Surface Wavenumber Spectrum Research Articles

Blocking oblique wave sound transmission through a multi-element barrier using alternate resonance tuning

Alternate Resonance Tuning (ART) utilizes a structural barrier subdivided into dynamic panel subsystems with different resonant behaviors. The underlying idea involves adjacent panel subsystems tuned differently to take advantage of the outofphase vibratory behavior, causing the 180° phase shift at different frequencies. In the intermediate range between the two resonance frequencies, the panels vibrate out of phase, leading to strong cancellation of the transmitted sound field. The method has been demonstrated analytically and experimentally for waves striking a barrier at normal incidence. The current work considers the effectiveness of ART to block the transmission of incident oblique waves, and considers both discrete frequencies and angles, and more realistic broadband random incidence fields. The research goal is to show that flexibility and controlled resonant behavior in subsystems can substantially block sound transmission, even for low structural damping. The subsystems alter the vibrating surface wavenumber spectra to reduce coupling between the structure and the acoustic field. Not only is the transmission of incident oblique waves reduced, but the transmitted and reflected waves radiate at a variety of angles due to the modification of the surface wavenumber spectrum. Applications include the development of lightweight flexible sound blocking barriers for vehicles and architectural spaces.

The GO4 Model in Near-Nadir Microwave Scattering From the Sea Surface

We introduce a practical and accurate model, referred to as “GO4,” to describe near-nadir microwave scattering from the sea surface, and at the same time, we address the issue of the filtered mean square slope (mss) conventionally used in the geometrical optics model. GO4 is a simple correction of this last model, taking into account the diffraction correction induced by the rough surface through what we call an effective mean square curvature (msc). We evaluate the effective msc as a function of the surface wavenumber spectrum and the radar frequency and show that GO4 reaches the same accuracy as the physical optics model in a wide range of incidence and frequency bands with the sole knowledge of the mss and msc parameters. The key point is that the mss entering in GO4 is not the filtered but the total slope. We provide estimation of the effective msc on the basis of classical sea spectrum models. We also evaluate the effective msc from near-nadir satellite data in various bands and show that it is consistent with model predictions. Non-Gaussian effects are discussed and shown to be incorporated in the effective msc. We give some applications of the method, namely, the estimation of the total sea surface mss and the recalibration of relative radar cross sections.

Airborne Observations of Fetch-Limited Waves in the Gulf of Tehuantepec

Abstract The authors present airborne observations of fetch-limited waves during strong offshore winds in the Gulf of Tehuantepec. The measurements, collected over a wide range of fetches, include one- and two-dimensional surface wavenumber spectra and turbulent fluxes in winds up to 25 m s−1. The evolution of the wave spectra is in good agreement with the fetch relationships from previous observations. The tails of the observed one-dimensional k1 spectra, in the dominant wave direction, exhibit a power law over a wide range of wavenumbers. The authors present the first quantification of the transition between the equilibrium and saturation ranges for the omnidirectional spectrum in the wavenumber domain. The energy density within the equilibrium range shows a dependence on the wave age. At wavenumbers higher than the spectral peak, the width of the spectrum in the direction orthogonal to the dominant waves is nearly independent of the wave age. However, in the azimuthal direction, the spreading of the spectrum decreases with increasing effective wave age. The bimodal directional distribution, characterized by the lobe amplitude and separation, shows a consistent scaling with both parameters collapsing when scaled by the square root of the wave age. The one-dimensional fetch-limited k1 spectrum is well parameterized with dependence on the effective fetch and friction velocity. At higher wavenumbers within the saturation range, although the one-dimensional saturation in the dominant wave direction is independent of the wind forcing, the saturation in the crosswind direction is weakly dependent on the effective wave age and on average 30% larger than that in the downwind direction. The results are discussed in the context of previous observations and current numerical wind-wave prediction models.

Innovative structural acoustic strategies to reduce sound transmission through lightweight flexible structures.

This paper describes research utilizing structural acoustics in novel ways to cancel the transmission of sound and vibration through multielement flexible barriers. Configurations analyzed include panels with different thickness and elastic modulus in different regions and layered structures connected by an elastic suspension. The purpose of the research is to demonstrate that flexibility and controlled resonant behavior can be used to block sound transmission even when structural damping is very low. Strategies are considered to alter vibrating surface wavenumber spectra to reduce coupling between the structure and the acoustic field. Another approach that can be employed is the utilization of structural wave cutoff with multielement multipath (MEMP) structures. Finally, multiple differentially tuned subsidiary elements acting as resonators can be used to greatly reduce the structural response. Examples of acoustic transmission loss through panel barriers using different strategies are presented, and the potential advantages and possible shortcomings of various approaches are evaluated. Possible configurations for layered sound reduction materials are proposed. The work has particular application to the reduction of vehicle interior noise and addresses the need for good acoustic performance of the lighter weight flexible structures that will be used in the future.

Validating physics-based clutter from seafloor roughness and biologic scattering

Two physics-based clutter models were developed for comparison and to study the merits and limitations of both approaches. The stochastic approach [Newhall and Arvelo, J. Acoust. Soc. Am. 118, 2041 (2005)] makes use of perturbation theory, to relate the mean seafloor scattering strength to the mean surface wavenumber spectrum, and the extrapolation of this spectrum to the Bragg wavenumber to generate the clutter distribution from the seafloor roughness. The semi-deterministic approach [Monjo and Arvelo, J. Acoust. Soc. Am. 118, 2041 (2005)] is based on 2-D power-law fractal realizations of the ocean floor, coherent modal addition, and the microscale bathymetric slopes. Biologic scattering was later included where spatial distribution and nonstationarity of schools of fish and individual marine mammals are realistically represented [Frankel et al. J. Acoust. Soc. Am. 119, 3437 (2006)] through individual-based modeling of their movements, school size, and target strengths. Clutter distributions from both approaches are compared against each other, for selected test cases, and against clutter measurements. [This effort was funded by the Maritime Sensing Program of the Office of Naval Research (ONR Code MS 321).]

Microwave Analytical Backscattering Models FROM Randomly Rough Anisotropic Sea Surface---Comparison with Experimental DATA in C and Ku Bands

The small slope approximation (SSA) and the Kirchhoff approach (KA) are applied to the prediction of microwave sea surface backscatter for both Ku and C bands for various wind speeds and incident angles. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally averaged Cand Ku-band radar backscattering data. The KA can be obtained rigorously for a perfectly-conducting surface, whereas for a dielectric surface, either the KA of order one (KA1) or the stationary phase (SP) method can be used. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally C and Ku bands radar backscattering data for incidence angles of interest for remote sensing. Since the SSA and KA formulations are expressed in polar coordinates, the backscattering coefficient is expressed in terms of surface height autocorrelation and its derivatives of oneand secondorders computed from integrating the sea spectrum multiplied by Bessel functions of the first kind. This allows to have for KA and first-order SSA (SSA-1), a single numerical integration over the radial distance instead of four, when the cartesian coordinates is chosen. Moreover, the azimuthal harmonic magnitudes of the backscattering coefficient according to the wind direction can 32 Bourlier and Berginc be performed separately. For an isotropic sea surface assumed to be perfectly conducting where the KA is valid, the deviation between SSA and KA models is smaller than the one computed from the SP model for HH polarization. For the VV polarization, the difference is greater, since the polarization term of SSA is given by the small perturbation method, whereas for the KA approach, it is equal to the Fresnel coefficient. For an anisotropic sea surface, the comparison of KA with SSA-1 leads to the same conclusion. The isotropic part and the second azimuthal harmonic of the backscattering coefficient are also compared with empirical backscattering models CMOD2-I3 and SASS-II valid in C and Ku bands, respectively.

Small-slope predictions of microwave backscatter from the sea surface

The small-slope approximation is applied to the prediction of microwave sea-surface backscatter. Numerical results are obtained assuming a non-directional surface wavenumber spectrum and compared with azimuthally averaged C- and Ku-band radar backscattering data. For vertical polarization, the predictions and measurements agree to within 3 dB at incidence angles of interest for remote sensing. Small-slope predictions of azimuthal scattering asymmetry do not agree as well with measurements. These predictions are found to be sufficiently dependent on the assumed wave directionality that they may be used to improve existing directional wave spectral models.

Statistical-dynamical model of wind-generated air/water interfaces

A new statistical-physical model is constructed for deep-ocean surface gravity waves in fully developed, directional wind-generated seas and analogous air/water interfaces. Basic assumptions are that surface elevation and velocity jointly form a Markoff process and that the Langevin equation describing surface motion at a point is that of a (linear) under-damped harmonic oscillator driven by a Gaussian wind-forcing term. Surface elevation and velocity are then jointly normal random processes, with explicit point covariance and spectra. From these, directional covariances and surface wavenumber spectra are obtained. Although the model is linear, and thus approximate at the high wavenumbers (breaking waves, etc.), agreement with experiment to date is good to excellent for both the second-order moments and (first-order) probability distributions. Furthermore, the model exhibits the required ν−4 falloff of directional spectra with high surface wavenumbers, and permits “dc” wave impulses, e.g., tsunamis, tidal bores, etc. Swell and capillary waves are handled similarly. These results are important in underwater acoustic scattering from water/air interfaces (e.g., sonar, communications applications), as well as for EM and acoustic scattering from air/water surfaces and oceanography. [Work supported by the Office of Naval Research, Code 412.]