Compressional Flow Research Articles

Estimating the Ionospheric Induction Electric Field Using Ground Magnetometers

AbstractThe ionospheric convection electric field is often assumed to be a potential field. This assumption is not always valid, especially when the ionosphere changes on short time scales min. We present a technique for estimating the induction electric field using ground magnetometer measurements. The technique is demonstrated on real and simulated data for sudden increases in solar wind dynamic pressure of 1 and 10 nPa, respectively. For the real data, the ionospheric induction electric field is 0.15 0.015 mV/m, and the corresponding compressional flow is 2.5 0.3 m/s. For the simulated data, the induction electric field and compressional flow reach 3 mV/m and 50 m/s, respectively. The induction electric field can locally constitute tens of percent of the total electric field. Inclusion of the induction electric field increased the total Joule heating by 2.4%. Locally the Joule heating changed by tens of percent. This corresponds to energy dissipation that is not accounted for in existing models.

Impact of surface rheology on droplet coalescence in uniaxial compressional flow

Impact of surface rheology on droplet coalescence in uniaxial compressional flow

Author Correction: Flexible filaments buckle into helicoidal shapes in strong compressional flows

Author Correction: Flexible filaments buckle into helicoidal shapes in strong compressional flows

Viscoplastic toroidal drop in compressional Stokes flow

We report the dynamics of a viscoplastic (Bingham) torus suspended in an unbounded Newtonian medium. In this study, the immiscible ambient fluid is subjected to an axisymmetric compressional (biaxial-extensional) flow. Numerical simulations applying the boundary integral formulation to the Stokes flow are performed for the torus drop having initially a circular cross section. The quasi-stationary dynamic simulation reveals that depending on the initial conditions and the capillary number (Ca), the Bingham number (Bn), and the viscosity ratio (λ), three different scenarios of the drop evolution are obtained for a range of viscosity ratio and Bingham number: collapsing toward the axis of symmetry, expanding infinitely, and having a stationary toroidal shape.

Approximating stationary deformation of flat and toroidal drops in compressional viscous flow using generalized Cassini ovals

Viscous drops, subject to a linear flow in an immiscible viscous fluid, deform. When the resulting drop shape is simple the problem can be addressed by an asymptotic approach or by approximating the deformation using known simple shapes. When the resulting deformation is more complex, the problem is usually addressed numerically. In this paper, we address the problem of drops that are deforming in an axisymmetric compressional (bi-axial extensional) flow. Yielded shapes are flat drops, flat drops with dimples and toroidal drops. The latter two are highly unstable. We propose to approximate the solution of this problem, approximating the shapes by using generalized Cassini ovals, defined herein. The analysis reproduced the branches with shapes of stationary stable flat drops and stationary unstable toroidal drops, available from numerical calculation. Furthermore, it predicts the point of loss of stability of the flat drop to exhibit the transition branch that leads into the formation of the toroidal shapes, and shows that this branch shows stationary, yet unstable, flat drops with ever growing dimples up to collapse.

Challenges in predicting Greenland supraglacial lake drainages at the regional scale

Abstract. A leading hypothesis for the mechanism of fast supraglacial lake drainages is that transient extensional stresses briefly allow crevassing in otherwise compressional ice flow regimes. Lake water can then hydrofracture a crevasse to the base of the ice sheet, and river inputs can maintain this connection as a moulin. If future ice sheet models are to accurately represent moulins, we must understand their formation processes, timescales, and locations. Here, we use remote-sensing velocity products to constrain the relationship between strain rates and lake drainages across ∼ 1600 km2 in Pâkitsoq, western Greenland, between 2002–2019. We find significantly more extensional background strain rates at moulins associated with fast-draining lakes than at slow-draining or non-draining lake moulins. We test whether moulins in more extensional background settings drain their lakes earlier, but we find insignificant correlation. To investigate the frequency at which strain-rate transients are associated with fast lake drainage, we examined Landsat-derived strain rates over 16 and 32 d periods at moulins associated with 240 fast-lake-drainage events over 18 years. A low signal-to-noise ratio, the presence of water, and the multi-week repeat cycle obscured any resolution of the hypothesized transient strain rates. Our results support the hypothesis that transient strain rates drive fast lake drainages. However, the current generation of ice sheet velocity products, even when stacked across hundreds of fast lake drainages, cannot resolve these transients. Thus, observational progress in understanding lake drainage initiation will rely on field-based tools such as GPS networks and photogrammetry.

Deformation of an axisymmetric viscoplastic drop in extensional/compressional flow

The dynamic and stationary deformations of a viscoplastic drop in an axisymmetric linear viscous flow is addressed through numerical analyses for a variety of governing parameters. A variation of the integral equation method used by Toose et al. (1996, 1999) is employed. It is demonstrated that a spherical drop embedded in compressional or extensional flow, which provides viscous stresses at the interface strong enough to yield the drop medium, deforms into oblate or prolate shapes, respectively. With the passage of time, the drops attain elongated (in extensional flow) or flattened (in compressional flow) forms. For moderate shear intensity, stable stationary states are established, with either entirely yielded or partially un-yielded flow inside the drop. When the velocity gradients exceed critical values the drop loses its stable shape and continues to deform indefinitely.

Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow

Abstract

Flexible filaments buckle into helicoidal shapes in strong compressional flows

The occurrence of coiled or helical morphologies is common in nature, from plant roots to DNA packaging into viral capsids, as well as in applications such as oil drilling processes. In many examples, chiral structures result from the buckling of a straight fiber either with intrinsic twist or to which end moments have been applied in addition to compression forces. Here, we elucidate a generic way to form regular helicoidal shapes from achiral straight filaments transported in viscous flows with free ends. Through a combination of experiments using fluorescently labeled actin filaments in microfluidic divergent flows and of two distinct sets of numerical simulations, we demonstrate the robustness of helix formation. A nonlinear stability analysis is performed and explains the emergence of such chiral structures from the nonlinear interaction of perpendicular planar buckling modes, an effect that solely requires a strong compressional flow, independent of the exact nature of the fiber or type of flow field. The fundamental mechanism for the uncovered morphological transition and characterization of the emerging conformations advance our understanding of several biological and industrial processes and can also be exploited for the controlled microfabrication of chiral objects.

Flow-induced buckling dynamics of sperm flagella.

The swimming sperm of many external fertilizing marine organisms face complex fluid flows during their search for egg cells. Aided by chemotaxis, relatively weak flows are known to enhance sperm-egg fertilization rates through hydrodynamic guidance. However, strong flows have the potential to mechanically inhibit flagellar motility through elastohydrodynamic interactions-a phenomenon that remains poorly understood. Here we explore the effects of flow on the buckling dynamics of sperm flagella in an extensional flow through detailed numerical simulations, which are informed by microfluidic experiments and high-speed imaging. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, Sp, which represents the ratio of viscous force to elastic force. For nonmotile sperm, the maximum buckling curvature and the number of buckling locations, or buckling mode, increase with increasing sperm number. In contrast, motile sperm exhibit a local flagellar curvature due to the propagation of bending waves along the flagellum. In compressional flow, this preexisting curvature acts as a precursor for buckling, which enhances local curvature without creating new buckling modes and leads to asymmetric beating. However, in extensional flow, flagellar beating remains symmetric with a smaller head yawing amplitude due to tensile forces. The flagellar beating frequency also influences the maximum curvature of motile sperm by facilitating sperm reorientation relative to the compressional axis of the flow near stagnation points. These combined simulations and experiments directly illustrate the microscopic elastohydrodynamic mechanisms responsible for inhibiting flagellar motility in flow and have possible implications for our understanding of external fertilization in dynamic marine systems.

Fluctuation analysis in the dynamic characteristics of continental glacier based on Full-Stokes model

Ice thickness has a great influence on glacial movement and ablation. Over the course of the change in thickness, area and external climate, the dynamic process of how glaciers change and whether a glacier’s changes in melting tend to be stable or irregular is a problem that needs to be studied in depth. In our study, the changes in the dynamic process of the No. 8 Glacier in Hei Valley (H8) under the conditions of different thicknesses in 1969 and 2009 were simulated based on the Full-Stokes code Elmer/Ice (http://www.csc.fi/elmer/). The results were as follows: (1) The thickness reduction in glaciers would lead to a decrease in ice surface tension and basal pressure and friction at the bottom, and the resulting extensional and compressional flow played an important role in the variations in glacial velocity. (2) The force at the bottom of the glacier was key to maintaining the overall stress balance, and the glaciers that often melted and collapsed in bedrock were more easily destroyed by the overall force balance and increased change rate of glacial thaw. (3) Temperature changes at different altitudes affected the ice viscous force. The closer the ice surface temperature was to the melting point, the greater the influence of temperature changes on the ice viscous force and ice surface velocity. Finally, we used the RCP 4.8 and 8.5 climate models to simulate the changes in H8 over the next 40 years. The results showed that with some decreases in ice surface compression and tension, the gravity component changes caused by local topography begin to control the ice flow movement on the surface of glacier, and melting of the glacial surface will appear as an irregular change. The simulation results further confirmed that the fluctuation in glacial dynamic characteristics could be attributed to the change in the gravity component caused by ablation.

Small-amplitude collective modes of a finite-size unitary Fermi gas in deformed traps

We have investigated collective breathing modes of a unitary Fermi gas in deformed harmonic traps. The ground state is studied by the Superfluid Local Density Approximation (SLDA) and small-amplitude collective modes are studied by the iterative Quasiparticle Random Phase Approximation (QRPA). The results illustrate the evolutions of collective modes of a small system in traps from spherical to elongated or pancake deformations. For small spherical systems, the influences of different SLDA parameters are significant, and, in particular, a large pairing strength can shift up the oscillation frequency of collective mode. The transition currents from QRPA show that the compressional flow patterns are nontrivial and dependent on the deformation. Finally, the finite size effects are demonstrated to be reasonable when progressing towards larger systems. Our studies indicate that experiments on small and medium systems are valuable for understanding effective interactions in systems with varying sizes and trap deformations.

Tidal and spatial variability of flow speed and seismicity near the grounding zone of Beardmore Glacier, Antarctica

ABSTRACTGPS measurements of tidal modulation of ice flow and seismicity within the grounding zone of Beardmore Glacier show that tidally induced fluctuations of horizontal flow are largest near the grounding line and decrease downstream. Seismic activity is continuous, but peaks occur on falling and rising tides. Beamforming methods reveal that most seismic events originate from two distinct locations, one on the grid-north side of the grounding zone, and one on the grid-south side. The broad pattern of deformation generated as Beardmore Glacier merges with the Ross Ice Shelf results in net extension along the grid-north side of the grounding zone and net compression along the grid-south side. During falling tides, seismic activity peaks on both sides because of increased vertical flexure across the grounding line. During rising tides, seismic activity in the region of extension on the grid-north side is relatively low because the tidal influence on both horizontal strain rate and vertical flexure is small. On the grid-south side during rising tides, however, tidally induced horizontal strain rates promote increased seismicity in regions of long-term compressional flow paths. Our study highlights how concurrent geodetic and seismic measurements provide insight into grounding-zone mechanics and their influence on ice-shelf buttressing.

Small Deformation Analysis for Stationary Toroidal Drops in a Compressional Flow

It is known that a toroidal drop freely suspended in a quiescent ambient fluid shrinks and forms a simply connected drop. However, if it is embedded in a compressional flow and has an initially circular cross section, then for a certain value of the major radius, it may attain a stationary toroidal shape. This value is called critical major radius $R_{cr}$ and depends on capillary number Ca that defines the ratio of viscous forces to surface tension: the smaller Ca, the larger $R_{cr}$. It is relatively insensitive to the drop-to-ambient fluid viscosity ratio $\lambda$ particularly for small Ca. For Ca $\lesssim$ 0.16 (or $R_{cr} \gtrsim 1$), a stationary shape is close to a torus with an elliptical cross section, whose major radius $R$ and flattening $\Delta$ depend on Ca. In fact, for small Ca, any of the three Ca, $R$, and $\Delta$ can be considered an independent variable and the other two its functions. This work obtains asymptotic behavior of Ca($R$) and $\Delta(R)$ as $R\rightarrow\infty$ and, as a result, of $\Delta$(Ca) as Ca $\rightarrow$ 0. Those analytical relationships are in a good agreement with the existing numerical results for Ca $\lesssim$ 0.06 (or $R_{cr} \gtrsim 1.5$) for various values of $\lambda$ and play the role similar to that in the well-known small deformation theories for spherical drops. The central part of the presented analytical analysis is a novel boundary-integral equation for the axisymmetric velocity field of the corresponding two-phase Stokes flow problem. The equation was derived based on the Cauchy integral formula for generalized analytic functions.

Quasi‐Static Granular Flow of Ice Mélange

We use Landsat 8 imagery to generate ice mélange velocity fields at Greenland's three most productive outlet glaciers: Jakobshavn Isbræ, Helheim Glacier, and Kangerdlugssuaq Glacier. Winter velocity fields are generally steady and highly uniform. Summer velocity fields, on the other hand, tend to be much more variable and can be uniform, compressional, or extensional. We rarely observe compressional flow at Jakobshavn Isbræ or extensional flow at Helheim Glacier, while both are observed at Kangerdlugssuaq Glacier. Transverse velocity profiles from all three locations are suggestive of viscoplastic flow, in which deformation occurs primarily in shear zones along the fjord walls. We analyze the transverse profiles in the context of quasi‐static flow using continuum rheologies for granular materials and find that the force per unit width that ice mélange exerts on glacier termini increases exponentially with the ice mélange length‐to‐width ratio and the effective coefficient at the fjord walls. Our estimates of ice mélange resistance are consistent with other independent estimates and suggest that ice mélange may be capable of inhibiting iceberg calving events, especially during winter. Moreover, our results provide geophysical‐scale support for constitutive relationships for granular materials and suggest a potential avenue for modeling ice mélange dynamics with continuum models.

Evolution and stationarity of liquid toroidal drop in compressional Stokes flow

Dynamics of fluid tori in slow viscous flow is studied. Such tori are of interest as future carriers of biological and medicinal substances and are also viewed as potential building blocks towards more complex particles. In this study the immiscible ambient fluid is subject to a compressional flow (i.e., bi-extensional flow), and it comprises a generalization of our earlier report on the particular case with viscosity ratio$\unicode[STIX]{x1D706}=1$(see Zabarankinet al.,J. Fluid Mech., vol. 785, 2015, pp. 372–400), where$\unicode[STIX]{x1D706}$is the ratio between the torus viscosity and that of the ambient fluid. It is found that, for all viscosity ratios, the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number,Ca. During these dynamic patterns the cross-sections exhibit various forms of deformation. The collapse and expansion dynamic modes are separated by a limited deformation into a deformed stationary state which appears to exist in a finite interval of the capillary number,$0<Ca<Ca_{cr}(\unicode[STIX]{x1D706})$, and is unstable to axisymmetric disturbances, which eventually cause the torus either to collapse or to expand indefinitely. The characteristic dimensions and shapes of these unstable stationary tori and their dependence on the physical parametersCaand$\unicode[STIX]{x1D706}$are reported.

Complete and comprehensive orientation of cylindrical microdomains in a block copolymer sheet

Significant progress in cylindrical microdomain orientation is reported for a polystyrene-block-poly(ethylene-co-butylene)-block-polystyrene triblock copolymer (SEBS-16) as analyzed by two-dimensional small-angle X-ray scattering. For this purpose, the morphological transition from sphere to cylinder was utilized. By applying compressional flow to the SEBS-16 specimen undergoing a morphological transition at 210 °C, superior cylinder orientation was achieved compared with the results obtained by applying the compressional flow to a cylindrical phase. The flow-treated specimens were further subjected to subsequent thermal annealing at 210 °C. It was found that the cylinder orientation proceeded by the subsequent thermal annealing even for flow-treated specimens with less oriented cylinders. Furthermore, the fraction of grains in which the plane of the hexagonal lattice of cylinders is oriented parallel to the specimen surface increased due to the subsequent thermal annealing, even for the specimen with the best cylinder orientation. Significant progress in cylindrical microdomain orientation is reported for a polystyrene-block-poly(ethylene-co-butylene)-block-polystyrene triblock copolymer (SEBS-16) as analyzed by two-dimensional small-angle X-ray scattering. To achieve this goal, the morphological transition from sphere to cylinder was utilized. By applying compressional flow to the SEBS-16 specimen undergoing a morphological transition at 210 °C, superior cylinder orientation was achieved compared with the results obtained by applying compressional flow to the SEBS-16 specimen containing the cylindrical phase.

Two touching spherical drops in a uniaxial compressional flow: The effect of interfacial slip

This study presents a semi-analytical solution for the problem of two touching drops with slipping interfaces pushed against each other in a uniaxial compressional flow at low capillary and Reynolds numbers. The jump in the tangential velocity at the liquid-liquid interface is modeled using the Navier slip condition. Analytical solutions of the contact force, the drop-scale stresses, and the drop-scale pressure are provided as functions of the slip coefficient α, the viscosity ratio κ, and the drop size ratio k. Since unequal drop sizes are considered, two problems are solved in the tangent sphere co-ordinate system to determine the steady state position: a pair of touching drops with its contact point at the origin of an axisymmetric straining flow, and two touching drops placed in a uniform flow parallel to the axis of symmetry of the drops. A general observation is that the effect of slip is manifested most strongly for drops whose viscosity is much greater than the suspending fluid κ≫1. For highly viscous drops, the flow and stress fields transition from those corresponding to solid particles for ακ ≪ 1, to those for inviscid drops in the limit ακ ≫ 1. The analytical expressions provided here for the contact force and the stress distributions will serve to provide the restrictions that complete the definition of the lubrication flow problem in the thin film between the two colliding drops. While the contact force that drains fluid out of the thin film is relatively unaffected by slip, the tangential stress and pressure in the near-contact region are mitigated significantly for ακ ≫ 1. The latter is expected to assist coalescence at high capillary numbers.

Liquid toroidal drop in compressional flow with arbitrary drop-to-ambient fluid viscosity ratio

Existing experiments show that a sufficiently fat toroidal drop freely suspended in another liquid shrinks towards its centre to form a spherical drop. However, recent simulations reveal that if a liquid torus with circular cross section is embedded in a compressional same-viscosity flow that acts to expand the torus, then depending on the torus radius R and a capillary number Ca characterizing the balance between the viscous forces and the interfacial tension, the torus may either coalesce, expand indefinitely or attain a stationary shape. For each Ca less than 0.2, there is a single value of R , called the critical radius, for which the torus attains the stationary shape. Here, the drop-to-ambient fluid viscosity ratio, λ, is assumed to be arbitrary. The corresponding two-phase Stokes flow problem is solved for a liquid toroidal drop with circular cross section in terms of stream functions in the toroidal coordinates. When λ=1, the stream functions admit a closed-form integral representation for a drop of arbitrary axisymmetric shape. ‘Stationary’ circular tori minimize a certain measure of the normal velocity over the interface, and as in the case of λ=1, their radii are expected to predict the critical ones for arbitrary λ and Ca in a certain range (e.g. for Ca<0.2 when λ=1). Streamlines about ‘stationary’ circular tori are analysed for various Ca and λ.

Liquid toroidal drop in compressional Stokes flow

The deformation of an immiscible toroidal drop embedded in axisymmetric compressional Stokes flow is analysed via the boundary integral formulation in the case of equal viscosity. Numerical simulations are performed for the drop having initially the shape of a torus with circular cross-section. The quasi-stationary dynamic simulations reveal that, when the viscous forces, proportional to the intensity of the flow, are relatively weak compared with the surface tension (the ratio of these forces is characterized by the capillary number,$Ca$), three different scenarios of drop evolution are possible: indefinite expansion of the liquid torus, contraction to the centre and a stationary toroidal shape. When the intensity of the flow is low, the stationary shapes are shown to be close to circular tori. Once the outer flow strengthens, the cross-section of the stationary torus assumes first an elliptic and then an egg-like shape. For the capillary number greater than a critical value,$Ca_{cr}$, toroidal stationary shapes were not found. Remarkably,$Ca_{cr}$is close to the critical capillary number found previously for a simply connected drop flattened in compressional flow. Thus, a new example of non-uniqueness of stationary drop shape in viscous flow is obtained. Approximate stationary solutions in the form of tori with circular and elliptic cross-sections are obtained by minimizing the normal velocity over the drop interface. They are shown to be in good agreement with the stationary shapes from quasi-dynamic simulations for the corresponding intervals of the capillary number.