Munk Spectrum Research Articles

Amplitude fluctuation effects in acoustic scattering due to shallow water internal waves

Amplitude fluctuation effects in acoustic scattering due to shallow water internal waves are examined using both adiabatic and coupled normal mode theory. The discussion is restricted to linear (nonsoliton) internal waves with a Garrett–Munk spectrum in this work. Coherent and incoherent effects, adiabatic versus coupled scattering, and the range, frequency, and internal wave amplitude sensitivity of the scattering will be discussed. Directions for future work will be discussed.

On acoustic tomography of internal waves

With the planned acoustic instrumentation of several of the worlds ocean basins, the possibility exists for measuring the strength of the internal wave field as a function of depth, time, and geographical position. The variability of internal‐wave energies and spectra over these parameters will provide information on the sources and sinks of internal waves. In the early eighties Flatte formulated an analytic, ray‐based framework for internal‐wave tomography. Analysis of the SLICE89 experiment combined with supercomputer numerical simulations have recently shown that internal waves have even stronger effects on signals transmitted over 1000 km than were expected from the early ray‐based theory plus the Garrett–Munk (GM) spectrum. It was found that the ray‐based theory is adequate for identifiable wavefronts that turn at depths below 100 m; energy that reaches very shallow depths and energy that stays near the sound‐channel axis do not behave so simply. The numerical simulations establish an internal‐wave s...

On Triad Interactions in a Linearly Stratified Ocean

Abstract Triad interactions in a linearly stratified ocean are studied numerically using a Garrett–Munk energy spectrum as the initial condition. It is found by bispectrum analysis that wave–mean flow interactions dominate and resonant interactions are limited to very large scales. Resonant triads of parametric subharmonic instability type play an insignificant role in the energy distribution. Local sum resonant triads provide the most effective energy transfer at very large scales. The analysis of triadic energy transfer rates suggests that triad configuration determines the energy flow pattern. When the modes with zero horizontal wavenumber are set to zero, resonant interactions arise. Thus, over most of the Garrett–Munk spectrum the energy level is low enough for resonance, but due to strong nonlinearities induced by horizontal currents, resonance is destroyed and wave–mean flow interactions dominate. If the energy level is reduced by a factor of 100, the number of resonant modes increases but wave–mea...

Thermal structures in the Kuroshio extension measured with a towed thermistor chain

Two-dimensional temperature data observed by use of a 275 meter towed thermistor chain deployed from an oceanographic research vessel USS MARYSVILLE, which cruised with a speed of 6.2 knots in July 1966 across the Kuroshio Extension in the North Pacific, are investigated. Two-dimensional variations of the distribution of the isotherms along the ship's track are analyzed with special reference to their slope, wavelength and wave height. The results show that the slope and wave height of isotherms have a tendency to increase as the temperature decreases. Even if the contribution of wave heights smaller than 1.5 m is neglected, i.e., contribution of large scale slope with a horizontal scale of 5–30 km is subtracted, this tendency is still detected. In contrast to this, the wavelength evaluated by the crest to crest method has no dependency on the temperature. Power spectrum of the isotherm depth is proportional tok−1.87 for 13°C andk−2.13 for 27°C, wherek is the wave number. It is shown that the spectra of warmer isotherms are relatively well approximated by −2 power law (Garrett and Munk spectrum) for internal waves rather than the −5/3 power law (Kolmogorov spectrum) for three dimensional isotropic turbulence.

Effects of perturbations on long‐range propagation

Results of numerical modeling of long‐range (greater than 500‐km) low‐frequency acoustic propagation in the ocean have been presented previously. These results were in qualitative agreement with measurements for the Heard Island Feasibility Test and the SLICE89 experiments. To quantify the differences between experimental and parabolic equation (PE) results, time‐dependent modal decomposition was applied to the received signals. This modal tomography gives us an indication of the depth‐dependent differences between the actual and assumed sound‐speed profiles. This work is extended to look at the effects of small perturbations in the sound‐speed field (i.e., internal waves) on the arrival pattern. Internal waves were modeled using a statistical realization of the Garrett–Munk spectrum. Results of the effects of internal waves on specific deep ocean mode functions and model group velocities are presented. a)Present address: Marine Physical Labs., Scripps Inst. of Oceanogr., UCSD, La Jolla, CA 92093.

Equatorial and off‐equatorial fine‐scale and large‐scale shear variability at 140°W

In April 1987, the mean vertical shear was unusually low in the upper 350 m at 0°N, 140°W. The surface winds, the equatorial undercurrent, and the 20–30 day instability waves were at seasonal minima, and the equatorial zone was recovering from an El Niño event which had suppressed the undercurrent earlier that year. Unexpectedly, fine‐scale fluctuations with a vertical wavelength of 40 m and a period of about 12 days produced shears up to 0.03s−1, in contrast to the 0.01 s−1 related to the undercurrent. This “shear wave” accounted for most of the shear between 40 and 120 m. Its space and time scales are consistent with the dispersion characteristics of Doppler‐shifted equatorial inertia‐gravity waves. Turbulence measurements indicate that the shear wave was strongly damped on a time scale of one wave period or less. These equatorial observations differ markedly from those made at the same place in November 1984, when surface winds, the undercurrent, and instability waves were strong and when there was no shear wave. Measurements taken in transit to and from the equator show an increase in internal wave energy and shear toward the equator that can be described by a Garrett and Munk spectrum modified to have constant spectral density and increasing bandwidth as the Coriolis parameter approaches zero.

Scaling turbulent dissipation in the thermocline

By comparing observations from six diverse sites in the mid‐latitude thermocline, we find that, to within a factor of 2, , where 〈εIW〉 is the average dissipation rate attributable to internal waves; N0 = 0.0052 s−1 is a reference buoyancy frequency; S10 is the observed shear having vertical wavelengths greater than 10 m; and SGM is the corresponding shear in the Garrett and Munk spectrum of internal waves. The functional form agrees with estimates by McComas and Müller and by Henyey, Wright, and Flatté of the rate of energy transfer within the internal wave spectrum, provided the energy density of the internal waves is treated as a variable instead of one of the constant parameters. Following Garrett and Munk, we assume that , where EIW is the observed energy density and EGM is the energy density used by Garrett and Munk. The magnitude of εIW is twice that of Henyey et al. and one third that of McComas and Müller. Thus the observations agree with predictions sufficiently well to suggest that (1) a first‐order understanding of the link between internal waves and turbulence has been achieved, although Henyey et al. made some ad hoc assumptions and Garrett and Munk's model does not match important features in the internal wave spectrum reported by Pinkel, and (2) the simplest way to obtain average dissipation rates over large space and time scales is to measure . Even though the observations were taken at latitudes of 42°−11.5°, the variability in the Coriolis parameter ƒ was too limited for a conclusive test of the ƒ dependence also predicted for 〈εIW〉 by the wave‐wave interaction models. An exception to the scaling occurs east of Barbados in the thermohaline staircase that is apparently formed and maintained by salt fingers. Although ε in the staircase is very low compared with rates at mid‐latitude sites, it is 8 times larger than predicted for ε due only to internal waves.

Stochastic simulation and first-order multiple scatter solutions for acoustic propagation through oceanic internal waves

The existing theory of acoustic propagation through an oceanic internal wave field with a Garrett and Munk spectrum is modified and, by numerical computation, is shown to be consistent. The fractional sound speed computation is rederived to satisfy the Garrett and Munk spectrum and used to compute a stochastic simulation of the internal wave sound speed fluctuation field. The Garrett and Munk spectrum in (ω, j) space has been normalized by 4π, and the acoustic scattering is redefined to accommodate scattering from the internal wave phase fronts as in an acoustic phase grating. These modifications are then used to compute the coherent acoustic intensity by two methods: a first-order multiple scatter approximation and a stochastic simulation. Also, the Rytov approximation is shown to be equivalent to the first-order multiple scatter approximation in the form of the stochastic parabolic equation method in the unsaturated region. The computational results show agreement in the weak scattering region using typical deep ocean values. The stochastic simulation method is accurate in the saturated and unsaturated regions; however, the method requires long computer execution times. Phase front fragments propagating along rays with sound speeds reduced by the stochastic internal wave field are used to discuss the computational results.

High‐frequency internal wave observations in the marginal ice zone

Three thermistor chains extending from 15 to 65 m were deployed from ice floes in the Marginal Ice Zone north of Svalbard in a triangle with sides of 500–800 m for a period of 7 days. Vertical displacement spectra indicate that the internal wave energy level is lower than the Garrett and Munk spectrum by a factor of 2–3 but higher than other observations in the Arctic. A group of internal waves (a wave train), with frequency of 2–3 cph was observed to propagate at 0.05 m/s through the triangle in a west‐southwesterly direction during a 4‐ to 6‐hour period. A case study of this wave train, where the horizontal phase differences between the three thermistor chains were analyzed, showed wavelengths of 100–200 m and phase velocities of 0.10–0.15 m/s. Observation of the density field and the velocity field indicated that stratification dominated over vertical shear. Consequently, the dispersion relation was calculated by solving numerically the vertical mode equation for internal waves in a shearless ocean. The estimated wavelengths and phase velocities agree with the dispersion relation for first‐mode internal waves. The generating mechanisms may be tidal oscillations associated with a seamount located east of the triangle, or ice keels moving in relation to the water creating lee waves in the pycnocline.