid surrounded by a Bingham fluid. We demonstrate that this flow can be nonlinearly stable at significant Reynolds numbers and produce stability bounds. Our analysis can be straightforwardly generalized to other flows in this class.

Effect of non-normal interactions on the interfacial instability of multilayer viscoelastic channel flows

The effect of non-normal interactions on the interfacial instability of multilayer pressure driven channel flow of viscoelastic fluids in the limit of vanishingly small Reynolds number has been investigated. Specifically, it is shown that for the upper convected Maxwell (UCM), the Oldroyd-B, and the modified Phan-Thien–Tanner (MPTT) constitutive models the short time dynamics are significantly influenced by non-normal effects both in two- and three-layer flows. Moreover, the departure from the normal exponential behavior is most pronounced in the velocity perturbations. Furthermore, in two- and three-layer symmetric flows, the non-normal effects that arise from the interaction of the interfacial mode with bulk mode dissipate very quickly and therefore do not significantly influence the growth of interfacial disturbances. However, in asymmetric three-layer flows the non-normal behavior that results from the interaction of the two interfacial modes can be very significant and can persist over very long time periods. Hence, non-normal behavior can play a very significant role in determining the growth/decay rate of interfacial disturbances. Our analysis shows that the discrepancy observed in the measured and predicted growth rates of interfacial disturbances in earlier investigations [J. Non-Newtonian Fluid Mech. 79 (1998) 315] can be attributed to the presence of non-normal interactions.

A User-centric Office Framework for Knowledge Workers

This article describes a successful experience on a software project of Technology Development Program (TDP) of Ministry Of Economic Affairs (MOEA) in Taiwan. It describes the design and implementation of a smart office task framework to automate system integration and to enable user-centric application. To achieve the goal of implicit knowledge accumulation and inheritance, we developed a service framework at the backend for integrating diverse systems seamlessly and an interface agent at the front for hiding complex efforts on manually binding different systems. Based on years of experience in components-based system development with multilayered flow architecture, the ACT (Advanced e-Commerce Technology) laboratory adapted Web Services to wrap various existing systems into a general RPC/RMI format, used ontology to define and integrate new functionalities semantically, and took advantage of agents to enable a user-centric office environment. The design rationale, application scenario, architecture, and future plan are presented.

The instability mechanism of single and multilayer Newtonian and viscoelastic flows down an inclined plane

The instability mechanism of single and multilayer flow of Newtonian and viscoelastic fluids down an inclined plane has been examined based on a rigorous energy analysis as well as careful examination of the eigenfunctions. These analyses demonstrate that the free surface instability in single and multilayer flows in the limit of longwave disturbances (i.e., the most dangerous disturbances) arise due to the perturbation shear stresses at the free surface. Specifically, for viscoelastic flows, the elastic forces are destabilizing and the main driving force for the instability is the coupling between the base flow and the perturbation velocity and stresses and their gradient at the free surface. For Newtonian flows at finite Re, the driving force for the interfacial instability in the limit of longwaves depends on the placement of the less viscous fluid. If the less viscous fluid is adjacent to the solid surface then the main driving force for the instability is interfacial friction, otherwise the bulk contribution of Reynolds stresses drives the instability. For viscoelastic fluids in the limit of vanishingly small Re, the driving force for the instability is the coupling of the base flow and perturbation velocity and stresses and their gradients across the interface. In the limit of shortwaves the interfacial stability mechanism of flow down inclined plane is the same as plane Poiseuille flows (Ganpule and Khomami 1998, 1999a, b).

Mathematical simulation on accumulation process of a blooming plankton Peridinium bipes (Dinophyceae) in a dam reservoir

The accumulation process of the blooming plankton Peridinium bipes was studied in this paper using a mathematical model based on a horizontal one-dimensional multi-layered flow model coupled with a vertical migration model of the Peridinium bipes community. The estimated accumulation process consisted of three processes: upward swimming and dispersion of Peridinium bipes cells, advection of the cells with the countercurrent of surface water, and entrainment and effluent of the cells with the plunging flow of inflow river water. The numerical analysis has revealed that the accumulation process helps Peridinium bipes to avoid hydraulic washout and it contributes to a contributes to a concentration of Peridinium bipes cells on the upper side of the reservoir.

Role of dynamic modulation on stability of multilayer Newtonian and viscoelastic flows down an inclined plane

In this study, we have theoretically investigated the effect of parallel superposition of modulation on the stability of two layer Newtonian and viscoelastic flows down an inclined plane and it has been demonstrated that dynamic modulation can be used to influence the interfacial stability of Newtonian and viscoelastic fluids down an inclined plane. In general, for small and O(1) Reynolds numbers, the effect of dynamic modulation on the interfacial stability of viscoelastic flows is much more pronounced, however, relatively large modulation amplitudes are required to achieve significant stabilization/destabilization. Moreover, it has been demonstrated that the influence of dynamic modulation on the stability of the interfacial mode is relatively insensitive to the inclination angle and the disturbance wavenumber. In addition, it has been shown that for Newtonian flows one cannot establish a relationship between the most effective modulation frequencies and the inertial time scales of the flow (i.e. 1/ Re 1, 1/ Re 2 or 1/(| Re 1− Re 2|) or the frequency of the most dangerous interfacial mode in absence of modulations. Similarly, for viscoelastic flows at small and O(1) Re, no clear connection between the most stabilizing or destabilizing modulation frequencies and the fluid time scales have been established (i.e. 1/ We 1, 1/ We 2 or 1/| We 1− We 2|). Finally, it has been shown that the mechanism of purely elastic and inertial interfacial instabilities in multilayer flows down an inclined plane is unchanged in the presence of dynamic modulation.

NUMERICAL STUDY OF MULTILAYERED FLOW REGIME IN DOUBLE-DIFFUSIVE CONVECTION IN A ROTATING ANNULUS WITH LATERAL HEATING

Numerical investigations are conducted to study the multilayered flow regime occurring in double-diffusive convection of an initially stably stratified salt-water solution in a uniformly rotating annulus with lateral heating. The finite difference method is used to solve the basic conservation equations for an axisymmetric, unsteady, rotating double-diffusive convection, and calculations are made for Ra η = 2×10 5 , N = 9.1, and Ta = 0, 10 7 -2.5 × 10 8 . Formation of layered flow structure, merging process of layers, corresponding temperature and concentration distributions, and Nusselt number (Nu) variation with time are examined. Numerical results show clearly the variation of azimuthal and radial velocity because of rotation within a shallow layer, which would be very difficult to measure experimentally. As the effect of rotation increases (Taylor number (Ta) increases), compared with the stationary case, the generation of rolls at the hot wall, the development and formation of layers, and the merging of adjacent layers are all delayed. The temperature profile within a layer looks similar to an inverse S shape, and the concentration profile is uniform because of the convective mixing

Multi-layer hydraulic exchange flows

Flows between ocean basins are often controlled by narrow channels and shallow sills. A multi-layer hydraulic control theory is developed for exchange flow through such constrictions. The theory is based on the inviscid shallow-water equations and extends the functional approach introduced by Gill (1977) and developed by Dalziel (1991). The flows considered are those in rectangular–cross-section channels connecting two large reservoirs, with a single constriction (sill and/or narrows). The exchange flow depends on the stratification in the two reservoirs, represented as a finite number of immiscible layers of (different) uniform density. For most cases the flow is ‘controlled’ at the constriction and often at other points along the channel (virtual controls) too. As with one- and two-layer hydraulics, controls are locations at which the flow passes from one solution branch to another, and at which (at least) one internal wave mode is stationary. The theory is applied to three-layer flows, which have two internal wave modes, predicting interface heights and layer fluxes from the given reservoir conditions. The theoretical results for three-layer flows are compared to a comprehensive set of laboratory experiments and found to give good agreement. The laboratory experiments also show other features of the flow, such as the formation of waves on the interfaces. The implications of the results for oceanographic flows and ocean modelling are discussed.

Numerical Study of Flows of Two Immiscible Liquids at Low Reynolds Number

We review our recent results on fingering, bamboo waves, and drop breakup in low Reynolds number flows composed of two viscous liquids under shear.

Evaluation of Atmospheric Transport Models for Use in Phase I1 of the Historical Public Exposures Studies at the Rocky Flats Plant

Five atmospheric transport models were evaluated for use in Phase I1 ofthe Historical Public Exposures Studies at the Rocky Flats Plant. Models included a simple straight‐line Gaussian plume model (ISCST2), several integrated puff models (RATCHET, TRIAD, and INPUFF2), and a complex terrain mode (TRAC). Evaluations were based on how well model predictions compared with sulfur hexafluoride tracer measurements taken in the vicinity of Rocky Flats in February 1991. Twelve separate tracer experiments were conducted, eac lasting 9 hr and measured at 140 samplers in arcs 8 and 16 km from the release point at Rocky Flats. Four modeling objectives were defined based on the endpoints of the overall study: (1) the unpaired maximum hourly average concentration, (2) paired time‐averaged concentration, (3) unpaired time‐averaged concentration, and (4) arc‐integrated concentration. Performance measures were used to evaluate models and focused on the geometric mean and standard deviation of the predicted‐to‐observed ratio and the correlation coefficient between predicted and observed concentrations. No one model consistently outperformed the others in all modeling objectives and performance measures. About 75% of the maximum hourly concentration predictions were within a factor of 5 of the observations. About 64% of the paired and 80% of the unpaired time‐averaged model predictions were within a factor of 5 of theobservations. The overall performance of the RATCHET model was somewhat better than the other models. All models appeared to experience difficulty defining plume trajectories, which was attributed to the influence of multilayered flow initiated by terrain complexities and the diurnal flow patterns characteristic of the Colorado Front Range.

Evaluation of atmospheric transport models for use in phase II of the historical public exposures studies at the Rocky Flats Plant.

Five atmospheric transport models were evaluated for use in Phase II of the Historical Public Exposures Studies at the Rocky Flats Plant. Models included a simple straight-line Gaussian plume model (ISCST2), several integrated puff models (RATCHET, TRIAD, and INPUFF2), and a complex terrain model (TRAC). Evaluations were based on how well model predictions compared with sulfur hexafluoride tracer measurements taken in the vicinity of Rocky Flats in February 1991. Twelve separate tracer experiments were conducted, each lasting 9 hr and measured at 140 samplers in arcs 8 and 16 km from the release point at Rocky Flats. Four modeling objectives were defined based on the endpoints of the overall study: (1) the unpaired maximum hourly average concentration, (2) paired time-averaged concentration, (3) unpaired time-averaged concentration, and (4) arc-integrated concentration. Performance measures were used to evaluate models and focused on the geometric mean and standard deviation of the predicted-to-observed ratio and the correlation coefficient between predicted and observed concentrations. No one model consistently outperformed the others in all modeling objectives and performance measures. About 75% of the maximum hourly concentration predictions were within a factor of 5 of the observations. About 64% of the paired and 80% of the unpaired time-averaged model predictions were within a factor of 5 of the observations. The overall performance of the RATCHET model was somewhat better than the other models. All models appeared to experience difficulty defining plume trajectories, which was attributed to the influence of multilayered flow initiated by terrain complexities and the diurnal flow patterns characteristic of the Colorado Front Range.

The Kwinana Coastal Fumigation Study: II – Growth of the Thermal Internal Boundary Layer

Aircraft measurements of potential temperature and turbulent kinetic energy are used to examine the growth of the thermal internal boundary layer (TIBL) in sea-breeze flows on four selected days of a coastal fumigation study performed in 1995 at Kwinana in Western Australia. The aircraft data, together with radiosonde measurements taken on the same days, show a multi-layered low-level onshore flow in the vertical with a superadiabatic layer extending to about 50 m above the water surface on all four days. On the first three days the layer above the superadiabatic layer was neutral, typically 200 m deep, capped by a stably stratified region, whereas on the remaining day it was fully stable. The occurrence of the neutral layer on most experimental days contrasts with the more usual situation involving an entirely stable onshore flow. A composite approach based on both temperature and turbulence data is used to provide a pragmatic but self-consistent definition of the TIBL height. The data for the first three days indicate that the TIBL grows rapidly into the neutrally stratified region to the top of the region within about 2 km from the coast, with a very slow subsequent growth into the stable stratification aloft. On the other hand, the TIBL grows only to about 200 m within a distance of 7 km from the coast on the fourth day due to a strong stable stratification.

Linear stability of multilayer plane Poiseuille flows of Oldroyd B fluids

The linear stability of plane Poiseuille flows of two and three-symmetrical layers is studied by using both longwave and moderate wavelength analysis. The considered fluids follow Oldroyd-B constitutive equations and hence the stability is controlled by the viscous and elastic stratifications and the layer thicknesses. For the three symmetrical-layer Poiseuille flow, competition between varicose (symmetrical) and sinuous (antisymmetrical) mode is considered. In both cases (two and three symmetrical layers), the additive character of the longwave formula with respect to viscous and elastic terms is largely used to determine stable arrangements at vanishing Reynolds number. It is found that if the stability of such arrangements is due simultaneously to viscous and elastic stratification (the flow is stable for longwave disturbance and the Poiseuille velocity profile is convex), then the Poiseuille flow is also stable with respect to moderate wavelength disturbances and the critical thickness ratio around which the configurations becomes unstable is given by longwave analysis. Note that a convex velocity profile means a positive jump of shear rate at the interface. Finally, the destabilization due to a moderate increase in the Reynolds number is considered and two distinct behaviors are pointed according to the convexity of the Poiseuille velocity profile. Moreover, an important influence of the thickness ratio on the critical wavenumber is found for three symmetrical layer case (for two layer case, the critical wave number is of order one and depends weakly on the thickness ratio).

Nonlinear Saturation of Baroclinic Instability in a Three-Layer Model

Abstract Application of the stability theorems for multilayer quasigeostrophic flows reveals that the three-layer model may be nonlinearly unstable while in linearly subcritical conditions, the instability being then due to explosive resonant interaction of Rossby waves. This contrasts with the Phillips two-layer model for which linear theory suffices to explain any instability and motivates this study of the nonlinear saturation of instability in the three-layer model. A rigorous bound on the disturbance eddy energy is calculated using Shepherd's method for a wide range of basic shear and channel width. The method is applied using stable basic flows whose stability is established by either Arnol'd's first or second theorem. For flows unstable through explosive interaction only, the bound indicates that the disturbance energy can attain as much as 40% of the basic flow energy, the maximum disturbance energy being obtained for flows close to linear instability. With regard to linear instability, an importa...

Convection induced by cooling at one side wall in two-dimensional non-rotating fluid —applicability to the deep Pacific circulation—

In recognition that similarity in the density balance leads to resemblance in circulation between the two-dimensional non-rotating and three-dimensional rotating systems which have similar density stratification, we investigate convection induced by cooling at one side wall and heating at the sea surface by using a two-dimensional non-rotating model as idealized representation for the deep Pacific circulation. In the model, various vertical profiles are taken for the side wall cooling, which are assumed to correspond to the density structure of the Anatarctic Circumpolar Current. In a small diffusivity range, two important features are found to be robust against change in the vertical profile of the side wall cooling. One is that the density stratification is horizontally almost uniform. The other is that the balance in the density equation between the vertical advection and the vertical diffusion holds in the interior. Consequently, the vertical density balance, together with the equation of continuity, determines the circulation pattern for the prescribed vertical profile of the side wall cooling. The multi-layered meridional flow, which is expected to exist in the deep Pacific, is shown to form for certain vertical profiles of the side wall cooling.

On Wave Interactions III. Miscellaneous Results

In this paper, a collection of results pertaining to resonant triads in fluid flow systems is presented. The main topic is the extension of the analysis by Mahoney for wind‐driven shear flows to general, layered flows, that is to say, flows which have piecewise continuous velocity and density profiles. It is seen how the results for calculating the triad interaction coefficients for two‐layer flows generalize and carry over for multilayer flows.