scholarly journals Exploring the turbulent velocity gradients at different scales from the perspective of the strain-rate eigenframe

2021 ◽  
Vol 910 ◽  
Author(s):  
Josin Tom ◽  
Maurizio Carbone ◽  
Andrew D. Bragg
Keyword(s):  
Strain Rate ◽  
Turbulent Velocity ◽  
Velocity Gradients

Abstract

scholarly journals Crevasse Deformation and Examples From Ice Stream B, West Antarctica (Abstract)

1988 ◽  
Vol 11 ◽  
pp. 211-211
Author(s):  
P. L. Vorriberger ◽  
I. M. Whillans
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Velocity Fields ◽  
Normal Strain ◽  
Lateral Shear ◽  
The Third ◽  
Velocity Gradients ◽  
Ice Stream ◽  
Wide Range ◽  
Ice Stream B

Crevasses are subject to rotation and bending according to the velocity field through which they travel. The objective of this study is to determine to what extent the velocity field can be inferred from measurements of the resulting shapes of crevasses.A quantitative model of crevasse deformation is developed, based on the following assumptions: (1) each crevasse is assumed to open perpendicularly to the principal extensional regional strain-rate, (2) the crevasse forms when the principal extensional strain-rate exceeds some specified critical value, and (3) velocity gradients are constant over the area of interest. The first two assumptions are reasonable and the third is necessary for an analytic solution of flow trajectories. The crevasse is carried along, rotated, and bent, and may continue to increase in length. Calculations are made for different velocity fields, and velocity fields are sought that produce crevasses similar to those found in three different areas of Ice Stream B.Hook-shaped crevasses occur just outside the chaotic zone at the ice-stream margin. These are similar to the curved marginal crevasses often found in the accumulation zone of valley glaciers. They are successfully modelled by combining strong lateral shear with slow flow of ice from the ice ridge into the ice stream. The curvature at the most sharply bent part of the crevasse is found to be a useful measure and, together with measurements of ice flow from the ridge, can be used to infer the rate of lateral shear. This rate compares favorably with the single measurement obtained so far (Bindschadler and others 1987).A pattern of splaying crevasses develops on the ice stream down-glacier of its narrowest part. These crevasses are similar to longitudinal crevasses found in the ablation zone of many valley glaciers. Models with linear variation in velocity cannot reproduce the observed pattern. However, we have been able to simulate higher-order variations by joining together successive linear models. The observed crevasse pattern is successfully produced if the side shearing varies as the third power of distance from the center of symmetry of the crevasse pattern. Such a variation is expected for a linear gradient in side-drag stress and a third-power constitutive relation for ice. The observed crevasse pattern is thus consistent with side drag varying linearly across the ice stream.The third example is the rotation of transverse crevasses, which occur in trains on the main part of the ice stream. This rotation is due to side shearing but its magnitude is also affected by turning of the flow line and by normal strain-rates. It is therefore possible to reproduce the observed pattern for a wide range of velocity fields, and so measurements of the orientation of transverse crevasses provide only an upper limit on side shearing within the main body of the ice stream.There are many other examples of crevasse patterns on Ice Stream Β and on other glaciers that can be studied in this way. We propose that important constraints can be placed on velocity gradients and on the flow dynamics by using quantitative modelling of crevasse shapes.

Statistical properties of velocity derivatives in a turbulent field

1971 ◽  
Vol 48 (1) ◽  
pp. 183-208 ◽  
Author(s):  
Françlois N. Frenkiel ◽  
Philip S. Klebanoff
Keyword(s):  
Probability Distribution ◽  
High Speed ◽  
Scale Structure ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Small Scale Structure ◽  
Velocity Gradients ◽  
Turbulent Field ◽  
Even Order ◽  
Gaussian Probability Distribution

High-speed digital computing methods are applied to the study of the statistical behaviour of turbulent velocity derivatives in a nearly isotropic turbulent field downstream of a grid. Higher-order correlations of turbulent velocity gradients, up to the eighth order, are measured. Contrary to the case of velocities, the higher even-order correlations of velocity gradients more clearly evidence the departure from a two-dimensional Gaussian probability distribution. Using non-Gaussian probability distribution laws the relations between different odd-and even-order correlations are obtained and compared with the experimental measurements. The conditions of similarity and isotropy are evaluated for the small-scale structure as evidenced by the behaviour of the turbulent velocity gradients. The concept of intermittency of the small-scale structure is also discussed.

scholarly journals Crevasse Deformation and Examples from Ice Stream B, Antarctica

1990 ◽  
Vol 36 (122) ◽  
pp. 3-10 ◽  
Author(s):  
P.L. Vornberger ◽  
I.M. Whillans
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Critical Value ◽  
Velocity Fields ◽  
The Third ◽  
Velocity Gradients ◽  
Ice Stream ◽  
Lateral Shearing ◽  
Extensional Strain ◽  
Ice Stream B

AbstractCrevasses, once formed, are subject to rotation and bending according to the velocity field through which they travel. Because of this, crevasse shapes can be used to infer something about the velocity field of a glacier. This is done using a model in which each crevasse opens perpendicularly to the principal extensional strain-rate, when that strain-rate exceeds some specified critical value, and is then deformed according to the same velocity gradients that formed the crevasse. This model describes how crevasses are formed, translated, rotated, bent, and lengthened.Velocity fields are sought for which calculations produce crevasses approximating those found in three example areas on Ice Stream B, Antarctica. The first example is the hook-shaped crevasses that occur just outside the chaotic shear zone at the ice-stream margin. They are used to infer a rate of lateral shearing, and side drag. The second example, a pattern of splaying crevasses, is satisfactorily simulated by a model with side-drag stress varying linearly across the ice stream. This confirms that this region is restrained almost entirely by side drag. The third example is transverse crevasses and their change in orientation, but many different velocity fields can produce the observed pattern. Of these three examples, the shapes of hook-shaped marginal crevasses and splaying crevasses can provide useful information whereas transverse crevasses are less helpful.

Velocity Gradients and the Evolution of Material Properties in a Narrow Layer near Surfaces of High Friction in Metal Forming Processes

2012 ◽  
Vol 504-506 ◽  
pp. 549-554 ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeau Ren Jeng
Keyword(s):  
Grain Size ◽  
Strain Rate ◽  
Material Properties ◽  
Metal Forming ◽  
Equivalent Strain ◽  
Experimental Results ◽  
Material Layer ◽  
Narrow Layer ◽  
Velocity Gradients ◽  
Equivalent Strain Rate

Theoretical solutions for several rigid plastic models used to describe plastic flow in metal forming processes are singular in the vicinity of maximum friction surfaces. In particular, velocity gradients and the equivalent strain rate approach infinity near such surfaces. Such singular behavior can be excluded from consideration by choosing another friction law or material model. However, a different approach is proposed in the present paper. The starting point of this approach is that many experiments show that velocity gradients are very high in the vicinity of surfaces of high friction and that a narrow material layer is formed near such surfaces whose properties are very different from the properties in the bulk. Taking into account that the equivalent strain rate has a significant effect on the evolution of material properties, this experimental fact suggests that a theory based on the singular plastic solutions can be developed to describe the formation of the aforementioned material layer. In the present paper such a theory is proposed to describe the evolution of grain size. It is assumed that, in addition to the equivalent strain rate, the material spin has an effect of the evolution of grain size. It is then shown that the solutions for the material spin are singular as well. The interrelation between the present theory and strain gradient theories of plasticity is discussed. It is shown that it is necessary to account for the strain rate gradient to propose a more adequate theory to deal with the material flow near surfaces of high friction. Some experimental results on the formation of the narrow layer of ultra-fine grains in the vicinity of the fraction surface in extrusion are presented. An illustrative example to relate these experimental results and the new theory is given.

scholarly journals Crevasse Deformation and Examples from Ice Stream B, Antarctica

1990 ◽  
Vol 36 (122) ◽  
pp. 3-10 ◽  
Author(s):  
P.L. Vornberger ◽  
I.M. Whillans
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Critical Value ◽  
Velocity Fields ◽  
The Third ◽  
Velocity Gradients ◽  
Ice Stream ◽  
Lateral Shearing ◽  
Extensional Strain ◽  
Ice Stream B

AbstractCrevasses, once formed, are subject to rotation and bending according to the velocity field through which they travel. Because of this, crevasse shapes can be used to infer something about the velocity field of a glacier. This is done using a model in which each crevasse opens perpendicularly to the principal extensional strain-rate, when that strain-rate exceeds some specified critical value, and is then deformed according to the same velocity gradients that formed the crevasse. This model describes how crevasses are formed, translated, rotated, bent, and lengthened.Velocity fields are sought for which calculations produce crevasses approximating those found in three example areas on Ice Stream B, Antarctica. The first example is the hook-shaped crevasses that occur just outside the chaotic shear zone at the ice-stream margin. They are used to infer a rate of lateral shearing, and side drag. The second example, a pattern of splaying crevasses, is satisfactorily simulated by a model with side-drag stress varying linearly across the ice stream. This confirms that this region is restrained almost entirely by side drag. The third example is transverse crevasses and their change in orientation, but many different velocity fields can produce the observed pattern. Of these three examples, the shapes of hook-shaped marginal crevasses and splaying crevasses can provide useful information whereas transverse crevasses are less helpful.

scholarly journals Crevasse Deformation and Examples From Ice Stream B, West Antarctica (Abstract)

1988 ◽  
Vol 11 ◽  
pp. 211
Author(s):  
P. L. Vorriberger ◽  
I. M. Whillans
Keyword(s):  
Velocity Field ◽  
Strain Rate ◽  
Velocity Fields ◽  
Normal Strain ◽  
Lateral Shear ◽  
The Third ◽  
Velocity Gradients ◽  
Ice Stream ◽  
Wide Range ◽  
Ice Stream B

Crevasses are subject to rotation and bending according to the velocity field through which they travel. The objective of this study is to determine to what extent the velocity field can be inferred from measurements of the resulting shapes of crevasses. A quantitative model of crevasse deformation is developed, based on the following assumptions: (1) each crevasse is assumed to open perpendicularly to the principal extensional regional strain-rate, (2) the crevasse forms when the principal extensional strain-rate exceeds some specified critical value, and (3) velocity gradients are constant over the area of interest. The first two assumptions are reasonable and the third is necessary for an analytic solution of flow trajectories. The crevasse is carried along, rotated, and bent, and may continue to increase in length. Calculations are made for different velocity fields, and velocity fields are sought that produce crevasses similar to those found in three different areas of Ice Stream B. Hook-shaped crevasses occur just outside the chaotic zone at the ice-stream margin. These are similar to the curved marginal crevasses often found in the accumulation zone of valley glaciers. They are successfully modelled by combining strong lateral shear with slow flow of ice from the ice ridge into the ice stream. The curvature at the most sharply bent part of the crevasse is found to be a useful measure and, together with measurements of ice flow from the ridge, can be used to infer the rate of lateral shear. This rate compares favorably with the single measurement obtained so far (Bindschadler and others 1987). A pattern of splaying crevasses develops on the ice stream down-glacier of its narrowest part. These crevasses are similar to longitudinal crevasses found in the ablation zone of many valley glaciers. Models with linear variation in velocity cannot reproduce the observed pattern. However, we have been able to simulate higher-order variations by joining together successive linear models. The observed crevasse pattern is successfully produced if the side shearing varies as the third power of distance from the center of symmetry of the crevasse pattern. Such a variation is expected for a linear gradient in side-drag stress and a third-power constitutive relation for ice. The observed crevasse pattern is thus consistent with side drag varying linearly across the ice stream. The third example is the rotation of transverse crevasses, which occur in trains on the main part of the ice stream. This rotation is due to side shearing but its magnitude is also affected by turning of the flow line and by normal strain-rates. It is therefore possible to reproduce the observed pattern for a wide range of velocity fields, and so measurements of the orientation of transverse crevasses provide only an upper limit on side shearing within the main body of the ice stream. There are many other examples of crevasse patterns on Ice Stream Β and on other glaciers that can be studied in this way. We propose that important constraints can be placed on velocity gradients and on the flow dynamics by using quantitative modelling of crevasse shapes.

scholarly journals Genesis and evolution of velocity gradients in near-field spatially developing turbulence

2017 ◽  
Vol 815 ◽  
pp. 295-332 ◽  
Author(s):  
I. Paul ◽  
G. Papadakis ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Strain Rate ◽  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Grid Element ◽  
Velocity Gradients ◽  
Developing Flow ◽  
Vorticity Vector ◽  
Spatially Developing Flow

This paper investigates the dynamics of velocity gradients for a spatially developing flow generated by a single square element of a fractal square grid at low inlet Reynolds number through direct numerical simulation. This square grid-element is also the fundamental block of a classical grid. The flow along the grid-element centreline is initially irrotational and becomes turbulent further downstream due to the lateral excursions of vortical turbulent wakes from the grid-element bars. We study the generation and evolution of the symmetric and anti-symmetric parts of the velocity gradient tensor for this spatially developing flow using the transport equations of mean strain product and mean enstrophy respectively. The choice of low inlet Reynolds number allows for fine spatial resolution and long simulations, both of which are conducive in balancing the budget equations of the above quantities. The budget analysis is carried out along the grid-element centreline and the bar centreline. The former is observed to consist of two subregions: one in the immediate lee of the grid-element which is dominated by irrotational strain, and one further downstream where both strain and vorticity coexist. In the demarcation area between these two subregions, where the turbulence is inhomogeneous and developing, the energy spectrum exhibits the best$-5/3$power-law slope. This is the same location where the experiments at much higher inlet Reynolds number show a well-defined$-5/3$spectrum over more than a decade of frequencies. Yet, the$Q{-}R$diagram, where$Q$and$R$are the second and third invariants of the velocity gradient tensor, remains undeveloped in the near-grid-element region, and both the intermediate and extensive strain-rate eigenvectors align with the vorticity vector. Along the grid-element centreline, the strain is the first velocity gradient quantity generated by the action of pressure Hessian. This strain is then transported downstream by fluctuations and strain self-amplification is activated a little later. Further downstream, vorticity from the bar wakes is brought towards the grid-element centreline, and, through the interaction with strain, leads to the production of enstrophy. The strain-rate tensor has a statistically axial stretching form in the production region, but a statistically biaxial stretching form in the decay region. The usual signatures of velocity gradients such as the shape of$Q{-}R$diagrams and the alignment of vorticity vector with the intermediate eigenvector are detected only in the decay region even though the local Reynolds number (based on the Taylor length scale) is only between 30 and 40.

Dislocation Substructures Produced During Tensile, Creep, and Fatigue Deformation of Ti3Al at 700°C

1977 ◽  
Vol 35 ◽  
pp. 272-273
Author(s):  
S. M. L. Sastry
Keyword(s):  
Intermetallic Compound ◽  
Strain Rate ◽  
Tensile Creep ◽  
Slip Systems ◽  
Slip Vector ◽  
Superlattice Structure ◽  
Slip Activity ◽  
Dislocation Arrangement ◽  
Ordered Intermetallic ◽  
Tangled Dislocation

Ti3Al is an ordered intermetallic compound having the DO19-type superlattice structure. The compound exhibits very limited ductility in tension below 700°C because of a pronounced planarity of slip and the absence of a sufficient number of independent slip systems. Significant differences in slip behavior in the compound as a result of differences in strain rate and mode of deformation are reported here.Figure 1 is a comparison of dislocation substructures in polycrystalline Ti3Al specimens deformed in tension, creep, and fatigue. Slip activity on both the basal and prism planes is observed for each mode of deformation. The dominant slip vector in unidirectional deformation is the a-type (b) = <1120>) (Fig. la). The dislocations are straight, occur for the most part in a screw orientation, and are arranged in planar bands. In contrast, the dislocation distribution in specimens crept at 700°C (Fig. lb) is characterized by a much reduced planarity of slip, a tangled dislocation arrangement instead of planar bands, and an increased incidence of nonbasal slip vectors.

Quantitative analysis of in situ straining experiments in the case of strong frictional forces

1978 ◽  
Vol 36 (1) ◽  
pp. 570-571
Author(s):  
F. Louchet ◽  
L.P. Kubin
Keyword(s):  
Strain Rate ◽  
Radiation Effects ◽  
Dislocation Line ◽  
Critical Length ◽  
Local Strain ◽  
Local Flow ◽  
Double Kink ◽  
Dislocation Densities ◽  
Frictional Forces ◽  
Local Strain Rate

Investigation of frictional forces -Experimental techniques and working conditions in the high voltage electron microscope have already been described (1). Care has been taken in order to minimize both surface and radiation effects under deformation conditions.Dislocation densities and velocities are measured on the records of the deformation. It can be noticed that mobile dislocation densities can be far below the total dislocation density in the operative system. The local strain-rate can be deduced from these measurements. The local flow stresses are deduced from the curvature radii of the dislocations when the local strain-rate reaches the values of ∿ 10-4 s-1.For a straight screw segment of length L moving by double-kink nucleation between two pinning points, the velocity is :where ΔG(τ) is the activation energy and lc the critical length for double-kink nucleation. The term L/lc takes into account the number of simultaneous attempts for double-kink nucleation on the dislocation line.

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