Simple Power Law Relationship Research Articles

A new type of overshoot phenomenon in wind wave development and its implication in remote sensing of the ocean

Laboratory measurements using both wave probes (contact and optical) and radar confirm the existence of a new type of overshoot phenomenon in the wind‐wave development processes. This type of overshoot which occurs at gravity‐capillary wavelengths is practically a function of local wind stress only. It is named the overshoot phenomenon of the third kind. With the existence of this overshoot it becomes obvious that the past assumed simple power law relationship between the rms value of surface slope at a fixed wavelength and the wind stress is untenable. Since such a relationship is one of the key assumptions invoked in the development of algorithms used to date in scatterometry, we have reexamined the published scatterometer data and pointed out the implications of this overshoot phenomenon. Recommendations for improvement of the performance of the scatterometer are also made in light of our new understanding of the wind‐wave development processes.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

Solar, geomagnetic and long term effects on thermospheric neutral kinetic temperatures at midlatitude

Measurements of midlatitude thermospheric neutral kinetic temperatures obtained from 1972 to 1979 have been used to investigate the effects of solar and geomagnetic activity, as well as long term effects, on the thermosphere. With these data a simple power law relationship between the temperature and solar activity (expressed as the 2.8 GHz solar radio flux) has been found to give a high correlation. In addition, a linear relationship between temperature changes and geomagnetic activity (expressed as Ap), as well as annual and semiannual effects have been found. The annual variation is found to be indistinguishable in phase from the annual variation of the solar declination angle. The present four parameter formulation gives a better fit to the data than is obtained with available empirical models of the thermosphere, and this has allowed us to investigate the properties and postulates of some of these models.

Fracture surface features of polyethylene pipe samples

AbstractSlow crack growth behavior of medium‐density polyethylene pipe samples has been investigated by applying standard and nonstandard fracture mechanics test methods. Slow crack growth rate varied by several orders of magnitude among the PE2306 materials from different manufacturers. Slow crack generated surfaces exhibit fibrous textures of varying degrees of coarseness when examined under the scanning electron microscope. When the measured fiber heights, δ/2, of these samples were plotted against the applied stress intensity factor, KI, they showed a simple power law relationship (of exponent 2). Assuming that the pulled‐out fibers transmit almost uniform tensile stresses across the crazed zone at the crack front, the Dugdale‐Barenblatt model was introduced to predict the fiber height. Although the model needs further modification, it provides a general power law relationship between the fiber height and the applied stress intensity factor.

Mid‐latitude thermospheric neutral kinetic temperatures, 1. Solar, geomagnetic, and long‐term effects

The effects of solar activity and geomagnetic activity on the nighttime mid‐latitude thermosphere kinetic temperatures have been investigated by using measurements obtained from 1972 through 1979. This study has been made by using the kinetic neutral temperatures obtained from the Doppler widths of the [O I] 15867K (630 nm) emission at Fritz Peak Observatory, Colorado (39.87°N, 105.5°W). During the time span of the measurements solar activity, expressed as the 2.8‐GHz solar radio flux, varied nearly five‐fold, while the corresponding thermospheric temperature almost doubled. With these data a single variable simple power law relationship gives a high correlation with the temperature. A linear relationship between temperature changes and geomagnetic activity, expressed by the index Ap, has also been found. The residuals from the data and these relations show strong annual and semiannual components, with the former undistinguishable in phase with the annual variation of the solar declination angle. A comparison of these results with empirical models shows that most of the presently available empirical models do not adequately represent the observed dependence of temperature on solar activity, in particular during times of high solar activity. It is also found that on the basis of four parameters, namely solar activity, solar declination, geomagnetic activity, and a semiannual variation (and its associated phase), it is possible to obtain a better fit for our data than with the available empirical models.

SOME SUSPENDED SEDIMENT YIELDS FROM SOUTH ISLAND CATCHMENTS, NEW ZEALAND1

ABSTRACT: Estimates of specific annual suspended sediment yields, some of which rank among the highest reported in the world, are presented for 33 basins of South Island, New Zealand. Yield from each basin was determined by combining a suspended sediment concentration rating with the complete flow record of each catchment stream gaging station. A multiple regression analysis between sediment yields and climatic, hydrologic and physiographic parameters of each basin demonstrates that most of the variance in yields is explained by catchment mean rainfall. Geology apparently has little influence on sediment yield as suspended sediment concentration ratings, from rivers draining catchments of differing lithology, and regolith, are indistinguishable. Specific suspended sediment yield prediction equations are given for four defined regions covering in area almost all South Island; and except for one area, feature rainfall as the principle independent variable. Differences between regions may be due to variations in intensity, frequency, and duration patterns of storms. It is proposed that a simple power law relationship between yield and rainfall provides useful suspended sediment yield estimates in mountainous regions of temperate maritime climate, provided catchments have not been modified extensively by man.

On the temporal coherence loss of strongly scintillating signals

In this paper, we have reprocessed a set of previously published intensity coherence time data to correct for wave front curvature. The spherical wave correction decreases the coherence time for a simple plane wave. Under conditions of strong scatter, theory predicts a simple power law relationship between the intensity coherence time and the phase turbulent strength. In the theory the power law index is simply related to the phase spectral index, which is usually assumed to be constant. Previously, this theory had been applied to test the consistency of the results. Evidence has recently come to light, however, that both the phase and in situ spectral indices vary systematically with changing perturbation strength. By accommodating this variation as well as the wave front curvature correction, we were able to greatly improve the theoretical fit to the intensity coherence time data.

High sediment yields from major rivers of the western Southern Alps, New Zealand (reply)

Suspended sediment yields have been determined by combining suspended sediment rating relationships with water flow records for gauged rivers of South Island, New Zealand. Rivers draining the Western Southern Alps have specific annual yields about 10 times higher than world average rates for mountainous areas. Their short steep catchments, rising in elevation from near sea level to over 3,000 m, support dense unmodified podocarp hardwood and beech forests below 1,000 m. The drainage basins are virtually undisturbed. A simple positive power law relationship between specific annual suspended sediment yields and the extremely high mean annual rainfalls explains almost all the variance in yield for catchments of the western region. This simple law may also hold for undisturbed catchments having a temperate maritime climate, in other areas of the world.

Frictional Effects in Fibrous Assemblies

It is shown that the initial load-deformation behavior of a wide range of fibrous assemblies, in which the forces are transmitted via a large number of frictional interactions, can be described by a simple power law relationship. The relationship was explored in detail for a polyester felt deformed in shear, and was used to make estimates of the number of fiber-to-fiber contacts and the interfiber contact forces in the assembly. The calculated values of these parameters were in reasonable agreement with direct measurements made by independent techniques.

Velocity and heat transfer measurements in thermal convection

Measurements were taken of the heat transport and vertical component of the fluid velocity in a horizontal layer of water heated from below. The heat transfer results were well correlated by a simple power law relationship and indicated the possibility of flow transitions even at relatively high Rayleigh numbers. The velocity measurements were obtained optically and compared to predictions of Kraichnan.

Motion of a turbulent buoyant thermal in a calm stably stratified atmosphere

A simple model for the motion of a turbulent buoyant thermal in a calm, stably stratified atmosphere is proposed. Using this model, the average motion of the thermal can be described in terms of its initial density difference, velocity and effective radius, and the three nondimensional gross parameters: mass entrainment constant, effective drag coefficient, and turbulence dissipation rate. Relations between the local turbulence field and the three gross parameters are discussed. Also, the maximum height a thermal can reach in a stable atmosphere for various initial conditions and gross parameters can be approximated by a simple power law relation.

Studies of plasma production at hypervelocity microparticle impact

This paper is concerned with an investigation of the plasma generated during the impact of hypervelocity microparticles with a metal target. A laboratory source of hypervelocity micron-sized iron particles is first described which utilizes a 2 MV Van de Graaff generator, followed by a discussion of the techniques used to determine the mass and velocity of the particles. On impact of the iron projectiles on a slatted molybdenum target, charge is generated, extracted from the region of impact by suitably biasing a gridded electrode, and subsequently detected using a conventional wideband electronic amplifier or an electron multiplier. It is shown statistically that during impact equal numbers of electrons and positive ions are produced - indicating plasma generation - and that the total charge released (Q) may be described empirically in terms of the mass (m) and velocity (v) of the particle by a simple power law relationship of the kind Qαmαvβ, with β = 3·2 ± 0·1 over the complete velocity range investigated (0·05 to 10 km s−1) and with α = 0·85 for v>1 km s−1 and 1·33 for v<1 km s−1. It is also shown that the charge extracted from the plasma reaches a maximum a few microseconds after impact and subsequently decays exponentially with a time constant of several micro-seconds.A crude mass analysis of the positive ions generated during the impact using a simple time-of-flight mass spectrometer has indicated that, over the velocity range investigated, the dominant ions in the spectrum are characteristic of the projectile and not the target material. From considerations of the relative abundance of the metal ions in the spectra, together with the known relative metal atom concentrations in the iron projectiles, the temperatures of the plasmas have been estimated (from Saha equilibrium considerations) to be of the order of several thousands of degrees Kelvin.In a detailed discussion, attempts are made to consider how the kinetic energy of the projectile is dissipated - eventually producing plasma - in terms of available theoretical models of hypervelocity impact. It is shown that the most satisfactory model of this very complex interaction appears to be one in which the relative importance of shock-wave propagation into the projectile and target materials is considered. Finally, a discussion of the properties and the temporal behaviour of the impact-produced plasma is presented in order to assess the relative importance of diffusion and recombination processes, thus to assist in the interpretation of the experimental results obtained in this study.

Concentration fluctuations and peak-to-mean concentration ratios in plumes from a ground-level continuous point source

Diffusion data collected by 63 incremental samplers during four short duration, continuous releases of 85Kr are used to examine concentration fluctuations and peak-to-mean concentration ratios in the atmosphere. Cumulative frequency distributions and the intensity of short-term concentrations are shown to be a function of the relative crosswind position within the mean plume. Peak-to-mean concentration ratios are shown as a function of relative crosswind position within the plume and the ratio of the durations of the mean and the peak (time ratio). The relationship between the intensity of concentration fluctuations and the relative crosswind position is similar to that reported for laboratory data. The relationship between peak-to-mean ratios and the time-ratio was found to differ from the simple power law relationship suggested by several workers. Previous estimates of the peak-to-mean/time ratio relationship for positions near the mean plume axis are shown to be too low.

A self-consistent polycrystalline model for creep under combined stress states

The application of the self-consistent polycrystalline model of inelastic deformation has been extended to include time-dependent (i.e. creep) behavior. Comparison of the predictions of a simple power-law micro-constitutive relation in the model with experiments suggests that an appreciable amount of the observed dependence of behavior on prior history of combined stressing can be explained by grain interaction effects. The existence of a flow potential for the self-consistent polycrystalline model is demonstrated, and flow potential surfaces, calculated from a simple power-law micro-constitutive relation, are shown for several cases of combined tension-torsion deformation. To a good approximation these surfaces exhibit a kinematic translation in stress space with prior deformation history.

Brightness-luminance relationships in an interior

Some four thousand numerical estimates of the brightness of the various objects, room surfaces and sources in a particular interior, under different lighting conditions, have been made by thirty-six observers. Details of this experiment are given in this paper, the precision of brightness measurement is discussed and the resulting irregular brightness-luminance relationships are presented. These results are examined together with those of related brightness studies and a pair of simple power-law relationships are put forward which are considered adequate approximations for interior lighting design purposes.

SPACED RESPONDING AND CHOICE: A PRELIMINARY ANALYSIS1

Pigeons were exposed to reinforcement both for short (2 < IRT < 3 sec) and long (10 < IRT < 11 sec) interresponse times. They developed bimodal interresponse-time distributions, which were decomposable into two independent component distributions under the control of the short and long contingencies respectively. The birds' allocation of responses between these two distributions was determined by a simple power-law relationship between reinforcement ratios, and response ratios derived from the component distributions. Comparison between this situation and concurrent choice situations raises the possibility that the power-law relation between ratios may be a more general law of choice than the matching of relative frequencies (probabilities).

Wind Shear for Small Thickness Layers

Wind shear in the lowest 10,000 it of the atmosphere was investigated utilizing two or more cinetheodolites (Contraves cameras) tracking a smooth spherical 100-gm balloon. These data indicate that a simple power law relationship exists between 1) layer thickness and the magnitude of the vector shear, 2) layer thickness and the magnitude of the mean extreme vector shell, and 3) magnitude of the mean shear and standard deviation for given layers. From this relationship it appear that wind shears for small layers (50, 100, 200 ft) may be derived from wind values obtained over large shear intervals (1000, 2000, 3000 ft) with present operational equipment such as the GMD-1. A relationship exists between wind speed and wind shear for various shear intervals such that as the wind speed increases to 30–40 ft sec−1, the mean shear increases; the shear decreases for higher wind speeds.

On a singular point in the Newtonian theory of hypersonic flow

An examination of the Newtonian inviscid theory of hypersonic flow past a sphere is made in the neighbourhood of the singular point which occurs at θ = 60°. A uniformly valid theory is developed in this neighbourhood which exhibits the limiting detached ‘free-layer’ behaviour postulated by Hayes and Lighthill in the limit as γ → 1. A complete solution is obtained which gives details of streamline and shock wave shape, pressure distribution, etc. for γ − 1 small.Reasons are given why the empirical ‘modified’ Newtonian theory of Lees proves to be a good approximation to experimentally determined pressure distributions.A novel check to the theory is provided by a simple power-law relation between the pressure on the sphere surface and the distance of the shock wave away from sphere at the same point.