Principal Strain Rate Research Articles

GPS-Derived Strain Rates on an Active Ice Shelf Rift

Ice shelves are important components of the Antarctic ice sheet due to their ice-ocean-atmosphere interface and vulnerability to global increases (or decreases) in atmospheric and oceanic temperatures. The development of rifts, which are fractures that penetrate through the entire ice shelf thickness, precede large tabular iceberg detachment and can lead to ice shelf break-up. Changes in strain rates on an active propagating rift system on the Amery Ice Shelf, East Antarctica are determined using in-situ Global Positioning System (GPS) measurements. Results for the 2002/03 Antarctic summer period (Dec-Feb) confirm previous observations by [2] that rift propagation occurs in episodic bursts separated by several days. Transverse-to-flow (i.e. parallel-to-rift) strain rates exceed longitudinal-to-flow (i.e. normal-to-rift) rates by up to a factor of 5 and maximum principal strain rates around the rift tip vary from 12 to 21 [x 10-3/yr]. A rotation in the direction of the principal strain is evident around the rift tip, indicating a change in the mechanics of rift fracture. It is demonstrated that cumulative sum analysis [12], obtained by differencing a pair of residual baseline time series situated approximately normal and parallel to the rift, is an effective method to detect small baseline length changes.

Strain-rate-dependent forming limit diagrams for sheet metals

Forming limit diagrams (FLDs) appear as one of the most applicable methods used for prediction of the instability in sheet metal forming. In this paper, the effects of strain rate on FLDs are analytically investigated over a wide range of strain rate (0.01/s—500/s). In order to obtain the strain-rate-dependent FLDs with the aid of imperfection concept, the motion equations (instead of equilibrium equations) are employed. Furthermore, in this study the critical strains, in plane strain loading, are numerically determined with respect to the principal strain rates at different material constants. For materials following the widely used Johnson—Cook constitutive law, the thermal softening due to the adiabatic conditions is taken into account. The results show that after a certain critical strain rate, by increasing the strain rate, localized necking is retarded and formability of sheet improves monotonically because of inertia effects. Finally, the comparison between numerical and available experimental FLDs for oxygen-free high conductivity (OFHC) copper is presented. This comparison shows that the theoretical results are in good agreement with the experimental observations.

Horizontal Deformation Rate Analysis Based on Multiepoch GPS Measurements in Shanghai

By applying integrated least-squares adjustment of multicampaigns geographic positioning system (GPS) measurements, the velocity of any GPS monument can be obtained. The resulting velocities are used to estimate the strain rate tensors and their variances under infinitesimal strain assumption in a discrete triangle. In this paper, the GPS measurements of five campaigns, which were carried out in Shanghai City from 2002 to 2005, are used to determine the velocity of each GPS monument. Then the horizontal strain rate tensors are calculated with the relative velocities of the sites obtained. The analysis of these principal strain rates together with a comparison of the geological information is performed. The patterns of the principal strain rates show a significant northwest to southeast extension zone in the southwestern part of Shanghai, which agrees well with the neo-tectonic activity of an existing geological fault, the so-called “Dachang–Zhoupu” fault.

Effects of Lewis number on the reactive scalar gradient alignment with local strain rate in turbulent premixed flames

The effects of Lewis number Le on the reactive scalar gradient alignment with the local strain rate have been studied using Direct Numerical Simulation data of freely propagating statistically planar turbulent premixed flames with Le ranging from 0.34 to 1.2. The alignment characteristics of the reaction progress variable gradient are explained using the statistics of dilatation rate, and flame normal and tangential strain rates. The strength of dilatation rate is shown to increase with decreasing Le and this effect becomes particularly strong for the flames with Le<1 because of thermo-diffusive instability. The dilatation rate is shown to be responsible for the preferential alignment of the reactive scalar gradient with the most extensive principal strain rate in the reaction zone for flames with Le close to unity, contrary to the alignment of scalar gradient with the most compressive principal strain rate in turbulent passive scalar transport. However, stronger dilatation rate effects in Le≪1 flames (e.g. Le=0.34) gives rise to the preferential alignment of the reactive scalar gradient with the most extensive principal strain rate for the major portion of the flame-brush. The scalar gradient alignment with local strain rate plays an important role in the transport of scalar dissipation rate and the flame surface density. The observed alignment with the most extensive principal strain rate destroys the scalar gradient and the magnitude of this sink is found to increase with decreasing Lewis number for a given turbulent Reynolds number and Damköhler number.

Limit analysis with anisotropic fibre-reinforced soil

Fibre reinforcement is a technology to improve the strength of soils used as fill in geotechnical structures. The properties of the fibre-reinforced sand are anisotropic because of the distribution of orientation of the fibres, which is characterised by a preferred bedding plane. The development of an anisotropic yield condition for fibre-reinforced sand is presented. Application of the kinematic approach of limit analysis to anisotropic frictional materials is demonstrated. An interesting implication of anisotropy is a lack of uniqueness in the internal friction angle along a shear surface with given orientation. The anisotropic internal friction angle was found to be a function of the major principal strain rate direction, and not just a function of the orientation of the shear surface. While the inclination of principal strain rate directions can be inferred from the kinematics of the mechanism for a given boundary value problem, the internal friction angle cannot be determined a priori as a unique function of orientation in space. Two examples are presented to illustrate the use of the kinematic approach for anisotropic frictional materials: retaining wall loading, and the bearing capacity of a footing.

Limit analysis with anisotropic fibre-reinforced soil

Fibre reinforcement is a technology to improve the strength of soils used as fill in geotechnical structures. The properties of the fibre-reinforced sand are anisotropic because of the distribution of orientation of the fibres, which is characterised by a preferred bedding plane. The development of an anisotropic yield condition for fibre-reinforced sand is presented. Application of the kinematic approach of limit analysis to anisotropic frictional materials is demonstrated. An interesting implication of anisotropy is a lack of uniqueness in the internal friction angle along a shear surface with given orientation. The anisotropic internal friction angle was found to be a function of the major principal strain rate direction, and not just a function of the orientation of the shear surface. While the inclination of principal strain rate directions can be inferred from the kinematics of the mechanism for a given boundary value problem, the internal friction angle cannot be determined a priori as a unique function of orientation in space. Two examples are presented to illustrate the use of the kinematic approach for anisotropic frictional materials: retaining wall loading, and the bearing capacity of a footing.

Investigation of three-dimensional structure of fine scales in a turbulent jet by using cinematographic stereoscopic particle image velocimetry

Cinematographic stereoscopic particle image velocimetry measurements were performed to resolve small and intermediate scales in the far field of an axisymmetric co-flowing jet. Measurements were performed in a plane normal to the axis of the jet and the time-resolved measurement was converted to quasi-instantaneous three-dimensional data by using Taylor's hypothesis. The quasi-instantaneous three-dimensional data enabled computation of all nine components of the velocity gradient tensor over a volume. The results based on statistical analysis of the data, including computation of joint p.d.f.s and conditional p.d.f.s of the principal strain rates, vorticity and dissipation, are all in agreement with previous numerical and experimental studies, which validates the quality of the quasi-instantaneous data. Instantaneous iso-surfaces of the principal intermediate strain rate (β) show that sheet-forming strain fields (i.e. β &gt; 0) are themselves organized in the form of sheets, whereas line-forming strain fields (β &lt; 0) are organized into smaller spotty structures (not lines). Iso-surfaces of swirling strength (a vortex identification parameter) in the volume reveal that, in agreement with direct numerical simulation results, the intense vortex structures are in the form of elongated ‘worms’ with characteristic diameter of approximately 10η and characteristic length of 60--100η. Iso-surfaces of intense dissipation show that the most dissipative structures are in the form of sheets and are associated with clusters of vortex tubes. Approximately half of the total dissipation occurs in structures that are generally sheet-like, whereas the other half occurs in broad indistinct structures. The largest length scale of dissipation sheets is of order 60η and the characteristic thickness (in a plane normal to the axis of the sheet) is about 10η. The range of scales between 10η (thickness of dissipation sheets, diameter of vortex tubes) to 60η (size of dissipation sheet or length of vortex tubes) is consistent with the bounds for the dissipation range in the energy and dissipation spectrum as inferred from the three-dimensional model energy spectrum.

Associating the mesoscale fiber organization of the tongue with local strain rate during swallowing

The tongue is an intricately configured muscular organ that undergoes a stereotypical set of deformations during the course of normal human swallowing. In order to demonstrate quantitatively the relationship between 3D aligned lingual fiber organization and mechanics during swallowing, the tissue's myoarchitecture and strain rate were imaged before and during the propulsive phase of a 3.0ml water bolus swallow. Mesoscale fiber organization was imaged with high-resolution diffusion tensor imaging (DTI) and multi-voxel myofiber tracts generated along maximum diffusion vectors. Tissue compression/expansion was obtained via lingual pressure-gated phase-contrast (PC) MRI, a method which determines local strain rate as a function of the phase shift occurring along an applied gradient vector. The co-alignment of myofiber tract direction and the localized principal strain rate vectors was obtained by translating the strain rate tensor into the reference frame with the primary axis parallel to the maximum diffusion vector using Mohr's circle, resulting in the generation of fiber-aligned strain rate (FASR). DTI tractography displayed the complete fiber anatomy of the tongue, consisting of a core region of orthogonally aligned fibers encased within a longitudinal sheath, which merge with the externally connected styloglossus, hyoglossus, and genioglossus fibers. FASR images obtained in the mid-sagittal plane demonstrated that bolus propulsion was associated with prominent compressive strain aligned with the genioglossus muscle combined with expansive strain aligned with the verticalis and geniohyoid muscles. These data demonstrate that lingual deformation during swallowing involves complex interactions involving intrinsic and extrinsic muscles, whose contractility is directed by the alignment of mesoscale fiber tracts.

Comparison of displacement speed statistics of turbulent premixed flames in the regimes representing combustion in corrugated flamelets and thin reaction zones

The curvature and strain rate dependence of local displacement speed Sd is compared between two three-dimensional simplified chemistry and transport based direct numerical simulation (DNS) datasets of turbulent premixed flames with comparable turbulent Reynolds number. One of these datasets has attributes of the corrugated flamelets regime (Karlovitz number Ka&amp;lt;1), and the combustion situation in the other belongs to the thin reaction zones regime (Ka&amp;gt;1). It has been found that the probability of finding negative displacement speed increases for the flame in the thin reaction zones regime in comparison to the flame in the corrugated flamelets regime. However, the mean displacement speed remains positive throughout the flame brush in both the flames. It is shown that the curved flame contribution in displacement speed St is principally responsible for the negative displacement speed in the flame representing the thin reaction zones regime. The alignment characteristics of scalar gradient with principal strain rates is found to be different in these two flames, which leads to significant differences in tangential strain rate and curvature dependence of the magnitude of the reaction progress variable gradient ∣∇c∣. This difference in ∣∇c∣ statistics leads to marked differences in the statistics of the combined reaction and normal diffusion component of displacement speed SLS=(Sr+Sn), which in turn leads to significant differences in Sd statistics between the corrugated flamelets and the thin reaction zones regimes. This difference has important implications in the context of flame surface density based reaction rate closure.

Influence of the Damköhler number on turbulence-scalar interaction in premixed flames. I. Physical insight

Scalar dissipation rate is a central quantity in turbulent flame modeling as it is closely related to the reaction rate. It is well known that turbulence-scalar interaction plays a vital role in turbulent flows with scalar mixing and thus on the scalar dissipation rate. This interaction process is characterized by the tensor inner product between the scalar gradient vector and the turbulence strain rate tensor and it is found to depend strongly on the Damköhler number, Da. Two direct numerical simulation data sets are analyzed in detail in order to understand the physics of Da dependence. The well known alignment of scalar gradient with the most compressive principal strain rate resulting in production of the scalar gradient by turbulence is observed for low (Da&amp;lt;1) Damköhler number flame, whereas the turbulence dissipates the scalar gradient in high Da flame. This dissipation of the scalar gradient in the high Da flame is because of its preferential alignment with the most extensive principal strain rate. Even for Da&amp;lt;1 flame, in the regions of intense heat release the scalar gradient has a tendency to align with the most extensive strain rate. This distinct change is because of strong competition between chemical strain rate, due to dilatation from the flame front and the local fluid dynamic strain rate. The alignment characteristics affect flame normal and tangential strain rate statistics. The flame normal strain rate is found to be positive throughout the flame brush when Da&amp;gt;1, whereas it is predominantly negative when Da&amp;lt;1. Despite this difference the mean tangential strain rate remains positive yielding flame surface area production. However, the production results via different physical mechanisms. Possible implications of these differences on the modeling of turbulent premixed flames are identified and explained.

Role of pressure in nonlinear velocity gradient dynamics in turbulence

To identify and understand the effect of pressure on turbulence velocity gradient dynamics, we study the velocity gradient evolution with the inviscid three-dimensional Burgers equation and the restricted Euler equation (REE). While the REE represents the incompressible limit of turbulence, the Burgers equation is taken to be the infinite Mach number model for the Navier-Stokes equation wherein the time scale of flow inertia is very small compared to that of pressure. Analytical fixed-point solutions for the velocity gradient tensor are obtained in the two cases. The results are compared and contrasted to isolate the role of pressure in shaping velocity gradient behavior. Of particular interest is the influence of pressure on (i) the strain rate eigenvalues; (ii) the sign of the intermediate principal strain rate; (iii) the tendency of vorticity to align with the intermediate principal strain rate; and (iv) the energy cascade direction. Importantly, the study provides valuable insight into the velocity gradient dynamics in highly compressible turbulence.

Coupling characteristics of stress and strain at different layers of different sub-regions in Yunnan and its adjacent areas

In this paper, we collect 6 361 waveform data to calculate the shear wave splitting parameters from a regional seismic network of 22 digital stations in Yunnan and its adjacent area from July 1999 to June 2005. By using the cross-correlation method, 64 splitting events of 16 stations are processed. We also collect the splitting results of eight earthquake sequences to present the characteristics of shear wave splitting in Yunnan and its adjacent areas. The orientations of maximum principal compressive stress of three sub-regions in this area are derived from the CMT focal mechanism solutions of 43 moderate-strong earthquakes provided by Harvard University by the P axis azimuth-averaging method. The principal strain rate at each observatory is deduced from the observations of Crustal Movement Observation Network of China during the period from 1999 to 2004. In addition, the data of Pn aniso-tropy and SKS splitting of Yunnan and its adjacent areas are also collected. We have discovered from this study that the continental lithosphere, as a main seismogenic environment for strong earthquake, can be divided into blocks laterally; the mechanical behavior of lithosphere varies with depth and can be divided into different layers in the vertical orientation; the information of crustal deformation obtained from GPS might be affected by the type of blocks, since there are different types of active blocks in Yunnan and its adjacent areas; the shear wave splitting in this region might be affected mainly by the upper crust or even the surface tectonics.

Relationship between non-cylindrical fold geometry and the shear direction in monoclinic and triclinic shear zones

We investigate the relationship between non-cylindrical fold geometry and the shear direction of the hosting high-strain zone by numerical modeling, and show that apical axes of non-cylindrical folds may develop into directions highly oblique to the shear direction if the zone has a pure shear component. The common practice of using well-developed sheath folds as indicators for the shear direction is not reliable and the use of immature non-cylindrical or sheath folds appears more reliable. Hinge lines of mature sheath folds approach parallelism with the fabric attractor (to which all material lines rotate), which can have variable angles with respect to the shear direction. In thinning zones, the fabric attractor is the direction of the maximum principal strain rate of the pure shear component and is parallel to the shear zone boundary. In thickening zones, it lies somewhere in the quadrant between the direction of the maximum principal strain rate of the pure shear component (perpendicular to the shear zone boundary) and the simple shear direction, and is generally oblique to the shear zone boundary. The exact location depends on the flow geometry of the shear zone.

GPS determination of the velocity and strain-rate fields on Schirmacher Glacier, central Dronning Maud Land, Antarctica

Global positioning system (GPS) campaigns were conducted during the 2003 and 2004 austral summer seasons to obtain insight into the velocity and strain-rate distribution on Schirmacher Glacier, central Dronning Maud Land, East Antarctica. GPS data were collected at 21 sites and analyzed to estimate the site coordinates, baselines and velocities. The short-term precision of the base station, MAIT, is estimated from the daily coordinate repeatability solutions during the two years. All GPS points on the glacier were constrained with respect to MAIT and nearby International GPS Service stations. Horizontal velocities of the glacier sites lie between 1.89 ± 0.01 and 10.88 ± 0.01 ma−1 to the north-northeast, with an average velocity of 6.21 ± 0.01 m a−1. The principal strain rates provide a quantitative measurement of extension rates, which range from (0.11 ± 0.01) × 10−3 to (1.48 ± 0.85) × 10−3a−1, and shortening rates, which range from (0.04 ± 0.02) × 10−3 to (0.96 ± 0.16) × 10−3a−1. The velocity and strain-rate distributions across the GPS network in Schirmacher Glacier are spatially correlated with topography, subsurface undulations, fracture zones/crevasses and the partial blockage of the flow by nunataks and the Schirmacher Oasis.

Flame residence time and strain rate in turbulent hydrogen non-premixed jet flames with coaxial air

Simultaneous measurements of velocity field and OH distribution were made using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) of OH radicals in turbulent hydrogen non-premixed jet flames with coaxial air. The OH radical was used to indicate the chemical reaction zone approximately. The flame surface represented by the OH layer is correlated well with the location of the stoichiometric velocity, U S, which is reformulated to account for the coaxial air effect. Furthermore, the region of high strain rate almost coincides with the inner edge of the OH layer. The local residence time on the flame surface, estimated from the mean value of the radial velocity on the OH layer, is proportional to ( x/ d eff) 0.7 where d eff is the effective jet diameter in the far-field region. Also, the mean value of the principal strain rate on the OH layer scales well with ( x/ d eff) −0.7 for a wide range of coaxial air flames. Finally, it is found that the local flame residence time is inversely proportional to the local strain rate and this inverse relation is also globally observed for turbulent non-premixed jet flames with and without coaxial air, if the coaxial air effect is taken into consideration.

Integral‐Rotation Linear‐Strain Model and Intraplate Deformation‐Strain Field of the Philippine Sea Plate

AbstractIn this paper, we create an integral‐rotation linear‐strain model (IRLSM) for the Philippine Sea plate (PHIL) on the basis of the ITRF2000 velocities of 7 sites on the PHIL. Our study indicates that the current‐day tectonic motion of PHIL is a clockwise rotation, which is consistent with the rotational direction estimated by NNR‐NUVEL‐1A, but largely different from the rotational pole position and angle velocity of NNR‐NUVEL‐1A. Our model can uniformly and accurately describe the current tectonic movement and interior deformation of PHIL as compared with Sella's rigid motion model (RMM). There is an intensive deformation‐strain field within the PHIL and there is consistent eastward deformation on the plate. The deformation rate is small near the central tectonic line and large near the eastern and western boundaries, small at the southern and northern ends and large in the central part. The eastward deformation rate on the Mariana Arc is as large as 48.4mm/a. The NS‐trending deformation on the plate differs evidently in the eastern and western parts with a very small rate in the eastern part and a larger rate near the Manila Trench in the western part. The northward deformation rate at the north end is 11.3mm/a and the southward deformation rate at the south end is 29.3mm/a. The principal strain field is divided into the eastern and western areas from the central tectonic line. In the eastern area, the tensile strain is very intensive, while the compressive strain is very weak. The principal tensile strain is in near‐EW direction, the principal tensile and compressive strain rates increase gradually from the central tectonic line to the east, and the principal tensile strain rate reaches the highest value of 8.58×10−8/a near the southeast boundary (148°E, 15°N). In the western area, the principal compressive strain is very strong in a direction of NW‐SE, while the principal tensile strain is rather weak. From the central tectonic line to the west, the principal compressive and tensile strain rates increase gradually and the principal compressive strain rate reaches the maximum value of 5.71×10−8/a near the northwest boundary (122°E, 23°N). Closely related to the intraplate and surrounding tectonic settings, the spatial variation of deformation‐strain field of PHIL can be considered as a reflection of tectonic stress field.

The Contemporary Tectonic Strain Rate Field of Continental China Predicted from GPS Measurements and its Geodynamic Implications

In Appling studies, the strain rate in China has been computed from using different methods, resulting in quite different estimates of the strain rate the geo-statistics from GPS velocity field of Chinese continent, we obtain the velocity value at each little regularly spaced grid point, by kriging interpolation and the component of strain rate for each volume element, using a method similar to the derivation of shape functions in the finite element algorithm. Therefore the distribution of the strain rate field in whole for the Chinese continent is presented. The result shows that the orientations of principal strain rates are consistent with those of the P and T axes of focal mechanisms. The distribution of maximum shear strain rate clearly delineates some major active fault zones surrounding the Tibetan Plateau. The maximum shear strain rate is comparable with that obtained from analysis of seismic moment release. In part of the Tibetan Plateau containing normal faults and pull-apart grabens, we obtain an extensional state of strain. The absolute value of the strain rate in West China is approximately 5 times larger than that of East China, and the pattern of the strain rate field in most of the Chinese continent is controlled by the India/Eurasia collision.

Interaction of turbulence and scalar fields in premixed flames

The interaction of turbulence with progress variable, c, field in a premixed flame is studied. This interaction is characterized by the correlation c,ieijc,j¯, where the overbar denotes an appropriate averaging process, c,i is the gradient of c in spatial direction i and eij is the turbulence strain rate. The importance of this term is recognized via a transport equation for the square of the magnitude of the scalar gradient in turbulent premixed flames. It is also shown that the above correlation forms a natural part of the tangential strain rate which appears in the flame surface density, Σ, equation. It is well known that this correlation is negative signifying the scalar gradient production by incompressible turbulence via the preferential alignment of the scalar gradient with the most compressive principal strain rate. This physical picture is commonly adopted for turbulent premixed flames also. Contrary to this, analyses of direct numerical simulation data for a turbulent premixed flame having flamelet combustion characteristics show the preferential alignment of the scalar gradient with the most extensive principal strain rate. This preferential alignment is because of flame influence on the flow via dilation. The above alignment pulls the isoscalar surfaces from each other yielding positive values for the above correlation inside the flame brush. Thus the turbulence, in addition to the molecular dissipation process, dissipates the scalar gradients in premixed flames when the Damköhler number (Da) is large. These dissipation processes are counteracted by chemical reactions which produce the scalar gradients. A simple RANS model for the above correlation is obtained by decomposing it into contributions from flame front and nonflame front regions of the flow as suggested by the DNS results. The model obtained here involves Da and represents the dissipation of the scalar gradients by the turbulence when Da is larger than unity. This model also recovers the production of the scalar gradient by the turbulence when Da is less than unity. Comparison of this model prediction with the DNS data of large Da flame is reasonable. The turbulence-scalar interaction in low and moderate Damköhler number flames still needs to be explored.

General Solving Method of Energy Dissipation Rate of Deforming Region in Upper-Bound Analysis for Coulomb Material

At present the energy dissipation rate per unit volume of deforming region is expressed with the function of principal strain rates in upper-bound analysis for Coulomb material and this restricts the application of deforming failure mechanisms in upper-bound method. In this paper, a general method of expressing the energy dissipation rate of deforming region with bulk strain rate was put forward and the conditions that the assumed velocity field of deforming region should meet were pointed out. The general method simplifies the solving process of the energy dissipation rate. Finally, the method was employed to calculate the energy dissipation rate of the logspiral shear zone and was proved practical.

Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. II. Experimental results

Results are presented from highly resolved dual-plane stereo particle image velocimetry (DSPIV) measurements for the structure, statistics, similarity, and scaling of all nine simultaneous components of the velocity gradient tensor fields ∂ui∕∂xj on the quasi-universal intermediate and small scales of turbulent shear flows. Measurements were obtained at three combinations of the outer-scale Reynolds number Reδ and the local mean shear rate S in the fully developed self-similar far field of a turbulent jet, and thus reflect the combined effects of the large-scale structure, spatial inhomogeneities, and anisotropies inherent in such a flow. Conditions addressed in this study correspond to local outer-scale Reynolds numbers Reδ=6,000 and 30,000 and local mean shear values Sδ∕uc=0 and 1.7, corresponding to Taylor-scale Reynolds numbers Reλ≈44 and 113 and shear rates Sk∕ε=0 and 2.1. Gradient fields investigated here include the individual velocity gradient component fields, the strain rate component fields and the associated principal strain rates, the vorticity component fields and their orientations with respect to the principal strain axes, the enstrophy and enstrophy production rate fields, and the true kinetic energy dissipation rate field. Results normalized on both inner- and outer-scale variables are presented to allow interpretation relative to the similarity and scaling implied by classical turbulence theory. For both Reδ values at S=0, results show that most aspects of these gradient fields are essentially in agreement with the predictions from homogeneous isotropic turbulence, while for S≠0 there are significant and consistent departures from isotropy. Results also provide direct measurements of the exponential scaling factors in the left and right tails of the velocity gradient distributions, as well as quantification of the inner (viscous) length scales in the enstrophy and dissipation rate fields. In addition, strong evidence for multifractal scale similarity at length scales greater than about twice the viscous length λν is found in both the enstrophy and dissipation rate fields.