Balanced ellipsoidal vortex equilibria in a background shear flow at finite Rossby number

2021 ◽  
Vol 926 ◽  
Author(s):  
William J. McKiver
Keyword(s):  
Shear Flow ◽  
Strain Rate ◽  
Second Order ◽  
Rossby Number ◽  
Strain Rates ◽  
Background Flow ◽  
Flow Parameters ◽  
Critical Strain Rate ◽  
Balanced Model ◽  
Background Shear

We consider a uniform ellipsoid of potential vorticity (PV), where we exploit analytical solutions derived for a balanced model at the second order in the Rossby number, the next order to quasi-geostrophic (QG) theory, the so-called QG+1 model. We consider this vortex in the presence of an external background shear flow, acting as a proxy for the effect of external vortices. For the QG model the system depends on four parameters, the height-to-width aspect ratio of the vortex, $h/r$ , as well as three parameters characterising the background flow, the strain rate, $\gamma$ , the ratio of the background rotation rate to the strain, $\beta$ , and the angle from which the flow is applied, $\theta$ . However, the QG+1 model also depends on the PV, as well as the Prandtl ratio, $f/N$ ( $f$ and $N$ are the Coriolis and buoyancy frequencies, respectively). For QG and QG+1 we determine equilibria for different values of the background flow parameters for increasing values of the imposed strain rate up to the critical strain rate, $\gamma _c$ , beyond which equilibria do not exist. We also compute the linear stability of this vortex to second-order modes, determining the marginal strain $\gamma _m$ at which ellipsoidal instability erupts. The results show that for QG+1 the most resilient cyclonic ellipsoids are slightly prolate, while anticyclonic ellipsoids tend to be more oblate. The highest values of $\gamma _m$ occur as $\beta \to 1$ . For large values of $f/N$ , changes in the marginal strain rates occur, stabilising anticyclonic ellipsoids while destabilising cyclonic ellipsoids.

scholarly journals Primary Transverse Crevasses

1969 ◽  
Vol 8 (52) ◽  
pp. 107-129 ◽  
Author(s):  
G. Holdsworth
Keyword(s):  
Strain Rate ◽  
Longitudinal Strain ◽  
Critical Strain ◽  
Strain Rates ◽  
A Value ◽  
Regional Strain ◽  
Critical Strain Rate ◽  
Rate Gradient ◽  
Lines Of Evidence ◽  
Longitudinal Strain Rate

Measurements of strain-rates on a temperate glacier in a region of initial transverse fracturing indicate a critical strain-rate of 3.5±0.5 × 10−5d−1, associated with a regional strain-rate gradient of 5 × 10−8d−1m−1. At only one section of the glacier is the theoretical longitudinal strain-rate (Nye, 1959[c]) in approximate agreement with the value measured at the surface at that point. Corresponding measurements on a polar glacier (temperature −27.9°C at 10 m depth during the summer) indicate that the critical strain-rate is about 0.6±0.05 × 10−5d−1, which is associated with a gradient of strain rate of about 3 × 10−9d−1m−1. At one section there is close agreement between the theoretical and measured longitudinal strain-rate. For the temperate glacier crevasse depths ranged from 23.5 to 28 m; in the polar glacier one crevasse was 23.9±0.5 m deep, assuming a wedge form. Only an approximate agreement with the measured values of depth is obtained by using the regional strain-rate values in Nye’s crevasse-depth formula.Over a distance of 1.2 km the temperate glacier transverse crevasse spacings are very variable, ranging from 30 m to 96 m, but initially the spacings range from 55 m to 96 m, and for the first four cases the spacingsvaries from 2.7dto 3.3d, wheredis the crevasse depth. In the cold ice, crevasse spacings are far more uniform, ranging from 57 m to 66 m. A value ofs≈ 2.5dis obtained in only one case. This greater uniformity of spacing may be explained in terms of the dynamics of flow. Despite large differences in thermal, dimensional and strain-rate parameters between the two glaciers, (1) the crevasse depths are closely similar, and (2) the spacings of crevasses are similar. It has been demonstrated from two lines of evidence that the assumption that the strain on an intercrevasse block is negligible is not correct. The direction of the principal extending strain-rate is, in the most reliable cases, perpendicular to the crevasse traces within 2° to 7°.

A quantitative criterion for predicting solid-state disordering during biaxial, high strain rate deformation

2021 ◽  
Author(s):  
Michael Becker ◽  
Desiderio Kovar
Keyword(s):  
Stress State ◽  
Strain Rate ◽  
Strain State ◽  
Biaxial Loading ◽  
High Strain ◽  
Md Simulations ◽  
Strain Rates ◽  
Critical Strain Rate ◽  
Wide Range ◽  
High Strain Rate Deformation

Abstract A criterion to predict the onset of disordering under biaxial loading based on a critical potential energy per atom was studied. In contrast to previous theories for disordering, this criterion incorporates the effects of strain rate and strain state. The strain state (or stress state) is defined by the combination of strain (or stress) magnitudes and directions that are applied to each sample during the simulation. Τhe validity of this criterion was studied using molecular dynamic (MD) simulations of Ag conducted over a wide range of biaxial strain rates, strain configurations, and crystal orientations with respect to the applied stress state. Biaxial strains were applied in two different planes, (112 ̅) and (001) in eight directions in each plane. Results showed that, when larger strain rates were applied, there was a transition from plastic deformation driven by the nucleation and propagation of dislocations to disordering and viscous flow. Although the critical strain rate to initiate disorder was found to vary in the range of ε ̇ = 1×1011 s-1 to ε ̇ = 4×1011 s-1, a consistent minimum PE/atom of -2.7 eV was observed over a broad range of strain states and for both crystallographic orientations that were studied. This indicates that the critical PE/atom is a material property that can be used to predict the onset of disordering under biaxial loading. Further, the results showed that this criterion can be applied successfully even when non-uninform strain states arise in the crystal.  

scholarly journals Steady and Oscillatory Shear Flow Behavior of Different Polysaccharides with Laponite®

Polymers ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 966
Author(s):  
Marcos Blanco-López ◽  
Álvaro González-Garcinuño ◽  
Antonio Tabernero ◽  
Eva M. Martín del Valle
Keyword(s):  
Shear Flow ◽  
Strain Rate ◽  
Critical Strain ◽  
Flow Behavior ◽  
Oscillatory Shear ◽  
Oscillatory Shear Flow ◽  
Critical Strain Rate ◽  
Zero Rate ◽  
Polymeric Solutions ◽  
The Impact

The rheological behavior, in terms of steady and oscillatory shear flow, of Laponite® with different polysaccharides (alginate, chitosan, xanthan gum and levan) in salt-free solutions was studied. Results showed that a higher polymer concentration increased the zero-rate viscosity and decreased the critical strain rate (Cross model fit) as well as increasing the elastic and viscous moduli. Those properties (zero-rate viscosity and critical strain rate) can be a suitable indicator of the effect of the Laponite® on the shear flow behavior for the different solutions. Specifically, the effect of the Laponite® predominates for solutions with large critical strain rate and low zero-rate viscosity, modifying significantly the previous parameters and even the yield stress (if existing). On the other hand, larger higher polymeric concentration hinders the formation of the platelet structure, and polymer entanglement becomes predominant. Furthermore, the addition of high concentrations of Laponite® increases the elastic nature, but without modifying the typical mechanical spectra for polymeric solutions. Finally, Laponite® was added to (previously crosslinked) gels of alginate and chitosan, obtaining different results depending on the material. These results highlight the possibility of predicting qualitatively the impact of the Laponite® on different polymeric solutions depending on the solutions properties.

scholarly journals Primary Transverse Crevasses

1969 ◽  
Vol 8 (52) ◽  
pp. 107-129 ◽  
Author(s):  
G. Holdsworth
Keyword(s):  
Strain Rate ◽  
Longitudinal Strain ◽  
Critical Strain ◽  
Strain Rates ◽  
A Value ◽  
Regional Strain ◽  
Critical Strain Rate ◽  
Rate Gradient ◽  
Lines Of Evidence ◽  
Longitudinal Strain Rate

Measurements of strain-rates on a temperate glacier in a region of initial transverse fracturing indicate a critical strain-rate of 3.5±0.5 × 10−5 d−1, associated with a regional strain-rate gradient of 5 × 10−8 d−1 m−1. At only one section of the glacier is the theoretical longitudinal strain-rate (Nye, 1959[c]) in approximate agreement with the value measured at the surface at that point. Corresponding measurements on a polar glacier (temperature −27.9°C at 10 m depth during the summer) indicate that the critical strain-rate is about 0.6±0.05 × 10−5 d−1, which is associated with a gradient of strain rate of about 3 × 10−9 d−1 m−1. At one section there is close agreement between the theoretical and measured longitudinal strain-rate. For the temperate glacier crevasse depths ranged from 23.5 to 28 m; in the polar glacier one crevasse was 23.9±0.5 m deep, assuming a wedge form. Only an approximate agreement with the measured values of depth is obtained by using the regional strain-rate values in Nye’s crevasse-depth formula.Over a distance of 1.2 km the temperate glacier transverse crevasse spacings are very variable, ranging from 30 m to 96 m, but initially the spacings range from 55 m to 96 m, and for the first four cases the spacing s varies from 2.7 d to 3.3 d, where d is the crevasse depth. In the cold ice, crevasse spacings are far more uniform, ranging from 57 m to 66 m. A value of s ≈ 2.5 d is obtained in only one case. This greater uniformity of spacing may be explained in terms of the dynamics of flow. Despite large differences in thermal, dimensional and strain-rate parameters between the two glaciers, (1) the crevasse depths are closely similar, and (2) the spacings of crevasses are similar. It has been demonstrated from two lines of evidence that the assumption that the strain on an intercrevasse block is negligible is not correct. The direction of the principal extending strain-rate is, in the most reliable cases, perpendicular to the crevasse traces within 2° to 7°.

Weakly nonlinear surface gravity waves in a depth-dependent background flow

2021 ◽  
Author(s):  
Zibo Zheng ◽  
Yan Li ◽  
Simen Ellingsen
Keyword(s):  
Shear Flow ◽  
Surface Waves ◽  
Second Order ◽  
Irregular Waves ◽  
Exceedance Probability ◽  
Wave Group ◽  
Background Flow ◽  
Geophysical Research ◽  
Weakly Nonlinear ◽  
Direct Integration Method

<p>An open ocean often has a wind driven shear-current near the surface that is able to significantly change the properties of surface waves. This work aims to investigate the effects of a vertically sheared background flow on weakly nonlinear waves with both a statistical study for irregular random waves and a deterministic study for a wave group.</p><p>We first extended the theory by Dalzell (1999) to allow for the effects of a horizontal background flow with arbitrary depth dependence. The extended theory is valid up to second order in wave steepness and is applicable for directional-spread waves of a broad bandwidth. The Direct Integration Method (Li & Ellingsen 2019) is used for the linear dispersion relation.</p><p>Using the theory, we examine the effects of an opposing and assisting shear, respectively, on the nonlinear properties of a short wave group on deep-water through comparisons to cases without a shear flow. A shear flow leads to wave crests (troughs) being either steepened or flattened, depending mainly on the direction of a shear relative to the propagation direction of the group and the strength of the depth-integrated velocity of a shear relative to the group velocity. We, furthermore, investigated skewness and kurtosis of a time record of the wave elevation for irregular waves in a background sheared flow, compared to a linear Gaussian random sea for surface waves only. We obtained the probability density function and exceedance probability for wave crests. Relevance for rogue wave formation is discussed.</p><p><strong>Key words</strong>: waves/free-surface flow, ocean surface waves, wave-current interaction</p><p> </p><p>References</p><p>Dalzell, J. F. "A note on finite depth second-order wave–wave interactions." Applied Ocean Research 21, no. 3 (1999): 105-111.</p><p>Li, Y., and Ellingsen, S. Å. "A framework for modeling linear surface waves on shear currents in slowly varying waters." Journal of Geophysical Research: Oceans 124, no. 4 (2019): 2527-2545.  </p>

Ductile-to-brittle Transition in Superplastic Silicon Nitride Ceramics

2002 ◽  
Vol 17 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Guo-Dong Zhan ◽  
Mamoru Mitomo ◽  
Rong-Jun Xie ◽  
Keiji Kurashima
Keyword(s):  
Silicon Nitride ◽  
Strain Rate ◽  
Deformation Temperature ◽  
Critical Strain ◽  
Strain Rates ◽  
High Deformation ◽  
Brittle To Ductile Transition ◽  
Brittle Transition ◽  
Critical Strain Rate ◽  
Ductile To Brittle Transition

The ductile-to-brittle transition was observed in a superplastic silicon nitride nanoceramic. This transition depends on strain rates and deformation temperatures. Generally, the material exhibits ductility at low strain rates and high deformation temperatures. At 1600 °C, the material is brittle when the strain rates are higher than 10−3/s. At a fixed strain rate of 10−3/s, the material exhibits brittleness when the temperatures are lower than 1550 °C. Moreover, critical strain rate for the brittle to ductile transition depends on deformation temperature. The critical strain rates increase with increases in the deformation temperature. When the deformation temperature is 1700 °C, the critical strain rates reach a maximum at 10−2/s. The extent of superplastic deformation in the present material was found to be limited not by intergranular cavitation but by the initiation and growth of surface cracks.

The effects of strain and strain rate on residual microstructures in copper

1986 ◽  
Vol 44 ◽  
pp. 420-421
Author(s):  
M. F. Stevens ◽  
P. S. Follansbee
Keyword(s):  
Strain Rate ◽  
Applied Stress ◽  
Threshold Stress ◽  
Rate Sensitivity ◽  
Viscous Drag ◽  
Strain Rates ◽  
Strain And Strain Rate ◽  
Threshold Strength ◽  
Mechanism Transition ◽  
Intrinsic Strength

The strain rate sensitivity of a variety of materials is known to increase rapidly at strain rates exceeding ∼103 sec-1. This transition has most often in the past been attributed to a transition from thermally activated guide to viscous drag control. An important condition for imposition of dislocation drag effects is that the applied stress, σ, must be on the order of or greater than the threshold stress, which is the flow stress at OK. From Fig. 1, it can be seen for OFE Cu that the ratio of the applied stress to threshold stress remains constant even at strain rates as high as 104 sec-1 suggesting that there is not a mechanism transition but that the intrinsic strength is increasing, since the threshold strength is a mechanical measure of intrinsic strength. These measurements were made at constant strain levels of 0.2, wnich is not a guarantee of constant microstructure. The increase in threshold stress at higher strain rates is a strong indication that the microstructural evolution is a function of strain rate and that the dependence becomes stronger at high strain rates.

scholarly journals A Review on Mechanical Properties of Natural Fibre Reinforced Polymer Composites under Various Strain Rates

2021 ◽  
Vol 5 (5) ◽  
pp. 130
Author(s):  
Tan Ke Khieng ◽  
Sujan Debnath ◽  
Ernest Ting Chaw Liang ◽  
Mahmood Anwar ◽  
Alokesh Pramanik ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Polymer Composites ◽  
Stress Transfer ◽  
Natural Fibre ◽  
Transfer Efficiency ◽  
Strain Rates ◽  
Reinforced Polymer ◽  
Fibre Reinforced Polymer ◽  
Fibre Matrix

With the lightning speed of technological evolution, the demand for high performance yet sustainable natural fibres reinforced polymer composites (NFPCs) are rising. Especially a mechanically competent NFPCs under various loading conditions are growing day by day. However, the polymers mechanical properties are strain-rate dependent due to their viscoelastic nature. Especially for natural fibre reinforced polymer composites (NFPCs) which the involvement of filler has caused rather complex failure mechanisms under different strain rates. Moreover, some uneven micro-sized natural fibres such as bagasse, coir and wood were found often resulting in micro-cracks and voids formation in composites. This paper provides an overview of recent research on the mechanical properties of NFPCs under various loading conditions-different form (tensile, compression, bending) and different strain rates. The literature on characterisation techniques toward different strain rates, composite failure behaviours and current challenges are summarised which have led to the notion of future study trend. The strength of NFPCs is generally found grow proportionally with the strain rate up to a certain degree depending on the fibre-matrix stress-transfer efficiency. The failure modes such as embrittlement and fibre-matrix debonding were often encountered at higher strain rates. The natural filler properties, amount, sizes and polymer matrix types are found to be few key factors affecting the performances of composites under various strain rates whereby optimally adjust these factors could maximise the fibre-matrix stress-transfer efficiency and led to performance increases under various loading strain rates.

scholarly journals Combined electrokinetic and shear flows control colloidal particle distribution across microchannel cross-sections

Soft Matter ◽  
2021 ◽  
Author(s):  
Varun Lochab ◽  
Shaurya Prakash
Keyword(s):  
Shear Flow ◽  
Cross Sections ◽  
Lift Force ◽  
Shear Flows ◽  
Colloidal Particle ◽  
Particle Distribution ◽  
Particle Migration ◽  
Flow Parameters

We quantify and investigate the effects of flow parameters on the extent of colloidal particle migration and the corresponding electrophoresis-induced lift force under combined electrokinetic and shear flow.

scholarly journals Experimental Study on Biaxial Dynamic Compressive Properties of ECC

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1257
Author(s):  
Shuling Gao ◽  
Guanhua Hu
Keyword(s):  
Strain Rate ◽  
Lateral Pressure ◽  
Deformation Modulus ◽  
Strain Curve ◽  
Peak Stress ◽  
Pressure Level ◽  
Strain Rates ◽  
Peak Strain ◽  
Stress Strain Curve ◽  
Toughness Index

An improved hydraulic servo structure testing machine has been used to conduct biaxial dynamic compression tests on eight types of engineered cementitious composites (ECC) with lateral pressure levels of 0, 0.125, 0.25, 0.5, 0.7, 0.8, 0.9, 1.0 (the ratio of the compressive strength applied laterally to the static compressive strength of the specimen), and three strain rates of 10−4, 10−3 and 10−2 s−1. The failure mode, peak stress, peak strain, deformation modulus, stress-strain curve, and compressive toughness index of ECC under biaxial dynamic compressive stress state are obtained. The test results show that the lateral pressure affects the direction of ECC cracking, while the strain rate has little effect on the failure morphology of ECC. The growth of lateral pressure level and strain rate upgrades the limit failure strength and peak strain of ECC, and the small improvement is achieved in elastic modulus. A two-stage ECC biaxial failure strength standard was established, and the influence of the lateral pressure level and peak strain was quantitatively evaluated through the fitting curve of the peak stress, peak strain, and deformation modulus of ECC under various strain rates and lateral pressure levels. ECC’s compressive stress-strain curve can be divided into four stages, and a normalized biaxial dynamic ECC constitutive relationship is established. The toughness index of ECC can be increased with the increase of lateral pressure level, while the increase of strain rate can reduce the toughness index of ECC. Under the effect of biaxial dynamic load, the ultimate strength of ECC is increased higher than that of plain concrete.

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