Surface expressions of internal tides constitute a significant component of the total recorded tide. The internal component is strongly modulated by the time-variable density structure, and the resulting perturbation of the recorded tide gives a welcome look at twentieth-century interannual and secular variability. Time series of mean sea level h SL (t) and total recorded M 2 vector a TT (t) are extracted from the Honolulu 1905-2000 and Hilo 1947-2000 tide records. Internal tide parameters are derived from the intertidal continuum surrounding the M 2 frequency line and from a Cartesian display of a TT (t), yielding a ST ϭ 16.6 and 22.1 cm, a IT ϭ 1.8 and 1.0 cm for surface and internal tides at Honolulu and Hilo, respectively. The proposed model a TT (t) ϭ a ST ϩ a IT cos IT (t) is of a phase-modulated internal tide generated by the surface tide at some remote point and traveling to the tide gauge with velocity modulated by the underlying variable density structure. Mean sea level h SL (t) [a surrogate for the density structure and hence for IT (t)] is coherent with a IT (t) within the decadal band 0.2-0.5 cycles per year. For both the decadal band and the century drift the recorded M 2 amplitude is high when sea level is high, according to ␦a TT ϭ O(0.1␦h SL ). The authors attribute the recorded secular increase in the Honolulu M 2 amplitude from a TT ϭ 16.1 to 16.9 cm between 1915 and 2000 to a 28°rotation of the internal tide vector in response to ocean warming.

Broadband acoustic signals were transmitted during November 1994 from a 75-Hz source suspended near the depth of the sound-channel axis to a 700-m long vertical receiving array approximately 3250 km distant in the eastern North Pacific Ocean. The early part of the arrival pattern consists of raylike wave fronts that are resolvable, identifiable, and stable. The later part of the arrival pattern does not contain identifiable raylike arrivals, due to scattering from internal-wave-induced sound-speed fluctuations. The observed ray travel times differ from ray predictions based on the sound-speed field constructed using nearly concurrent temperature and salinity measurements by more than a priori variability estimates, suggesting that the equation used to compute sound speed requires refinement. The range-averaged ocean sound speed can be determined with an uncertainty of about 0.05 m/s from the observed ray travel times together with the time at which the near-axial acoustic reception ends, used as a surrogate for the group delay of adiabatic mode 1. The change in temperature over six days can be estimated with an uncertainty of about 0.006°C. The sensitivity of the travel times to ocean variability is concentrated near the ocean surface and at the corresponding conjugate depths, because all of the resolved ray arrivals have upper turning depths within a few hundred meters of the surface.

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During the Acoustic Engineering Test ͑AET͒ of the Acoustic Thermometry of Ocean Climate ͑ATOC͒ program, acoustic signals were transmitted from a broadband source with 75-Hz center frequency to a 700-m-long vertical array of 20 hydrophones at a distance of 3252 km; receptions occurred over a period of six days. Each received pulse showed early identifiable timefronts, followed by about 2 s of highly variable energy. For the identifiable timefronts, observations of travel-time variance, average pulse shape, and the probability density function ͑PDF͒ of intensity are presented, and calculations of internal-wave contributions to those fluctuations are compared to the observations. Individual timefronts have rms travel time fluctuations of 11 to 19 ms, with time scales of less than 2 h. The pulse time spreads are between 0 and 5.3 ms rms, which suggest that internal-wave-induced travel-time biases are of the same magnitude. The PDFs of intensity for individual ray arrivals are compared to log-normal and exponential distributions. The observed PDFs are closer to the log-normal distribution, and variances of log intensity are between (3.1 dB) 2 ͑with a scintillation index of 0.74͒ for late-arriving timefronts and (2.0 dB) 2 ͑with a scintillation index of 0.2͒ for the earliest timefronts. Fluctuations of the pulse termination time of the transmissions are observed to be 22 ms rms. The intensity PDF of nonidentified peaks in the pulse crescendo are closer to a log-normal distribution than an exponential distribution, but a Kolmogorov-Smirnov test rejects both distributions. The variance of the nonidentified peaks is (3.5 dB) 2 and the scintillation index is 0.92. As a group, the observations suggest that the propagation is on the border of the unsaturated and partially saturated regimes. After improving the specification of the ray weighting function, predictions of travel-time variance using the Garrett-Munk ͑GM͒ internal-wave spectrum at one-half the reference energy are in good agreement with the observations, and the one-half GM energy level compares well with XBT data taken along the transmission path. Predictions of pulse spread and wave propagation regime are in strong disagreement with the observations. Pulse time spread estimates are nearly two orders of magnitude too large, and ⌳-⌽ methods for predicting the wave propagation regime predict full saturation.

In this paper Creamer's ͓͑1996͒. J. Acoust. Soc. Am. 99, 2825-2838͔ transport equation for the mode amplitude coherence matrix resulting from coupled mode propagation through random fields of internal waves is examined in more detail. It is shown that the mode energy equations are approximately independent of the cross mode coherences, and that cross mode coherences and mode energy can evolve over very similar range scales. The decay of cross mode coherence depends on the relative mode phase randomization caused by coupling and adiabatic effects, each of which can be quantified by the theory. This behavior has a dramatic effect on the acoustic field second moments like mean intensity. Comparing estimates of the coherence matrix and mean intensity from Monte Carlo simulation, and the transport equations, good agreement is demonstrated for a 100-Hz deep-water example.

An efficient method is presented to numerically simulate stochastic internal-wave-induced sound-speed perturbation fields in deep ocean environments. The sound-speed perturbation field is represented as an internal-wave eigenfunction expansion in which WKB amplitude scaling and stretching of the depth coordinate are exploited. Individual realizations of the sound-speed perturbation field are constructed by evaluating a multidimensional fast Fourier transform of a complex-valued function whose modulus has a known simple form and whose phase is random. Approximations made are shown to be consistent with approximations built into the Garrett–Munk internal-wave spectrum, which is the starting point of this analysis. Both time-varying internal-wave fields in three space dimensions and frozen fields in a vertical plane are considered.

A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate program's 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions. Much of the analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. Further, it is shown that the collection of the many eigenrays that form one of the resolved arrivals is nonlocal, both spatially and as a function of launch angle, which places severe restrictions on theories that are based on a perturbation expansion about a background ray.

Recent results relating to ray dynamics in ocean acoustics are reviewed. Attention is focused on long-range propagation in deep ocean environments. For this class of problems, the ray equations may be simplified by making use of a one-way formulation in which the range variable appears as the independent (timelike) variable. Topics discussed include integrable and nonintegrable ray systems, action-angle variables, nonlinear resonances and the KAM theorem, ray chaos, Lyapunov exponents, predictability, nondegeneracy violation, ray intensity statistics, semiclassical breakdown, wave chaos, and the connection between ray chaos and mode coupling. The Hamiltonian structure of the ray equations plays an important role in all of these topics.