scholarly journals Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone

2017 ◽  
Author(s):  
Gaute Linga ◽  
Joachim Mathiesen ◽  
François Renard
Keyword(s):  
Fluid Velocity ◽  
Self Similar ◽  
Stress Heterogeneity

scholarly journals A laboratory study of sediment deformation: stress heterogeneity and grain-size evolution

1996 ◽  
Vol 22 ◽  
pp. 167-175 ◽  
Author(s):  
Neal R. Iverson ◽  
Thomas S. Hooyer ◽  
Roger Leb. Hooke
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Normal Stress ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Local Stress ◽  
Large Strains ◽  
Self Similar ◽  
Deformation Stress ◽  
Stress Heterogeneity

In shearing sediment beneath glaciers, networks of grains may transiently support shear and normal stresses that are larger than spatial averages. Consistent with studies of fault-gouge genesis, we hypothesize that crushing of grains in such networks is responsible for surrounding larger grains with smaller grains. At sufficiently large strains, this should minimize stress heterogeneity, favor intergranular sliding and abrasion rather than crushing, and result in a self-similar grain-size distribution.This hypothesis is tested with a ring-shear device that slowly shears a large annular sediment sample to high strains. Shearing and comminution of weak equigranular (2.0–3.3 mm) sediment resulted in a self-similar grain-size distribution with a fractal dimension that increased with shear strain toward a steady value of 2.85. This value is significantly larger than that of gouges produced purely by crushing, 2.6, but it is comparable to values for tilts thought to be deforming beneath modern glaciers, 2.8 to nearly 3.0. At low strains, under a steady mean normal stress of 84 kPa, variations in normal stress measured locally ranged in amplitude from 50 to 300 kPa with wavelengths that were 100 times larger than the initial grain diameter. Crushing of grains, observed through the transparent walls of the device, apparently caused the failure of grain networks. At shearing displacements ranging from 0.7 to 1.0 m, the amplitude of local stress fluctuations decreased abruptly. This change is attributed to fine sediment that distributed stresses more uniformly and caused grain networks to fail primarily by intergranular sliding rather than by crushing of grains. Sliding between grains apparently produced silt by abrasion and resulted in a fractal dimension that was higher than if there had been only crushing.A size distribution with a fractal dimension greater than 2.6 is probably a necessary but not sufficient condition for determining whether a basal till has been highly deformed. Stress heterogeneity in subglacial sediment that is shearing through its full thickness should contribute to the erosion of underlying rock.

Local implications for self-similar turbulent plume models

2007 ◽  
Vol 575 ◽  
pp. 257-265 ◽  
Author(s):  
M. M. SCASE ◽  
C. P. CAULFIELD ◽  
P. F. LINDEN ◽  
S. B. DALZIEL
Keyword(s):  
Radial Velocity ◽  
Phase Boundary ◽  
Fluid Model ◽  
Fluid Velocity ◽  
Ambient Fluid ◽  
Self Similar ◽  
The Difference ◽  
Two Fluid Model ◽  
Natural Way ◽  
Total Fluid

The local implications of the well-known flux conservation equations of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1956, p.1) for plumes and jets are considered. Given the vertical velocity distributions of a model plume or jet, the divergence-free radial velocity distributions are calculated. It is shown that in general the velocity of the plume boundary is not described by the local total fluid velocity in this way. A two-fluid model tracking the evolution of both ‘plume’ and ‘ambient’ fluid is proposed which resolves this apparent inconsistency and also provides a way of explicitly describing the mixing process within a model plume. The plume boundary acts as a phase boundary across which ambient fluid is entrained, and the plume boundary moves at the velocity of the plume fluid. The difference between the plume-fluid radial velocity and the total fluid velocity quantifies in a natural way the purely horizontal entrainment flux of ambient fluid into the plume across the phase boundary at the plume edge.

scholarly journals Axisymmetric spreading of surfactant from a point source

2017 ◽  
Vol 832 ◽  
pp. 777-792 ◽  
Author(s):  
Shreyas Mandre
Keyword(s):  
Fluid Velocity ◽  
Radial Distance ◽  
Domain Size ◽  
Fluid Interface ◽  
Viscous Forces ◽  
Constant Rate ◽  
Adsorbed Phase ◽  
Self Similar ◽  
Marangoni Stress ◽  
Dissolved Phase

Guided by computation, we theoretically calculate the steady flow driven by the Marangoni stress due to a surfactant introduced on a fluid interface at a constant rate. Two separate extreme cases, where the surfactant dynamics is dominated by the adsorbed phase or the dissolved phase, are considered. We focus on the case where the size of the surfactant source is much smaller than the size of the fluid domain, and the resulting Marangoni stress overwhelms the viscous forces so that the flow is strongest in a boundary layer close to the interface. We derive the resulting flow in a region much larger than the surfactant source but smaller than the domain size by approximating it with a self-similar profile. The radially outward component of fluid velocity decays with the radial distance $r$ as $r^{-3/5}$ when the surfactant spreads in an adsorbed phase, and as $r^{-1}$ when it spreads in a dissolved phase. Universal flow profiles that are independent of the system parameters emerge in both the cases. Three hydrodynamic signatures are identified to distinguish between the two cases and verify the applicability of our analysis with successive stringent tests.

scholarly journals Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
M. Khan ◽  
S. Abelman ◽  
D. P. Mason ◽  
F. M. Mahomed
Keyword(s):  
Differential Equation ◽  
Fluid Velocity ◽  
Cylindrical Tube ◽  
Initial Approximation ◽  
Steady State Solution ◽  
Polar Coordinates ◽  
Sisko Fluid ◽  
Unidirectional Flow ◽  
Self Similar ◽  
Cylindrical Polar Coordinates

The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates. The exact steady-state solution for the nonlinear problem is obtained. The reduction of the nonlinear initial value problem is carried out by using a similarity transformation. The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponentnand the material parameterbof the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.

Quantum vortex dynamics under the tangent representation of the local induction approximation

2014 ◽  
Vol 740 ◽  
pp. 5-16 ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Fluid Model ◽  
Fluid Velocity ◽  
Tangent Vector ◽  
The Self ◽  
Complete Agreement ◽  
Coordinate Frame ◽  
Normal Fluid ◽  
Quantum Vortex ◽  
Self Similar ◽  
Local Induction Approximation

AbstractWe derive the local induction approximation (LIA) for a quantum vortex filament in the arclength coordinate frame where the tangent vector is the unknown function. The equation for the tangent vector to the filament is then converted to a potential form, which ends up being a type of nonlinear Schrödinger equation that governs the tangential LIA model (T-LIA). Such a formulation was previously derived by Umeki for the standard fluid model (in the absence of superfluid friction terms). While it is challenging to generalize many of the exact solutions found for the standard LIA to the quantum LIA model, we demonstrate that the T-LIA model facilitates this generalization nicely. Indeed, under the T-LIA model, we are able to construct a variety of solutions. The Hasimoto solution related to elastica is one of the fundamental solutions present for the standard fluid model; however, using the T-LIA model, we are able to demonstrate the existence of such a solution, thereby extending the Hasimoto solution to the superfluid case. In the zero-temperature limit, purely self-similar solutions are shown to exist for the T-LIA model. As the superfluid warms (so that the influence of the normal flow is no longer negligible), the analogue to the self-similar solution is a new class of solutions, which depend on the similarity variable as well as a time-dependent additive scaling. In other words, the self-similar structures gradually deform as the magnitude of the normal-fluid velocity increases, which makes complete physical sense. When dealing with small deviations from the central axis of alignment, we can describe such solutions analytically. There exists a family of helical vortex filaments in the presence of a normal fluid impinging on the vortex, in complete agreement with the previously studied results for the LIA model. Finally, a number of soliton solutions are shown to exist in different regimes of the T-LIA model.

On the rarefaction waves of the two-dimensional compressible Euler equations for magnetohydrodynamics

2020 ◽  
Vol 17 (03) ◽  
pp. 591-612
Author(s):  
Jianjun Chen ◽  
Geng Lai ◽  
Wancheng Sheng
Keyword(s):  
Euler Equations ◽  
Magnetic Fluid ◽  
Fluid Velocity ◽  
Goursat Problem ◽  
Two Dimensional ◽  
Interaction Zone ◽  
Rarefaction Waves ◽  
Plane Symmetric ◽  
Half Angle ◽  
Self Similar

The expansion of a wedge of magnetic fluid into vacuum is studied in this paper. The magnetic fluid away from the sharp corner of a wedge expands into the vacuum as two plane-symmetric rarefaction waves, and the problem can be reduced to the interaction of these two rarefaction waves. In order to determine the flow in the interaction zone, we formulate a Goursat problem for the two-dimensional, self-similar Euler equations of magnetohydrodynamic. This system is of mixed type, and the type at each point is determined by the local fluid velocity and the local magneto-acoustic speed. We establish that the system is uniformly hyperbolic in the interaction zone when the half-angle of the wedge is less than some angle [Formula: see text], while the existence of a global classical solution to the Goursat problem is proven by a method of characteristic decomposition.

Investigation of the Velocity Field in the Wave Rivulet Flowing Down the Vertical Plate

2013 ◽  
Vol 8 (3) ◽  
pp. 82-88
Author(s):  
Alexey Bobylev ◽  
Dmitriy Markovich ◽  
Sergey Kharlamov
Keyword(s):  
Velocity Field ◽  
Vertical Plate ◽  
Fluid Velocity ◽  
Longitudinal Velocity ◽  
Low Frequency ◽  
Self Similar ◽  
The Waves

Joint measurements of thickness and fluid velocity in wavy rivulets were performed using PIV and LIF methods. The stagnant regions in which fluid moves with the velocity of the waves were found under the humps of low-frequency highamplitude waves. The profiles of longitudinal velocity of the fluid were reconstructed for different regions of the waves. These profiles greatly deviate from self-similar parabolic profiles in the stagnant regions and in the regions of capillary precursor of the waves

scholarly journals A laboratory study of sediment deformation: stress heterogeneity and grain-size evolution

1996 ◽  
Vol 22 ◽  
pp. 167-175 ◽  
Author(s):  
Neal R. Iverson ◽  
Thomas S. Hooyer ◽  
Roger Leb. Hooke
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Normal Stress ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Local Stress ◽  
Large Strains ◽  
Self Similar ◽  
Deformation Stress ◽  
Stress Heterogeneity

In shearing sediment beneath glaciers, networks of grains may transiently support shear and normal stresses that are larger than spatial averages. Consistent with studies of fault-gouge genesis, we hypothesize that crushing of grains in such networks is responsible for surrounding larger grains with smaller grains. At sufficiently large strains, this should minimize stress heterogeneity, favor intergranular sliding and abrasion rather than crushing, and result in a self-similar grain-size distribution.This hypothesis is tested with a ring-shear device that slowly shears a large annular sediment sample to high strains. Shearing and comminution of weak equigranular (2.0–3.3 mm) sediment resulted in a self-similar grain-size distribution with a fractal dimension that increased with shear strain toward a steady value of 2.85. This value is significantly larger than that of gouges produced purely by crushing, 2.6, but it is comparable to values for tilts thought to be deforming beneath modern glaciers, 2.8 to nearly 3.0. At low strains, under a steady mean normal stress of 84 kPa, variations in normal stress measured locally ranged in amplitude from 50 to 300 kPa with wavelengths that were 100 times larger than the initial grain diameter. Crushing of grains, observed through the transparent walls of the device, apparently caused the failure of grain networks. At shearing displacements ranging from 0.7 to 1.0 m, the amplitude of local stress fluctuations decreased abruptly. This change is attributed to fine sediment that distributed stresses more uniformly and caused grain networks to fail primarily by intergranular sliding rather than by crushing of grains. Sliding between grains apparently produced silt by abrasion and resulted in a fractal dimension that was higher than if there had been only crushing.A size distribution with a fractal dimension greater than 2.6 is probably a necessary but not sufficient condition for determining whether a basal till has been highly deformed. Stress heterogeneity in subglacial sediment that is shearing through its full thickness should contribute to the erosion of underlying rock.

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar
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