Random Internal Wave Field Research Articles

Algorithms for determining the spectral-energy characteristics of a random field of internal waves from fluctuations of lidar echo signals.

The possibility of measuring the frequency-angular spectra of the mode components of a random field of small-amplitude pycnoclinic internal waves by the lidar method is theoretically studied. Equations are obtained for retrieving the spectra of internal waves from the measured spectra of relative fluctuations in the lidar echo signal power, if the profiles of the Väisälä frequency and light attenuation coefficient are known. The procedure for retrieving the spectra of a two-mode field is illustrated by a numerical experiment using real hydrological and hydro-optical data obtained in a region of the Barents Sea.

Signal processing and tracking of arrivals in ocean acoustic tomography.

The signal processing for ocean acoustic tomography experiments has been improved to account for the scattering of the individual arrivals. The scattering reduces signal coherence over time, bandwidth, and space. In the typical experiment, scattering is caused by the random internal-wave field and results in pulse spreading (over arrival-time and arrival-angle) and wander. The estimator-correlator is an effective procedure that improves the signal-to-noise ratio of travel-time estimates and also provides an estimate of signal coherence. The estimator-correlator smoothes the arrival pulse at the expense of resolution. After an arrival pulse has been measured, it must be associated with a model arrival, typically a ray arrival. For experiments with thousands of transmissions, this is a tedious task that is error-prone when done manually. An error metric that accounts for peak amplitude as well as travel-time and arrival-angle can be defined. The Viterbi algorithm can then be adapted to the task of automated peak tracking. Repeatable, consistent results are produced that are superior to a manual tracking procedure. The tracking can be adjusted by tuning the error metric in logical, quantifiable manner.

Statistics of mode amplitudes in shallow water environments: Effects of random linear internal waves and nonlinear internal wave packets.

In shallow water environments there is presently an incomplete understanding of the relative acoustical importance of the random linear internal-wave field compared to nonlinear internal waves packets. Using the random coupled mode theory of [Creamer (1996)], the nonlinear internal wave mode coupling theory of [Colosi (2007)], and Monte Carlo numerical simulation we are able to demonstrate the important propagation physics when the two internal wave fields act alone, and simultaneously. Importantly, we find that for acoustic frequencies less than roughly 500 Hz and for propagation ranges of order 10s of kms mode propagation though the random internal wave field is very nearly adiabatic, and that cross mode coherences decay rapidly within the first 10 km. A surprising consequence of the decay of cross mode coherence is that the mean intensity will be to first order insensitive to nonlinear internal wave packets if they are located past the de-coherence range. It will also be shown that uncorrelated modes have important implications for the approach to saturation. The adiabatic nature of mode propagation though the random internal wave field may have important implications for shallow water acoustic remote sensing.

Coherence function of a sound field in an oceanic waveguide with horizontally isotropic statistics

The mean value and the coherence function of a sound field propagating in an oceanic waveguide with random inhomogeneities are important statistical characteristics of this field, which are needed for many practical applications. Closed equations for the coherence function were obtained in many works for both two dimensional and three dimensional geometries. For the 3D case, these equations are too involved even for a numerical treatment. In this paper, explicit expressions for the mean field and the coherence function due to a point omnidirectional monochromatic source in a 3D waveguide are derived for the case of random inhomogeneities, which are statistically isotropic in a horizontal plane. The solutions are much simpler than those obtained previously due to the cylindrical symmetry of the problem. The theory developed is used to study numerically the mean field and the coherence function in an oceanic waveguide perturbed by a random field of internal waves with the Garrett-Munk spectrum.

Applying data nullspace projection method on matched-field source localization in a random internal wave field

In a random internal wave field where temporal varying water-column soundspeed profiles are very difficult to measure, matched-field source localization methods can be greatly degraded due to water-column model mismatch. In this paper, the data nullspace projection is applied to this source localization technique to reduce the effect of unknown water-column soundspeed variations. The basis of this method is to project the acoustic signal onto a data nullspace that is insensitive to water-column soundspeed fluctuations. This method only requires the mean and the second-order statistics of temporal varying water-column soundspeed profiles to calculate soundspeed empirical-orthogonal-functions. It does not require measurements of the exact soundspeed field, i.e., each snapshot, for the matched-field processing. In a simulation test case, a linear wave model is used to generate a random internal wave field, an acoustic source continuously transmits a single frequency tone, and the matched-field processing is implemented with the signal received on both a VLA and a HLA, respectively, for localizing the source position. The simulation results show that applying the data nullspace projection method can dramatically improve the robustness and accuracy of the matched-field source localization, resulting in a random internal wave field.

Effects of internal gravity waves on acoustic pulse propagation in the atmospheric wave guides

Recently developed theoretical model of a random internal wave field in the atmosphere is used for calculating the statistical characteristics of the parameters of acoustic pulses propagating in the atmospheric wave guides. The variances, frequency spectra and spatial structure functions of the internal wave-associated fluctuations of the acoustic pulse travel times and grazing angles are calculated and compared to those obtained in the experiments on pulse sounding of the atmosphere. The effects analyzed here include: a scattering of acoustic waves from highly anisotropic wind speed and temperature inhomogeneities into the so-called acoustic shadow zones; a discrete character of the observed frequency spectra of the fluctuations of acoustic pulse parameters in the range 1min-1h; an error caused by internal waves in determining of the angle of arrival of the acoustic signal in the waveguide.

Statistical Description of Ray Chaos in an Underwater Acoustic Waveguide

An approximate analytical approach is developed to describe the chaotic behavior of ray trajectories in a deep-water acoustic waveguide up to three to five thousands of kilometers in length. The ray dynamics is investigated using the Hamiltonian formalism expressed in terms of the canonical action-angle variables. A realistic waveguide model is used, with refractive-index fluctuations due to the random field of internal waves. The Fokker-Planck equation is obtained for the action variable, and it is shown that the range dependence of this variable can be approximated by the Wiener random process, which represents the simplest model of diffusion. Formulas are derived for calculating the probability density of the coordinate and other ray characteristics. An approximate expression is found for the smoothed field intensity of a point source. For illustrating and testing the formulas obtained, their predictions are compared with the results of numerical solutions of ray equations and the results of field calculations by the parabolic equation method.

Estimating internal wave statistics from underwater acoustic transmission scintillation measurements on the New Jersey shelf with a 3-D stochastic model

The acoustic intensity expected after transmission through random inhomogeneities in an ocean waveguide is analytically expressed in terms of modal dispersion, attenuation, and energy redistribution in a 3-D multiple forward scattering formulation [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)]. This approach is used to model forward scattering through a random internal wavefield. Scattering from the density and compressibility inhomogeneities caused by the internal waves is approximated with the Rayleigh–Born series. The model is used to estimate the rms internal-wave height from low-to-mid-frequency underwater acoustic transmission scintillations measured during the Main Acoustic Clutter experiment of 2003 in the New Jersey Strataform area. Estimated internal wave height standard deviations matched those obtained from independent temperature and CTD measurements and suggest that the internal wave field was not temporally stationary.

Structure and variability of semidiurnal internal tides in Mamala Bay, Hawaii

Moored current meter and temperature observations and results from a three‐dimensional primitive equation model are used to examine the energetic semidiurnal internal tides present in Mamala Bay on the south coast of Oahu, Hawaii. The steady, harmonic component of the internal tide is characterized by large vertical displacements in the central region of the bay (35 m amplitude for the M2 constituent), and enhanced alongshelf baroclinic currents at the headlands on either end of the bay (0.27 m s−1). Seasonal changes in amplitude and phase are observed. The model captures the qualitative spatial structure of the observations. Baroclinic energy flux estimates, from the mooring observations and the numerical simulations, suggest that internal tide energy propagates into the bay and does not originate within the bay. The model indicates that internal wave generation occurs over the flanks (500–1000 m depth) of the ridge, predominantly on the east side, with perhaps some additional contribution on the west from an energetic internal tide generated north of Oahu. Wave superposition is believed to account for the alongshelf spatial structure of currents and displacements. Incoherent modulations of the internal tide occur that are not related to local changes in stratification, at least on superannual timescales. Factors contributing to this signal may include stratification variations at the deep generation sites, mesoscale activity, and/or the shoaling of a random internal wave field into the bay from the open ocean.

Experimental and theoretical study of the vertical coherence of the sound field in a shallow sea

The combined effect of multiple scattering by random inhomogeneities of a waveguide and bottomcaused sound absorption is known to be a fundamental factor that governs the formation of the sound field in a shallow sea [1, 2]. A number of publications [2–6] present statistical analyses of the fluctuation phenomena that accompany the sound propagation in shallow sea regions. In these publications, most attention is paid to studying the evolution of the intensities of normal waves under the effect of scattering by the random field of internal waves. It is shown that in natural conditions, in addition to the inhomogeneities of the water column, one should take into account the irregular boundaries of the sound channel, which can also affect the correlation characteristics of the sound field. In this paper, we present experimental data on the vertical coherence of the sound field on a fixed path in the Barents Sea. We also compare the experimental data with theoretical calculations based on a model of sound scattering by the rough sea surface.

The structure of the turbulent wake and the random internal wave field generated by a moving sphere in a stratified fluid

We present experimental results on the structure of the turbulent wake of a sphere and on the frequencies associated with the vortex shedding in a stratified fluid. The strong correlation between the random internal wave field emitted by the wake and the coherent structures of the turbulent wake is demonstrated.

Distortion of gravity wave spectra measured from ground-based stations

The attenuation induced by time averaging of ground based measurements of internal gravity waves is made scale dependent by the Doppler shifts resulting from mean atmospheric motions, leading to some distortion of the experimental spectra versus vertical wavenumber. This spectral distortion mainly affects the large wavenumber range where the spectral level may be strongly underestimated, even for a few minutes averaging time in the case of vertical velocity measurements. Numerical evaluations of the spectral attenuation are presented, assuming a standard model of the random internal wave field.

Diffusion by internal waves

A perturbation analysis of the Lagrangian equations of motion is used to examine the diffusion induced by a random field of internal waves. At second order there is a random field of shearing motion in the horizontal plane. We calculate the single‐particle, two‐particle, and patch diffusivities that result from this motion. Patch and two‐particle diffusivity both increase as scale raised to the power of 4/3 for an internal wave field in which the spectrum of horizontal velocity varies as ω−2.

Simultaneous spatial and temporal measurements of the internal wave field during MATE

A statistical description of the deep ocean internal wave field is presented using measurements from the Midocean Acoustic Transmission Experiment, conducted near Cobb Seamount in the NE Pacific (46°46′N, 130°47′W) during June–July 1977. The unique feature of this experiment is the variety of data obtained simultaneously from the same location: time series of temperature and velocity, and vertical and horizontal profiles of temperature. A generalized form of the Garrett‐Munk (GM) internal wave spectrum is developed and used to interpret the data. This spectral model is specified by three parameters, , t, and p (energy level, wave number bandwidth, and frequency spectral slope, respectively). The variety of measurement types permit these three model parameters to be estimated from more than one measurement. The overall best fit values to the MATE data were p = 2.7 (GM use p = 3), t = 3.1 m−1 s (equivalent to j* = 6, twice the GM value), and (within 20% of the GM level). Although significant differences were found in the values of the bandwidth (t) and spectral slope (p) from those specified by Garrett‐Munk, the deviations are consistent with the behavior expected in a random internal wave field.

Acoustic propagation with an oceanic sound‐speed model including a random field of internal waves

Flatte and Tappert [J. Acoust. Soc. Am. 58, 1151–1159 (1975)] have shown that internal waves cause significant fluctuations in the transmission of acoustic energy through the ocean volume, comparable in size and frequency to the fluctuations observed in field experiments. They use the parabolic equation method to propagate acoustic signals. The random component of the sound‐speed field is modeled by a linear superposition of internal wave eigenmodes. Each eigenmode amplitude is selected independently from a complex Gaussian distribution. Using an improved version of their simulation, range versus loss data are generated for up to 100 h of simulated time at 0.5‐h intervals. The source of 100 Hz is located on the axis of the canonical profile. The ensemble average and variance of the acoustic signal, as a function of receiver location, are computed. [Work supported by NUSC.]

Wave propagation through random media: Contributions from ocean acoustics

Recent theoretical and experimental progress in understanding sound transmission through a random field of internal waves is reviewed. Some attempt is made to place this work in historical relation to similar efforts in radio-wave propagation through the ionosphere and light propagation through the atmosphere. It is emphasized that internal waves as a random medium possess several new features unfamiliar to those dealing with homogeneous isotropic turbulence. The effect of a background deterministic wave-speed variation (the ocean sound channel) is central to the theoretical treatment, which is based on a path-integral solution of the parabolic wave equation. A distinction is made between two sections of the saturated region and some emphasis is placed on the region of partial saturation. Comparison with experiment is discussed with examples from the two-point mutual coherence function of time, frequency, and vertical separation; the intensity correlation in time, frequency, and vertical separation; the spectra of phase and log intensity, pulse propagation, and the higher moments of intensity.

A Statistical Description of Temperature Finestructure in the Presence of Internal Waves

We have developed a statistical model describing a random field of internal waves passively oscillating a random, locally horizontally uniform temperature finestructure. Here we define finestructure to be non-internal wavelike temperature fluctuations of any vertical scale caused by phenomena such as horizontal intrusions or geostrophic eddies. The model allows one to examine the effects of finestructure upon all relevant measurable statistical quantities of the temperature field as a function of the vertical scale of the finestructure. Also, the effects of the time variation of the finestructure itself are considered. The model was fit to data obtained during the 3-week Mid-ocean Acoustic Transmission Experiment (MATE) in summer 1977 new Cobb seamount in the northeastern Pacific. Various spectra and coherences estimated from temperature time series and vertical profiles were used to make an assessment of the finestructure as well as establish the consistency of the model. Temperature variance measured at frequencies above the local Väisäiä frequency was used to estimate the magnitude of the high vertical wavenumber finestructure. This high wavenumber finestructure (0.05–1 m−1) with a (wavenumber)−−2.5 dependence can consistently explain all the observed variance in the measured high vertical wavenumber spectra. At lower wavenumbers (0.002–0.020 m−1) a (wavenumber)−2 dependence was observed, and the spectral level found to be approximately equally divided between finestructure and internal waves advecting a constant temperature gradient. The contribution of the finestructure effects to the internal wave frequency spectrum was found to be about a factor of 10 less than that of internal waves advecting a constant temperature gradient.

On the scattering of sound by internal waves in the ocean

The parabolic approximation to the wave equation is applied to the calculation of the spectral density of amplitude and phase fluctuations of a plane sound wave propagating through a random field of internal waves in the ocean. The dependence of the predicted spectra on wave number and frequency shows that the lowest-mode internal waves dominate the phase variance, while the amplitude fluctuations are controlled by intermediate scales. The results are compared with previous theories and available data. There is a discrepancy between observed amplitude spectra and predictions based on the internal wave models. It is concluded that internal waves are not solely responsible for the scattering of sound in the ocean and that other effects must contribute.

On the scattering of sound by internal waves in the ocean

The parabolic approximation to the wave equation is applied to the calculation of the spectral density of amplitude and phase fluctuations of a plane sound wave propagating through a random field of internal waves in the ocean. The dependence of the predicted spectra on wave number and frequency shows that the lowest mode internal waves dominate the phase variance, while the amplitude fluctuations are controlled by intermediate scales. The results are compared with previous theories and available data. There is a discrepancy between observed amplitude spectra and predictions based on the internal wave models. It is concluded that internal waves are not solely responsible for the scattering of sound in the ocean and that other effects must contribute.

Gaussianity of internal waves

Present theories of nonlinear interactions within a random internal wave field depend upon the assumption of quasi-Gaussian statistics; i.e., the nonlinearities are assumed to be perturbations on a Gaussian base state. Examination of horizontal current, temperature, and vertical displacement data has been ambiguous as to the correctness of this assumption. This report describes the time variability of the probability distribution of the east and north velocity components and the up (vertical displacement) variable of the internal wave experiment (IWEX ); the goal is to test for the Gaussianity of internal waves. In order to use the classical chi-square and the two-tailed Kolmogorov-Smirnov goodness-of-fit tests the correlation or spectral structure of the data must be considered. Starting with artificially generated Gaussian random time series that are white in frequency space, the Gentleman and Sande (1966) method is used to incorporate desired spectral shapes into the series, which are then used to find, for the two goodness-of-fit tests, new confidence levels that recognize the presence of an internal wavelike correlation structure in the data. The degree of Gaussianity of the east, north, and up variables throughout IWEX is discussed in this light and compared with results of previous investigations. It is concluded from the IWEX data that temperature and displacement are more likely to be Gaussian than are current data, that small kurtosis is characteristically associated with non-Gaussian current data, that negative skewness contributes to non-Gaussian temperature/displacement data, and that bursts of high variance may precede times of non-Gaussian behavior. No consideration was given to the frequency domain behavior of the data other than to the overall spectral shape for use in generating the artificial data. In this sense, then, this report is a preliminary study only, because the temporal evolution of the statistics of the various frequency bands in the internal wave field is the underlying question of importance.