Hemispherical Bosses Research Articles

The vertebrate fauna of the Upper Permian of Niger—VII. Cranial anatomy and relationships of Bunostegos akokanensis (Pareiasauria)

ABSTRACT We describe newly recovered cranial material of Bunostegos akokanensis, a pareiasaurian reptile known from the Upper Permian Moradi Formation of northern Niger. Bunostegos is highly autapomorphic, with diagnostic cranial features including two or three hemispherical bosses located above and between the external nares; laterally projecting supraorbital ‘horn’ formed by an enlarged postfrontal; large foramen present on ventral surface of postfrontal; and hemispherical supratemporal boss located at posterolateral corner of skull roof. We addressed the phylogenetic position of Bunostegos by incorporating it into a cladistic analysis of 29 parareptilian taxa (including all 21 currently valid pareiasaurs) and 127 cranial and postcranial characters. The results of this analysis place Bunostegos as more derived than middle Permian forms such as Bradysaurus and as the sister taxon to the clade including Deltavjatia plus Velosauria. Certain characters, such as the pattern of cranial ornamentation and the size and placement of the tabulars, appear to be more similar to more derived pareiasaurs such as Elginia from Scotland and Arganaceras from Morocco, but the most parsimonious tree topology indicates that these features were evolved independently in the Nigerien form. The lack of both dicynodont herbivores and Glossopteris, combined with the presence of a giant herbivorous captorhinid, indicates a markedly different community structure in the Permian of Niger compared with those for contemporaneous southern Pangean basins (i.e., Karoo, Luangwa, Ruhuhu). The endemic tetrapod fauna of Niger supports the theory that central Pangea was biogeographically isolated from the rest of the supercontinent by desert-like conditions during Late Permian times. SUPPLEMENTAL DATA—Supplemental materials are available for this article for free at www.tandfonline.com/UJVP

Scattering from a Metamaterial Hemispherical Boss on an Infinite Plane

An exact solution is presented to the problem of scattering of a plane electromagnetic wave from a metamate- rial hemispherical boss located on an infinite conducting plane, using the method separation of variables. The formulation is based on an image technique, where the original problem is replaced by that of scattering of two plane waves by the corresponding sphere in the absence of the infinite plane. The solution is obtained by expressing all the electromagnetic fields associated with the problem in terms of vector spherical wave functions, and then imposing the appropriate bound- ary conditions. Numerical results are presented as normalized backscattering cross sections for hemispherical bosses of different sizes and types, for both transverse electric and transverse magnetic polarizations of the incident wave.

Modeling scattering from azimuthally symmetric bathymetric features using wavefield superposition

In this paper, an approach for modeling the scattering from azimuthally symmetric bathymetric features is described. These features are useful models for small mounds and indentations on the seafloor at high frequencies and seamounts, shoals, and basins at low frequencies. A bathymetric feature can be considered as a compact closed region, with the same sound speed and density as one of the surrounding media. Using this approach, a number of numerical methods appropriate for a partially buried target or facet problem can be applied. This paper considers the use of wavefield superposition and because of the azimuthal symmetry, the three-dimensional solution to the scattering problem can be expressed as a Fourier sum of solutions to a set of two-dimensional scattering problems. In the case where the surrounding two half spaces have only a density contrast, a semianalytic coupled mode solution is derived. This provides a benchmark solution to scattering from a class of penetrable hemispherical bosses or indentations. The details and problems of the numerical implementation of the wavefield superposition method are described. Example computations using the method for a simple scattering feature on a seabed are presented for a wide band of frequencies.

Scattering and absorption of electromagnetic waves on a plane with hemispherical bosses

AbstractWe apply multiple scattering equations to study the scattering of electromagnetic waves on a perfectly conducting plane surface with a random dense distribution of hemispherical bosses. We derive a multipole solution up to third order to analyze close range interactions between nearby bosses. Results show significant improvement of accuracy compared with the traditional dipole approximation solution. Absorption on a lossy embossed surface is obtained from the field solution for the perfectly conducting surface. The surface current and absorption enhancement factor are further computed numerically. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2681–2686, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22855

Room acoustics auralization studies of laterally incident boss-model scattering

Computation of room impulse responses by commercial auralization programs typically employs simplified Lambert models to account for nonspecular scattering. However, Lambert scattering models, developed primarily for diffuse lighting computation, have limited validity in acoustics. Instead, in this study, surface scattering from hemispherical bosses on walls is computed with numerical models based on exact classical solutions. Scattering impulse responses for auralization are calculated with various configurations of bosses on infinite planes on both sides of a binaural receiver (approximately 7–10 m away). The physical sound field is analyzed along with the resulting subjective effects of varying boss size and scatterer density.

On the averaged electric fields near perfectly conducting and insulating rough boundaries

Roughness modelled as small objects scattered upon conducting or insulating surfaces is discussed. Using the image technique to remove the supporting surface, the polarisability of the individual objects as well as their concentration on the surface are linked with an effective surface displacement. Conditions for the averaged field over the displaced surface are derived and physical interpretations of the terms involved are provided. The closest neighbour interaction is taken into account in the case of hemispherical bosses using image reflections in spheres. To elucidate the impact of roughness, solutions of some basic electrostatic problems, namely the roughened parallel-plate capacitor and a point source facing a planar conducting or insulating rough surface, are examined in some detail. Special attention is paid to image singularities responsible for the field reflected by a rough boundary.

Multiple scattering of a plane electromagnetic wave by hemispherical bosses on an infinite plane

An analytic solution to the problem of scattering of a plane electromagnetic wave by a system of hemispherical bosses on a perfectly conducting ground plane is obtained using the solution of scattering by a system of full spheres and the method of images. The system considered is replaced by a system of complete spheres in the absence of the ground plane, but with the given incident plane wave and also a supplement, image plane wave, chosen such that the boundary conditions for the total field are satisfied at all points where the ground plane is located in the original problem. Numerical results for a different system of simulations are presented for the normalized backscattering cross section versus the angle of incidence.

Effective boundary conditions for the Laplace equation with a rough boundary

The problem of replacing Dirichlet or Neumann conditions on a stochastically embossed surface by approximate effective conditions on a smooth surface is studied for potential fields satisfying the Laplace equation. A combination of ensemble averaging and multiple-scattering techniques is used. It is shown that for the Dirichlet case the effective boundary condition becomes mixed and establishes a relation between the averaged field and its normal derivative. For the Neumann problem the normal derivative on the smooth surface equals a suitable combination of first- and second-order derivatives tangent to the surface. Explicit results are given for small boss concentration and illustrated with the examples of spheroidal and spherical bosses. For the Dirichlet case with hemispherical bosses, direct numerical-simulation results are presented up to area coverages of 75%. An application of the results to the calculation of the added mass of a rough sphere in potential flow, of the capacitance of a rough spherical conductor, and of the transmission and reflection of long water waves at a smooth-rough bottom transition aids in their physical interpretation.

Sound produced by turbulent boundary layer flow over a finite region of wall roughness, and over a forward facing step

An analysis is made of the sound produced during low Mach number turbulent flow over a roughened section of a nominally plane, rigid wall. The wall is roughened over a finite distance in the mean flow direction, and the roughness elements are modeled by a random distribution of hemispherical bosses. The individual bosses constitute surface inhomogeneities at which near field pressure fluctuations of the turbulence Reynolds stresses are diffracted into sound. Each boss is acoustically equivalent to a dipole source, and their collective radiation intensity is proportional to the sixth power of the mean flow velocity and the wetted area of the roughened section of the wall. Additional dipole sources of sound are located in the neighbourhoods of the boundaries of the roughened region. Experiment suggests that the strongest of these occur at the forward facing, smooth-torough transition, where the boundary layer is displaced outwards from the wall. The noise generated there is equivalent to that produced by the same turbulence convecting over a forward facing step of rounded profile, and is predicted to exceed that from the distributed dipoles provided the roughness is confined to a region of moderate extent in the flow direction. The sound produced by a rounded forward facing step is also compared with that from a discontinuous step of the same height in the hypothetical case in which the turbulence Reynolds stress sources are the same.

The turbulent boundary-layer rough-wall pressure spectrum at acoustic and subconvective wavenumbers

The rough-wall turbulent boundary-layer wall pressure spectrum differs from that on a smooth wall because the strengths of the turbulence Reynolds stresses responsible for the pressure fluctuations are increased by surface roughness, and because the near fields of those enhanced pressure sources are redistributed in wavenumber by diffraction by the roughness elements. In this paper, analyses are performed that indicate that, except at very low frequencies, the diffractive component dominates the spectrum in the low-wavenumber and acoustic domains. The diffraction calculations are performed exactly for a plane wall roughened by a distribution of rigid hemispherical bosses, and a comparison is made with corresponding predictions obtained when only the first non-trivial term is retained in an expansion of the rough-wall boundary condition about that for a plane wall. These calculations take no account of interstitial flows and possible wake formation by the roughness elements, and an empirical model of the spectrum is proposed to incorporate these effects and recommended for use in applications. The values of adjustable coefficients that enter the proposed formula are estimated by reference to published experimental data on the radiation of sound by a rough-wall boundary layer. Such data are incomplete, however, and further experiments need to be performed to validate the model.

An experimental study of the coherent under-ice reflectivity of sound in the Greenland Sea Marginal Ice Zone (MIZ)

The coherent component of acoustic under-ice reflectivity was investigated as a function of frequency and grazing angle in the MIZ. Measured reflectivity was compared with scattering theory predictions to test the hypothesis of ridge scattering dominance in the MIZ. Explosive source acoustic signals were received on a vertical array, during the Marginal Ice Zone Experiment (MIZEX 84), and deconvolved to separate the direct and ice-reflected arrivals. Ice-reflected signals received on individual hydrophones at different ranges and depths, and on different days, were aligned in time and coherently ensemble averaged within a moving 10-deg grazing angle window. The resulting reflectivity was found to decrease with increasing frequency from 64–256 Hz and with increasing grazing angle from 12–35 deg. Comparison was made with predictions from smooth elastic plate theory, perturbation theory for a rough pressure release surface, perturbation theory for a rough elastic surface, Twersky theory for hemispherical bosses on a plane, and Twersky theory for infinite, semielliptical cylinders on a plane. The Twersky theory for semielliptical cylinders gave a significantly better fit to the data than the other theories. This suggests that, although the under-ice topography may be a good deal more complicated, scattering may, nevertheless, be dominated by remnants of elongated pressure ridge keels. Remote sensing data, taken during the experiment, showed that the ice cover was primarily composed of small floes (< 200 m in diameter). Laser ice-surface height measurements were analyzed to obtain the pressure-ridge sail-height distribution. The Twersky theory modeling gave predictions within 1 dB of the measured mean reflectivity when a ridge keel-to-sail ratio of 6.5 was assumed.

The influence of viscous surface stress on the production of sound by turbulent boundary layer flow over a rough wall

A theory is proposed of the production of sound by turbulent boundary layer flow over a rough wall. Attention is confined to the case in which the roughness elements are embedded entirely within the viscous sublayer, and the radiation is determined by estimating the diffraction of the turbulence nearfield by those elements. The principal objective is to ascertain the influence of viscous wall stresses on the diffraction mechanism, the calculations being performed with and without account being taken of the “no slip” condition at the wall. The latter corresponds to a simplified version of the inviscid diffraction theory of Howe [1] in which a sand roughened wall is modeled by a distribution of rigid hemispherical bosses on a rigid plane. It is concluded that, over the whole frequency range in which “roughness noise” is expected to be important, the inviscid diffraction theory underestimates the radiated noise relative to that of the viscous theory by at most 2 or 3 dB.

A multibounce, single‐scatter ray theoretic model for underice predictions

This study describes the propagated and scattered acoustic field from a point source to a point receiver in an approximate underice environment characteristic of the deep Arctic Ocean. Our model considers both the azimuthal and vertical redistribution of scattered energy caused by a rough surface overlying an upwardly refracting, linear sound‐speed profile. The model considers one nonspecular surface scattering per path (connecting the source with the receiver) coupled with any number of specular interactions, each of which suffers losses due to scattering into nonspecular directions, i.e., consistent with conservation of energy. The propagation model is based on ray theory, while the scattering model uses Twersky's scattering cross section for hard or soft planar surfaces roughened by hard or soft, hemispherical bosses. The model calculates intensity as a function of position and direction. Bistatic results at all frequencies show that for hard and soft surfaces the strongest scattered field is produced directly above the submerged source, and that the total scattered energy levels increase as frequency increases. Monostatic geometries and effects of distributions of boss sizes will also be considered. [Work supported by NRL and ONR.]

An assessment of second-order perturbation theory for scattering of sound by hard, statistically rough surfaces

Perturbation theory and boss models for rough surface scattering are compared for the case of a surface bossed with oblate hemispheroids (height a≤radius b). In particular, the surface consists of identical, hard, hemispheroidal bosses sparsely and independently distributed on a hard plane by means of a uniform probability law. To apply perturbation theory we compute the surface correlation function, operate on that function, and compute an effective boundary admittance. Finally, we compare that admittance with (farfield) near-exact results for hemispherical bosses and for oblate hemispheroidal bosses. Calculations of the magnitude of the reflection coefficient ‖R‖ are presented showing that for low frequencies, i.e., kb=0.1, the discrepancy is approximately 70% for a=b but less than 10% for a/b=0.1. In general, the error decreases as grazing angle increases and decreases as a→0. Thus, at low frequencies perturbation theory is shown to give excellent results for ‖R‖ when a/b≪1, despite the discontinuous and infinite slope in the surface where the bosses meet the base plane. We also examine the effects of increasing frequency for hemispherically bossed surfaces, and in particular, we see errors as large as 3 dB for sparse, hemispherical bosses with a=b=5 m and frequencies less than 60 Hz. We conclude that perturbation theory is excellent in the case of oblate hemispheroids, shows significant percentage errors for hemispheres and should not be used for prolate hemispheroids.

On the long range propagation of sound over irregular terrain

The theory of sound propagation over randomly irregular, nominally plane terrain of finite impedance is discussed. The analysis is an extension of the theory of coherent scatter originally proposed by Biot [1] for an irregular rigid surface. It combines Biot's approach, wherein the surface irregularities are modeled by a homogeneous distribution of hemispherical bosses, with more conventional analyses in which the ground is modeled as a smooth plane of finite impedance. At sufficiently low frequencies it is shown that the interaction of the surface irregularities with the near field of a ground-based source leads to the production of “surface waves”, which are effective in penetrating the ground shadow zone predicted for a smooth surface of the same impedance.

On the generation of sound by turbulent boundary layer flow over a rough wall

The production of sound by scattering of the near field of low Mach number boundary-layer turbulence by a rough, rigid wall is examined on the basis of Lighthill’s theory ( Proc. R. Soc. Lond . A 211, 564 (1952)) of aerodynamic noise. The radiation is expressed in terms of the turbulence pressure spectrum on a control surface that is parallel to the mean plane of the wall and at a stand-off distance equal to the height of the wall roughness elements, the surface irregularities being modelled by a distribution of hemispherical bosses on an otherwise plane wall. The intensity of the sound produced by unit area of the wall varies as the sixth power of the main stream velocity and, for given wall roughness, increases as the boundary-layer thickness decreases. These conclusions are in accord with experimental observations reported by Hersh { AIAA paper no. 83-0786) of the generation of high frequency sound by turbulent flow from sand-roughened pipes, and it is shown how, for moderately rough pipes, the theory reproduces the spectral characteristics of Hersh’s data.

Dispersive propagation of grazing coherently scattered sound at a rough surface

Our purpose has been to learn about sound scatter from the ocean bottom by using laboratory models. Previously we have reported measurements of the amplitude of the grazing coherent sound scatter from slightly rough surfaces; we have verified that the cylindrically diverging scattered (boundary) wave amplitude can surpass the spherically diverging direct wave amplitude from a point source. This is true for both deterministically and randomly rough surfaces. Now we compare the dispersive propagation velocity v of these waves over surfaces constructed of rigid spherical and hemispherical bosses, and of rigid corrugations of half‐cylinders and wedges, with the free field speed c over the smooth surface. From Tolstoy [J. Acoust. Soc. Am. 72, 960–972 (1979)] one expects the dispersion to be (c − v)/c = 12e2k2 with maximum value 0.1% at kh = 1 for close‐packed rigid hemispherical bosses. There are similar expressions for other roughness elements, where e is the scattering parameter which depends on the shapes, ...

Acoustic Boundary Wave Generation and Shadowing at a Seamount

Abstract : The interaction of a sound field and a seamount has been studied by physically modeling the ocean surface over 2 dimensional and 3 dimensional models of Dickens Seamount. By using a smooth ocean surface, and one with a surface of scaled Rayleigh roughness to model a 35 knot wind, the relative contributions are determined for off-axis scattering elements, multiple reflection from the ocean surface, and diffraction over the crest of the seamount. Boundary wave generation over a randomly rough plane surface is studied experimentally. The ratio of boundary wave amplitude to volume wave amplitude is found to be proportional to (frequency) to the 3/2 power and (range) to the 1/2 power and the ratio of the empirical scattering parameter to the rms height of the roughness elements is found to be approximately 0.3. The spatial correlation length of the randomly rough surface takes the place of the center-to-center separation of the hemispherical bosses used in Tolstoy's theoretical treatment. (Author)

Coherent sound scatter from a rough interface between arbitrary fluids with particular reference to roughness element shapes and corrugated surfaces

The theory of Biot scatter, previously formulated for small hemispherical or almost hemispherical roughness elements on a hard wall or on an interface between fluids of differing densities ρ1≠ρ2 but same sound velocity c1 = c2, is here extended to more general cases ρ1≠ρ2, c1 = c2 involving spheroidal and cylindrical roughness elements. The conditions of smallness are, in terms of the spacing h and radii d of the roughness elements, kd<kh?1. Of special interest, in this and in previously studied cases, has been the prediction of a boundary wave associated with the roughness and traveling along the surface at slightly subsonic speeds, the existence and properties of which have been verified experimentally in the rigid wall case [H. Medwin et al., J. Acoust. Soc. Am. 66, 1131–1134 (1979)]. The theory is basically different from other approaches to rough surfaces scattering in that the emphasis is on nonstochastic models and, more importantly, in that it incorporates nearfield dipole interactions between steep-sided scatters as well as explicit diffraction effects. The procedure is to first establish the basic small scatterer approximations for any of shape, then to sum the contributions of planar distributions of such scatterers; this leads to a simple boundary condition, of first order in kd, applied to a plane z = const. Critical in this derivation are (1) the concept of virtual mass of the scatterer (Lighthill) and (2) a condition of imbeddedness which says that, in a system of coordinates moving with the fluid, a scatterer does not move normally to the interface. The latter condition ensures that the backscatter from a small hemispherical or hemicylindrical roughness element protruding into the half-space (ρ1,c1) is equivalent to that from a whole spheroid or cylinder in a full space (ρ1,c1). These generalized boundary conditions allow one to determine directly the conditions of existence and the amplitude of the boundary wave excited by a point source of sound on or near the rough interface. Of particular interest are: (a) The case of hemicylindrical corrugations where, for d/h?0.4, boundary wave amplitudes can be substantially larger than for hemispherical bosses, at least for directions of travel normal to the corrugations; in other directions the amplitude is multiplied by a factor cos2 ψ, where ψ is the angle between the horizontal wavenumber vector and the normal to the corrugation axes. (b) The sensitivity of the boundary mode to all parameters and, in particular, to ρ1/ρ2 and c1/c2. Calculation shows that, insofar as underwater sound experiments are concerned, the boundary mode is most likely to be observed near the ocean floor, rather than near the surface. But whereas the rough sediment–water interface can support a boundary wave, its existence and amplitude depend critically on the values of the above parameters. Pebbles or nodules scattered evenly on the ocean floor should provide the best conditions for observing this mode; conversely, measurement of boundary wave amplitudes could in principle be used to measure the mean density of nodules. As suggested elsewhere [I. Tolstoy, J. Acoust. Soc. Am. 69, 1290–1298 (1981)] this effect will be especially well marked under shadow zone conditions. It may also be relevant to other fields of acoustics, such as aeroacoustics or concert hall acoustics.

Boundary wave generation by coherent multiple scatter at a randomly rough rigid surface

In a series of papers starting in 1979 (J. Acoust. Soc. Am. 66, 1135–1144), I. Tolstoy has shown that the Biot boundary conditions for coherent scatter from a low roughness surface [J. Acoust. Soc. Am. 44, 1616–1622 (1968)] can be applied effectively to various deterministically rough interfaces such as hemispherical or ellipsoidal bosses between dissimilar fluids, or between a solid and a fluid. A boundary wave is predicted that is particularly strong at near grazing scatter provided that the low roughness criterion holds: ka < kh ⩽ 1, where a is the radius of the hemispherical bosses, h is the distance between them. Since it diverges cylindrically rather than spherically, the boundary wave can become stronger than a direct wave propagating over a smooth plane surface. Previously, this “Biot boundary wave” has been experimentally verified in the fluid over a rigid plane surface constructed of hemispherical scattering elements [H. Medwin et al., J. Acoust. Soc. Am. 66, 1131–1134 (1979)]. The Biot boundary...