scholarly journals Stability of lubricated viscous gravity currents. Part 1. Internal and frontal analyses and stabilisation by horizontal shear

2019 ◽  
Vol 871 ◽  
pp. 970-1006 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
M. Grae Worster
Keyword(s):  
Viscous Fluid ◽  
Pressure Gradient ◽  
Dynamic Pressure ◽  
Jump Discontinuity ◽  
Local Analysis ◽  
Instability Criterion ◽  
Shear Stresses ◽  
Horizontal Shear ◽  
Dynamical Regimes ◽  
Inner Region

A novel viscous fingering instability, involving a less viscous fluid intruding underneath a current of more viscous fluid, was recently observed in the experiments of Kowal & Worster (J. Fluid Mech., vol. 766, 2015, pp. 626–655). We examine the origin of the instability by asking whether the instability is an internal instability, arising from internal dynamics, or a frontal instability, arising from viscous intrusion. We find it is the latter and characterise the instability criterion in terms of viscosity difference or, equivalently, the jump in hydrostatic pressure gradient at the intrusion front. The mechanism of this instability is similar to, but contrasts with, the Saffman–Taylor instability, which occurs as a result of a jump in dynamic pressure gradient across the intrusion front. We focus on the limit in which the two viscous fluids are of equal density, in which a frontal singularity, arising at the intrusion, or lubrication, front, becomes a jump discontinuity, and perform a local analysis in an inner region near the lubrication front, which we match asymptotically to the far field. We also investigate the large-wavenumber stabilisation by transverse shear stresses in two dynamical regimes: a regime in which the wavelength of the perturbations is much smaller than the thickness of both layers of fluid, in which case the flow of the perturbations is resisted dominantly by horizontal shear stresses; and an intermediate regime, in which both vertical and horizontal shear stresses are important.

Viscous banding instabilities: non-porous viscous fingering

2021 ◽  
Vol 926 ◽  
Author(s):  
Katarzyna N. Kowal
Keyword(s):  
Free Surface ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Dynamic Pressure ◽  
Viscous Fingering ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Viscosity Contrast ◽  
Slope Discontinuity ◽  
Rigid Walls

We demonstrate a novel instability found within unconfined viscous bands/rims, or free-surface flows involving a longitudinal viscosity contrast. Such instabilities may be described as viscous banding instabilities, non-porous viscous fingering instabilities or unconfined viscous fingering instabilities of free-surface flows involving the intrusion of a less viscous fluid into a band of more viscous fluid. A consequence of this work is that viscous fingering instabilities, widely known to occur in porous media following the seminal work of Saffman & Taylor (Proc. R. Soc. Lond. A, vol. 245, 1958, pp. 312–329), also occur in non-porous environments. Although the mechanism of the viscous banding instability is characteristically different from that of the Saffman–Taylor instability, there are important similarities between the two. The main similarity is that a viscosity contrast leads to instability. A distinguishing feature is that confinement, such as the rigid walls of a Hele-Shaw cell, is not necessary for viscous banding instabilities to occur. More precisely, Saffman–Taylor instabilities are driven by a jump in dynamic pressure gradient, whereas viscous banding instabilities, or non-porous viscous fingering instabilities, are driven by a jump in hydrostatic pressure gradient, directly related to a slope discontinuity across the intrusion front. We examine the onset of instability within viscous bands down an inclined plane, determine conditions under which viscous banding instabilities occur and map out a range of behaviours in parameter space in terms of two dimensionless parameters: the viscosity ratio and the volume of fluid ahead of the intrusion front.

Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

2020 ◽  
Vol 16 ◽  
Author(s):  
Adel Alblawi ◽  
Saba Keyani ◽  
S. Nadeem ◽  
Alibek Issakhov ◽  
Ibrahim M. Alarifi
Keyword(s):  
Carbon Nanotubes ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Pressure Rise ◽  
Shear Stresses ◽  
Left Wall ◽  
Coupled Equations ◽  
The Right

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered as very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profile. The analytical expressions for the pressure gradient and wall shear stresses are obtained. Term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. Final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behaviour is depicted near the left wall due to ciliated tips whereas the temperature is an increasing function of B and ߛ and decreasing function of ߶.

Dense GPS derived deformation and rotation of intraplate blocks in Central Europe - comparison to seismicity and volcanism

2021 ◽  
Author(s):  
Zhiguo Deng ◽  
Torsten Dahm
Keyword(s):  
High Precision ◽  
Velocity Fields ◽  
Shear Stresses ◽  
Intraplate Seismicity ◽  
Strain Rates ◽  
Horizontal Shear ◽  
Regional Patterns ◽  
Quaternary Volcanism ◽  
Intraplate Deformation ◽  
Horizontal Strain

<p>Intraplate deformation is often small but can nowdays be resolved from high precision GNSS velocity fields derived from decade-long time series and high precision network or point wise  solutions if uncertainties are smaller than ~0.2 mm/a.</p><p>If local effects are discarded, dense velocity fields may resolve regional patterns of intraplate deformation and motion, which are related to the bending of lithospheric plates, to mantle upwelling, the diffuse or zoned deformation along structural weaknesses or faults, and the rotation of rigid blocks within a plate. </p><p>We derive for the first time, dense high precision network solutions at 323 GNSS stations in Germany and adjacent areas and resolve regions experiencing uplift with velocities of up to ~2 mm/a, rotational relative motions with angular velocities of ~0.7±0.3 mas/a, and horizontal shear along an extended,  NS trending zone with strain rates in the range of 10-8 1/a. </p><p>We integrate European dense velocity solutions into our dataset to discuss the geodynamic context to European microplate motions, the Alpine collision, the structure of the European mantle, Quaternary volcanism and historical seismicity. </p><p>Unexpectedly, the zones of high horizontal strain rates only partly correlate to seismicity. Such a non-correlation between ongoing horizontal strain and seismicity has been recognized before. We discuss possible reasons for the absence of intraplate seismicity in regions experiencing recent strain, including the stress shadow effects if the strain buildup is reducing shear stresses from plate tectonics. The combination of GNSS derived dense velocity fields with time dependent seismicity models may change our current understanding of intraplate seismicity and impact the assessment of intraplate seismic hazard in future. </p>

scholarly journals Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field

2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Mhd Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent Viscosity

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.

scholarly journals Turbulence structure of non-uniform rough open channel flow

2018 ◽  
Vol 40 ◽  
pp. 05039
Author(s):  
Priscilla Williams ◽  
Vesselina Roussinova ◽  
Ram Balachandar
Keyword(s):  
Pressure Gradient ◽  
Channel Flow ◽  
Friction Velocity ◽  
Open Channel ◽  
Open Channel Flow ◽  
Shear Stresses ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Rough Bed ◽  
The Mean

This paper focuses on the turbulence structure in a non-uniform, gradually varied, sub-critical open channel flow (OCF) on a rough bed. The flow field is analysed under accelerating, near-uniform and decelerating conditions. Information for the flow and turbulence parameters was obtained at multiple sections and planes using two different techniques: two-component laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). Different outer region velocity scaling methods were explored for evaluation of the local friction velocity. Analysis of the mean velocity profiles showed that the overlap layer exists for all flow cases. The outer layer of the decelerated velocity profile was strongly affected by the pressure gradient, where a large wake was noted. Due to the prevailing nature of the experimental setup it was found that the time-averaged flow quantities do not attained equilibrium conditions and the flow is spatially heterogeneous. The roughness generally increases the friction velocity and its effect was stronger than the effect of the pressure gradient. It was found that for the decelerated flow section over a rough bed, the mean flow and turbulence intensities were affected throughout the flow depth. The flow features presented in this study can be used to develop a model for simulating flow over a block ramp. The effect of the non-uniformity and roughness on turbulence intensities and Reynolds shear stresses was further investigated.

scholarly journals Ice-Ocean Interaction On Ronne Ice Shelf, Antarctica

1990 ◽  
Vol 14 ◽  
pp. 341
Author(s):  
A. Jenkins ◽  
C.S.M. Doake
Keyword(s):  
Cold Water ◽  
Sea Water ◽  
Freezing Point ◽  
Accumulation Rate ◽  
Weddell Sea ◽  
Shear Stresses ◽  
Strain Rates ◽  
Horizontal Shear ◽  
Ice Shelf ◽  
Ice Stream

A detailed glaciological study of Ronne Ice Shelf has been undertaken along a flowline extending from Rutford Ice Stream grounding line to the ice front. Measurements of velocity, surface elevation, ice thickness, surface temperature and accumulation rate have been made at a total of 28 sites; at 17 of these ice deformation rates are also known. Although no direct measurements of basal conditions have been made, these can be deduced from observations made at the surface. Assuming the ice shelf to be in a steady state, the basal mass balance can be calculated at points where strain-rates are known. Information on the spatial distribution of basal saline ice layers can also be obtained from radio-echo sounding data. The derived pattern of basal melting and freezing influences both the ice shelf and the underlying ocean. Vertical heat advection modifies the temperature distribution within the ice shelf, which determines its dynamic response to driving and restraining forces through the temperature-dependent ice-flow law. Using measured strain-rates and calculated temperature profiles, the restraint generated by horizontal shear stresses can be derived for points on the flowline. It is the cumulative effect of these forces which controls the discharge of grounded ice from Rutford Ice Stream. Cooling of sea-water to its pressure melting point by melting of ice at depth has two important results. The outflow of cold, dense Ice Shelf Water, produced by this mechanism, is a major source of Antarctic Bottom Water, formed as it mixes at depth with the warmer waters of the Weddell Sea (Foldvik and Gammelsrod, 1988). If the cold water is forced up to shallower depths, frazil ice will be produced as the pressure freezing point rises, resulting in basal accretion if this occurs beneath the ice shelf.

scholarly journals Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

2019 ◽  
Vol 877 ◽  
pp. 167-195 ◽  
Author(s):  
Feng-Yuan Zuo ◽  
Antonio Memmolo ◽  
Guo-ping Huang ◽  
Sergio Pirozzoli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Shear Stresses ◽  
Mean Flow ◽  
Conical Shock

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

Slender-body theory for steady sheared plumes in very viscous fluid

2008 ◽  
Vol 612 ◽  
pp. 21-44 ◽  
Author(s):  
ROBERT J. WHITTAKER ◽  
JOHN R. LISTER
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Experimental Studies ◽  
Slender Body ◽  
Slender Body Theory ◽  
Dimensionless Parameters ◽  
Dynamical Regimes ◽  
Body Theory ◽  
Good Agreement

A simple model based on slender-body theory is developed to describe the deflection of a steady plume by shear flow in very viscous fluid of the same viscosity. The key dimensionless parameters measuring the relative strengths of the shear, diffusion and source flux are identified, which allows a number of different dynamical regimes to be distinguished. The predictions of the model show good agreement with many, but not all, observations from previous experimental studies. Possible reasons for the discrepancies are discussed.

scholarly journals Development and Forcing of the Rear Inflow Jet in a Rapidly Developing and Decaying Squall Line during BAMEX

2009 ◽  
Vol 137 (4) ◽  
pp. 1206-1229 ◽  
Author(s):  
Joseph A. Grim ◽  
Robert M. Rauber ◽  
Greg M. McFarquhar ◽  
Brian F. Jewett ◽  
David P. Jorgensen
Keyword(s):  
Pressure Gradient ◽  
Dynamic Pressure ◽  
Radar Data ◽  
Squall Line ◽  
System Evolution ◽  
Formative Stage ◽  
Bow Echo ◽  
Mesoscale Convective ◽  
Forcing Mechanisms ◽  
Inflow Jet

Abstract This study examines the development, structure, and forcing of the rear inflow jet (RIJ) through the life cycle of a small, short-lived squall line over north-central Kansas on 29 June 2003. The analyses were developed from airborne quad-Doppler tail radar data from the NOAA and NRL P-3 aircraft, obtained over a 2-h period encompassing the formation, development, and decay of the squall line during the Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX). The strengthening of the system-relative rear inflow to 17 m s−1 was concurrent with the formation of a bow echo, an increased dynamic pressure gradient beneath the rearward-tilted updraft, and two counterrotating vortices at either end of the bow. The later weakening of the RIJ to 8 m s−1 was concurrent with the weakening of the bow, a decreased dynamic pressure gradient at midlevels behind the bow, and the weakening and spreading of the vortices. In a modeling study, Weisman quantified the forcing mechanisms responsible for the development of an RIJ. This present study is the first to quantitatively analyze these mechanisms using observational data. The forcing for the horizontal rear inflow was analyzed at different stages of system evolution by evaluating the contributions of four forcing mechanisms: 1) the horizontal pressure gradient resulting from the vertical buoyancy distribution (δPB), 2) the dynamic pressure gradient induced by the circulation between the vortices (δPV), 3) the dynamic irrotational pressure gradient (δPI), and 4) the background synoptic-scale dynamic pressure gradient (δPS). During the formative stage of the bow, δPI was the strongest forcing mechanism, contributing 50% to the rear inflow. However, during the mature and weakening stages, δPI switched signs and opposed the rear inflow while the combination of δPB and δPV accounted for at least 70% of the rear inflow. The δPS forced 4%–25% of the rear inflow throughout the system evolution.

Sign in / Sign up

Export Citation Format

Share Document