Length Scale Of Variation Research Articles

Rapid compression of grid-generated turbulence by a moving shock wave

Most of the previous work on turbulence amplification by shock wave interaction is limited to shock wave/boundary layer types of interactions where additional effects due to shock wave oscillation, streamline curvature, and flow separation complicate the understanding of the physics involved in this phenomenon. The present experimental study has focused on interactions of a normal shock with grid-generated turbulence in a shock tube. The decaying turbulence behind the grid is characterized by a variation of length scales with downstream distance and is subjected to an interaction with the reflected shock traveling in the opposite direction. Considerable amplification of turbulence has been found after the interaction which depends on the length scale of the incoming flow. Spectral analysis has also indicated that large eddies are amplified more than small eddies during interactions with shock waves of the same strength.

The effect of different scalings in the modelling of nonlinearity elastic plates with rapidly varying thickness

In this paper we deal with the bending of a nonlinearly elastic plate with rapidly varying thickness, assuming it to have a St. Venant-Kirchhoff's constitutive law. Our analysis is centered on the case when the plate mean thickness and the periodic variation length scale are of different order. The associated limiting model is a fourth order system posed on the plate's midplane, and with coefficients, determinated by the geometry of the plate, depending on the velocity of the mean thickness variation. The two-dimensional limiting problem generalizes nonlinear models already known in the literature for constant thickness plates. Finally, numerical results for plates with rib-like stiffeners are presented.

Magmatic processes at superfast spreading mid‐ocean ridges: Glass compositional variations along the East Pacific Rise 13°–23°S

Major and minor element analyses of 496 natural volcanic glass samples from 141 locations along the superfast spreading (150 mm/yr) East Pacific Rise (EPR), 13°–23°S, and near‐ridge seamounts comprise 212 chemical groups. We interpret these groups to represent the average composition of individual lava flows or groups of closely related flows. Groups slightly enriched in K2O (T‐MORB) are distributed variably along the axis, in contrast to the Galapagos Spreading Center where T‐MORB are extremely rare. This result is consistent with the interpretation that T‐MORB magmas arise from low‐melting temperature, K‐rich heterogeneities in the subaxial EPR mantle. The Galapagos Spreading Center, which is migrating to the west in an absolute reference frame, is underlain by mantle previously processed and depleted in the T‐MORB component during melting events giving rise to earlier EPR magmas. Excluding T‐MORB, there are nearly monotonic, twofold increases in K/Ti and K/P of axial lavas from 23°S to 13°S. From 22°S to 17°S these gradients correlate with isotopic ratios, but north of 17°S there is a reversal of isotopic gradients, indicating (recent?) decoupling of the isotopic and minor element ratios in the subaxial mantle. A strong, southward increase in degree of differentiation for approximately 200 km north of the large offset at 20.7°S correlates with a gradient in bathymetry, consistent with previous interpretations that this offset is propagating to the south. Samples from recently abandoned ridges associated with this dueling propagator mainly carry the distinctive, evolved fractionation signatures of rift propagation, suggesting that propagating rift tips have been abandoned preferentially to failing rift tips. Glass compositional variations south of this offset are consistent with rift failure on the southern limb within 40 km of the offset, and possibly also south of 22°S; the latter region may be affected by deformation accompanying northward growth of the Easter Microplate. Near‐ridge seamounts on the Pacific Plate between 18°–19°S comprise two distinct populations: those aligned approximately parallel to the spreading direction are extremely variable in major element composition, but consistently enriched in Sr relative to nearby axial lavas; smaller seamounts aligned approximately parallel to the direction of absolute plate motion are uniformly depleted in minor elements and Sr relative to axial lavas. The degree of differentiation of axial lavas between 18°–19°S can be related to the structural development of the rift axis and/or vigor of hydrothermal activity of individual segments. Glass compositional variations indicate that magmatic segmentation occurs on several different scales at the superfast spreading rate of this area. Primary magmatic segmentation mainly reflects mantle source variations, the boundaries of which correlate with the largest physical offsets in the rise axis between the Easter Microplate and Garrett Transform Zone. A secondary magmatic segmentation, defined by the along‐axis continuity of similar parental magma compositions or liquid lines of descent, occurs with a length scale varying from 11 to 185 km, with an average of 69 ±57 (1σ) km. The boundaries of these segments mainly occur at overlapping spreading centers. All first‐, second‐ and third‐order physical offsets correspond to secondary magmatic segment boundaries, but some secondary magmatic segment boundaries also occur at small, fourth‐order ridge axis discontinuities. The secondary magmatic segments define the length scale of mantle melting variations, mainly variations in extent of melting, but not the scale of melt extraction processes that feed the axis. This scale must be smaller than that of the secondary magmatic segments and probably corresponds to the length scale of fourth‐order physical discontinuities along axis. There is a good positive correlation of average secondary magmatic segment length with spreading rate for four well‐sampled areas varying from 20 to 150 mm/yr. Secondary magmatic segments also become more variable in axial length with increasing spreading rate. The average lengths of secondary magmatic segments are smaller than those predicted by gravitational instability considerations at all spreading rates. Superposed on the axial magmatic segmentation are variations reflecting subaxial magmatic temperature, defined by extent of magmatic differentiation, which bears little systematic relation to physical or other kinds of magmatic segmentation. At 13°–23°S, the length scale of this variation is 217±60 (1σ) km, approximately corresponding to the wavelength of “rolls” in the gravity field observed off‐axis. Taken together, the various kinds and scales of magmatic variations observed for this superfast spreading ridge suggest that regional temperature of the upwelling asthenosphere, magma supply to the axis, and crustal magmatic temperature reflect independent, regionally decoupled processes.

Optimization of the Smagorinsky Model with Variable CS.

The Smagorinsky model is the most popular and useful subgrid-scale (SGS) model of the large eddy simulation (LES). In previous studies of the LES, the Smagorinsky model with the constant coefficient Cs has been applied to several flow fields. Because there are various scales of turbulence, it is difficult to describe the engineering-type flow fields by using a constant Smagorinsky coefficient. Recently, improvement of the SGS model was made by considering Cs in the Smagorinsky model as the nonconstant coefficient. The SGS length scale variation was studied by Yoshizawa, and the form of variable Cs was presented from a statistical analysis. In this paper, this SGS model was optimized in both the decay of isotropic turbulence and the plane channel flow turbulence simultaneously, and an attempt to construct the new SGS model as the more universal Smagorinsky model was mode.

Heating of astrophysical plasma by mildly-relativistic non-thermal protons

We study the energy deposited collisionally by mildly-relativistic, non-thermal protons as they travel away from a spatially localised acceleration region. In particular, we generalise previous results for energy deposition by monodirectional protons in a medium of homogeneous magnetic field, to the case where the protons have a range of pitch angles and traverse a region of spatially varying magnetic field (field strength variation length scale ≫ gyroradius). The possibility of multiple traversals of protons in a region contained between two regions of field strengthening is also considered. By way of illustration, the results are applied to proton energy deposition in the solar atmosphere.

Some measurements of turbulence over an antarctic ice shelf

AbstractProfiles of wind speed, temperature and turbulent fluxes of heat and momentum in the lowest 32 m have been measured at a station on an antarctic ice shelf. During the antarctic winter the surface layer often shows strong static stability, with temperature gradients as large as 1 Km−1 in the lowest few metres. the surface inversion is destroyed during periods of high wind speed but the wind profile shows significant deviation from the expected logarithmic form under such conditions. Measurements of stress at 5 m indicate that the roughness length of the snow surface is about lO−4 m.At 5 m height, the variations of the dimensionless wind shear, ϕm, and potential temperature gradient, ϕT, agree with previously determined forms of the Monin‐Obukhov similarity functions. Above 5 m, the behaviour of ϕm and ϕT is only qualitatively similar and surface‐layer similarity theory does not provide a good description of the profiles.Turbulence length scales have been deduced from vertical velocity power spectra. Under near‐neutral conditions, the ratio of turbulence length scale to measurement height is observed to decrease with increasing height of measurement. This observation is consistent with the variation of turbulence length scale with height implied by the measurements of ϕm. It is suggested that the stability of the overlying atmosphere restricts the depth of the turbulent boundary layer and hence the length scales of turbulence within this layer. Increasing stability causes a decrease of turbulence length scales at all levels.The ratios of turbulence kinetic energy to stress and temperature variance to heat flux are examined. Measurements are somewhat scattered, but the distribution of values varies little with height or stability. the form of the distribution suggests that large‐scale motions, possibly internal gravity waves, may be playing an important role in boundary‐layer processes.

Subgrid-scale modeling with a variable length scale

Length scale variation in subgrid-scale (SGS) modeling is studied using the results from a two-scale direct-interaction approximation. The length scale variation is generated by the advection of SGS eddies by grid-scale ones. This effect leads to the variation of a characteristic SGS length scale around the filter width in the Smagorinsky model. The present model shows that the usual Smagorinsky constant is not a universal constant in large eddy simulation of various types of turbulence.

On the scale of baroclinic instability in deep, compressible atmospheres

A simple model of linearized, inviscid baroclinic instability in an adiabatic, hydrostatic, compressible atmosphere of arbitrary (though finite) depth, based on the well-known Eady model, is used to investigate the variation of growth rates and favoured horizontal length scales as functions of δ, the ratio of the model depth D to the density scale height Hs. Both geometric height coordinates (with w = 0 horizontal boundary conditions) and log-pressure (with ω = 0 boundary conditions) are considered. For δ > 3 and a given zonal velocity scale, growth rates are significantly reduced relative to comparable instabilities in an incompressible fluid (δ = 0), and may be suppressed altogether in a laterally-bounded channel for large enough δ at a given value of static stability. Where instability does occur, the length scales favoured are longer than for an incompressible fluid, and are generally comparable to a deformation radius based on D (rather than Hs). The relationship between these results and those obtained in comparable recent studies (which have found scales comparable to a deformation radius based on Hs to be important) is examined. Some implications for the role of baroclinic instability in the atmospheres of the major planets are also discussed.

On the scale of baroclinic instability in deep, compressible atmospheres

AbstractA simple model of linearized, inviscid baroclinic instability in an adiabatic, hydrostatic, compressible atmosphere of arbitrary (though finite) depth, based on the well‐known Eady model, is used to investigate the variation of growth rates and favoured horizontal length scales as functions of δ, the ratio of the model depth D to the density scale height Hs. Both geometric height coordinates (with w = 0 horizontal boundary conditions) and log‐pressure (with ω = 0 boundary conditions) are considered. For δ > 3 and a given zonal velocity scale, growth rates are significantly reduced relative to comparable instabilities in an incompressible fluid (δ = 0), and may be suppressed altogether in a laterally‐bounded channel for large enough δ at a given value of static stability. Where instability does occur, the length scales favoured are longer than for an incompressible fluid, and are generally comparable to a deformation radius based on D (rather than Hs). The relationship between these results and those obtained in comparable recent studies (which have found scales comparable to a deformation radius based on Hs to be important) is examined. Some implications for the role of baroclinic instability in the atmospheres of the major planets are also discussed.

Observations of boundary layer structure made during the 1981 KONTUR experiment

AbstractData collected by two aircraft over the German Bight during the 1981 KONTUR experiment are described. Turbulence data were obtained throughout the depth of the mixed layer in near‐neutral to slightly convective conditions. Similarity theory generally orders the data well and shows the effect of stability on turbulence structure under these conditions. The humidity flux profile, however, is found to depend on conditions at the top of the mixed layer.Spectral analysis is used to investigate the variation of turbulence length scales with height and the mixed layer eddy structure. Differences in spectra from alongwind and acrosswind sampling directions are found, particularly near the surface. Spectra of the transverse wind component show that two‐dimensional roll circulations were generally present in the mixed layer and became more pronounced with increasing instability.

Interaction between freestream turbulence and vortex shedding for a single tube in cross-flow

The effect of freestream turbulence on the flow past a circular cylinder (tube) was studied experimentally for Reynolds numbers between 2 × 10 4 and 6 × 10 4 . Investigations were carried out for uniform (non-turbulent) flow and for turbulent flows having turbulence intensities between 1.3 and 4.1%. The variations in the pressure forces and shedding frequencies were found to be related to the variations in different length scales in the near-wake region.

Scalar length scale variations in premixed turbulent flames

A general formulation and closure of a two-point two-time covariance balance equation is applied to the problem of calculating scalar length scale variations in premixed turbulent flames. Situations are considered in which the turbulent combustion zone consists either of a single thin wrinkled flame or of packets of reactants and products separated from each other by thin flames. The objective of the present work is to investigate the variation with location within the turbulent flame of characteristic dimensions of these packets or flame wrinkles. A normal or oblique planar flame configuration is considered. A similar formulation has previously been applied to calculation of time scales in premixed turbulent flames. Predicted packet passage time pdf's, autocovariances, mean packet time variations and power spectral densities all show satisfactory agreement with experimental data. However, the predicted time scales do not provide much information about the shape and size of the burning packets or wrinkles. The present paper includes predictions for both normal and transverse scales of these packets or wrinkles. It is found that the normal and transverse dimensions vary with position in different ways, resulting in an anisotropy of the scalar field. Insufficient experimental data has been found to permit a quantitative comparison with these predictions. However, where a qualitative comparison is possible, this lends support to the results of the analysis.

The rupture process and asperity distribution of three great earthquakes from long-period diffracted P-waves

Maximum earthquake size varies considerably amongst the subduction zones. This has been interpreted as a variation in the seismic coupling, which is presumably related to the mechanical conditions of the fault zone. The rupture process of a great earthquake indicates the distribution of strong (asperities) and weak regions of the fault. The rupture process of three great earthquakes (1963 Kurile Islands, M W = 8.5; 1965 Rat Islands, M W = 8.7; 1964 Alaska, M W = 9.2) are studied by using WWSSN stations in the core shadow zone. Diffraction around the core attenuates the P-wave amplitudes such that on-scale long-period P-waves are recorded. There are striking differences between the seismograms of the great earthquakes; the Alaskan earthquake has the largest amplitude and a very long-period nature, while the Kurile Islands earthquake appears to be a sequence of magnitude 7.5 events. The source time functions are deconvolved from the observed records. The Kurile Islands rupture process is characterized by the breaking of asperities with a length scale of 40–60 km, and for the Alaskan earthquake the dominant length scale in the epicentral region is 140–200 km. The variation of length scale and M W suggests that larger asperities cause larger earthquakes. The source time function of the 1979 Colombia earthquake ( M W = 8.3) is also deconvolved. This earthquake is characterized by a single asperity of length scale 100–120 km, which is consistent with the above pattern, as the Colombia subduction zone was previously ruptured by a great ( M W = 8.8) earthquake in 1906. The main result is that maximum earthquake size is related to the asperity distribution on the fault. The subduction zones with the largest earthquakes have very large asperities (e.g. the Alaskan earthquake), while the zones with the smaller great earthquakes (e.g. Kurile Islands) have smaller scattered asperities.

A parameterized model for the evolution of isotopic heterogeneities in a convecting system

Laboratory experiments are used to illustrate how steady convective flows, while efficient at stirring an initial heterogeneity within a single cell, do not produce dispersal of heterogeneous material over scales large compared to the depth. Long-range dispersal requires that the flow be time dependent on a time scale comparable to the overturn time. Convection in an internally heated layer has this property and numerical solutions are used to study the way in which it disperses a set of neutrally buoyant particles that were initially confined to a small space. The horizontal dispersal of these particles is reasonably well represented by an effective diffusivity of 0.3 cm 2/s for a Rayleigh number of 10 6. The concept of an effective diffusivity is then applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems with spatial variations generated by horizontal variations in degree of melting 1.8×10 9 years ago. The present-day average ε value one would measure in such a system depends on the average degree of melting, the amplitude and length scale of variations in partial melt, and the effective diffusivity assumed. Especially in the case of Nd the differences in average ε value between a uniform and a spatially variable (but with the same average) melting case can be significant. The range of ε values about the average is controlled by the competing effects of generation by the differences in enrichment factor and decay due to the effective diffusivity.

Some effects due to variations in turbulence integral length scales on the pressure distribution on wind-tunnel models of low-rise buildings

The work described here consists of results from wind-tunnel tests on models of the Building Research Establishment's experimental building at Aylesbury. The use of several scale models of this building in uniform and in simulated atmospheric boundary-layer flows together with the results from the full-scale experiments allowed an assessment of the effect of variations in the ratio of the longitudinal-turbulence integral length scale to body dimension ( L x / D). This confirmed that the values of L x / D have to be modelled correctly even in a non-homogeneous, non-isotropic turbulent flow in order to obtain model results that are representative of the full-scale situation. The present results also appear to confirm explanations given for similar results for homogeneous, isotropic turbulent flows.

Scattering from volume variability

Acoustic scattering cross sections for medium fluctuations are derived from the funadmental wave equation. Analysis of the effect of a finite scattering volume is made. Fluid velocity fluctuations are shown to produce no backscatter at scattering angle θ = 180° independent of the statistical form of the velocity field and valid for both atomspheric and oceanic cases. Scattering cross sections for the atmospheric and oceanic cases are compared. Temperature fluctuations for the atmospheric case result in a scattering cross section proportional to a cos2 θ factor whereas for the oceanic case no such factor arises. Using a cylindrically symmetric form about the vertical direction for temperature fluctuations, explicit expressions for the angular dependence of the scattering cross sections are obtained. These results depend strongly on the parameter α, the ratio of the vertical length scale of the temperature variability to the horizontal length scale. For a typical echo sounder operating at 20 kHz, scattering strengths based on observed one dimensional spectra of temperature microstructure are of order −120 dB if isotropy is assumed (α = 1). For the layered case, where the horizontal scale of the variability is larger than the horizontal dimension of the scattering volume, the same values of variability yield, scattering strengths are of order −70 dB. These results can be applied at other frequencies provided the medium variability spectrum is known.

MATH]-TEXTURE EFFECTS ON MAGNETIC RESONANCE IN SUPERFLUID 3He

We calculate the effects on the satellite frequencies in NMR due to the changes in spatial variation length scale of the [MATH] vector.

Impinging Circular Turbulent Jets

The normal impingement of turbulent circular jets on smooth walls is studied both experimentally and analytically. This type of flow can be divided into three distinct flow regions: the free-jet region; the impingement region; and the wall-jet region. The impingement region is the most important. It is shown that the impingement region occupies about 14% of the impingement height above the wall, whereas it extends about 22% of the impingement height radially. Semi-empirical methods to predict axail variations of velocity and static pressure are developed. Similarity of velocity and static pressure profiles is investigated and it is shown that these profiles are well described by the Gaussian error function. Variation of pertinent length scales are obtained empirically using dimensional analysis so that the time-averaged velocity and pressure fields in the impingement region can be predicted. A method to predict the wall shear stress in the impingement region is developed.

Gene flow and selection in a cline.

A model of the effect of gene flow and natural selection in a continuously distributed, infinite population is developed. Different patterns of spatial variation in selective pressures are considered, including a step change in the environment, a "pocket" in the environment and a periodically varying environment. Also, the problem of the effect of a geographic barrier to dispersal is analyzed. The results are: (1) there is a characteristic length scale of variation of gene frequencies, (see PDF). The population cannot respond to changes in environmental conditions which occur over a distance less than the characteristic length. The result does not depend either on the pattern of variation in selective pressures or on the exact shape of the dispersal function. (2) The reduction in the fitness of the heterozygote causes a cline in gene frequencies to become steeper. (3) A geographic barrier to dispersal causes a drastic change in the gene frequencies at the barrier only when almost all of the individuals trying to cross the barrier are stopped.

Hydrodynamic equations for plasmas in strong magnetic fields - I: Collisionless approximation

A system of hydrodynamic equations for the description of a collisionless plasma is derived. The equations for motion perpendicular to the magnetic field are an extension of those of CHEW et al. (1956). Hydrodynamic description of motion along the magnetic field is possible if v||t0/L|| is a small parameter (v|| is the thermal velocity parallel to the magnetic field, t0 the characteristic time, L|| the characteristic length scale for variation of macroscopic quantities along the magnetic field). The method of deriving the hydrodynamic equations is an extension of a method used by GRAD (1949). This extension is necessary because in collisionless plasma thermal energy is not equally distributed over all degrees of freedom. Therefore one has to consider two heat-flux vectors for the transport in thermal energy of parallel and perpendicular degrees of freedom separately. These independent heat-flux vectors are caused by gradients of the parallel and perpendicular temperature respectively. Thus one arrives at a system of equations for 16 moments of the distribution function.