Ocean Wave Field Research Articles

Generation of spatial internal waves in a rotating ocean by moving non-stationary disturbances

In a general linear statement, the kinematic structure of spatial internal waves generated by a uniformly moving area of oscillating surface pressures in a continuously stratified ocean of constant depth is studied. The earth's rotation effects are considered. Possible types of ocean wave fields with a constant Brunt-Vaisala frequency are examined. The wave regimes for individual modes of internal and gyroscopic waves are classified on the basis of estimating the integrals asymptotically.

A simple derivation of Hasselmann's nonlinear ocean‐synthetic aperture radar transform

We present a simple derivation of Hasselmann's nonlinear spectral transform for the synthetic aperture radar imaging of ocean wave fields and discuss some of its implications.

Aircraft laser sensing of sound velocity in water: Brillouin scattering

A new real-time data source for sound speed in the upper 100 m has recently been proposed for exploratory development at the Naval Oceanographic and Atmospheric Research Laboratory. This data source would be generated via a ship- or aircraft-mounted, optical pulsed laser using the technique of spontaneous Brillouin scattering. This system should be capable (from a single 10 ns 500 mJ pulse) of yielding range resolved (≈ 1 m resolution) sound speed profiles in water to depths of 75–100 m to an accuracy of 1 m/s. At aircraft speeds of 300 miles/h (134 m/s) and a laser pulse repetition rate of 10 pps, vertical profiles of sound speed would be obtained spatially every 13 m. These 100 m profiles would provide the capability of rapidly monitoring the upper-ocean vertical structure for much of the world's oceans and for most seasons. They would provide new perspectives on upper-ocean mixing and the oceanic internal wave field. These profiles would also provide an extensive, new, subsurface-data source to existing real-time, operational ocean nowcast/forecast systems. The present systems are dependent on sparse bathythermograph data and information inferred from sea-surface data. Extension of the 100 m profiles to depth using existing and proposed techniques would further increase the value of the laser-derived information.

Air‐sea fluxes and surface layer turbulence around a sea surface temperature front

The response of the lower marine atmospheric boundary layer to sharp changes in sea surface temperature was studied in the Frontal Air‐Sea Interaction Experiment (FASINEX) with aircraft and ships measuring mean and turbulence quantities, sea surface temperature, and wave state. Changing synoptic weather on 3 successive days provided cases of wind direction both approximately parallel and perpendicular to a surface temperature front. For the wind perpendicular to the front, both wind over cold‐to‐warm and warm‐to‐cold surface temperatures occurred. For the cold‐to‐warm case, the unstable boundary layer was observed to thicken, with increased convective activity on the warm side. For the warm‐to‐cold case, the surface layer buoyant stability changed from unstable to neutral or slightly stable, and the sea state and turbulence structure in the lower 100 m were immediately altered, with a large decrease in stress and slowing of the wind. Measurements for this case with two aircraft in formation at 30 and 100 m show a slightly increased stress divergence on the cold side. The turbulent velocity variances changed anisotropically across the front: the streamwise variance was practically unchanged, whereas the vertical and cross‐stream variances decreased. Model results, consistent with the observations, suggest that an internal boundary layer forms at the sea surface temperature front. The ocean wave, swell, and microwave radar backscatter fields were measured from several aircraft which flew simultaneously with the low‐level turbulence aircraft. Significant reductions in backscatter and wave height were observed on the cold side of the front.

Remote sensing of ocean wave spectra by interferometric synthetic aperture radar

THE two-dimensional power spectra of ocean waves are of great interest not only to oceanographers but also in practical applications such as wave forecasting, trans-oceanic ship routing, and design of coast and offshore installations. Remote sensing of ocean surface waves can be difficult using conventional synthetic aperture radar (SAR) techniques, but waves can be observed clearly by SAR in the interferometric configuration (INSAR)1,2. This improvement is due to the ability of INSAR to provide images of the local surface velocity field, in contrast to conventional SAR for which the imaging process is related indirectly to the complex modulation of the surface reflectivity by longer waves and currents. Here we show that INSAR can be used to obtain wavenumber spectra that are in agreement with power spectra measured in situ. This new method thus has considerable potential to provide instantaneous spatial information about the structutre of ocean wave fields.

A canonical statistical theory of oceanic internal waves

We use the methods of statistical mechanics to develop a theoretical relationship between the observed oceanic spectra and the probability distributions usually studied in statistical mechanics. We also find that the assumption that in terms of Lagrangian variables the oceanic internal wave field is near canonical equilibrium (i.e. the internal wave modes are populated in accordance with a Maxwell–Boltzmann-type distribution) yields expressions for the various marginal or reduced Eulerian spectra associated with both moored and towed measurements which are in striking qualitative agreement with experiment. In developing this theory it is important to distinguish carefully between Lagrangian and Eulerian variables. The important difference between the two sets of variables is due to the advective nonlinearity (i.e. (v∇) v where v is the Eulerian velocity) which is present only in the Eulerian frame. Our method treats the dynamics within the Lagrangian frame, where because of the absence of the advective nonlinearity it is fundamentally simpler, and then transforms to the Eulerian or measurement frame. We find that at small wavenumbers the four-dimensional Eulerian frequency wavenumber spectrum is approximately equal to the corresponding Lagrangian frequency wavenumber spectrum. At large wavenumbers, however, advective contributions become important and the two types of spectra are significantly different. While from a Lagrangian frame point of view the system is entirely wavelike, at large wavenumbers the Eulerian spectrum is not confined to the dispersion surface and the system, from an Eulerian frame point of view, is not wavelike. Further, the three-dimensional Eulerian wavenumber spectrum exhibits a large-wavenumber advective tail which decays as a power law and results in one-dimensional marginal spectra which are in excellent qualitative agreement with experiment. The above features are exhibited independent of the detailed nature of the underlying Lagrangian frequency wavenumber spectrum.

Introduction: Studies of ocean wave spectra from the Shuttle Imaging Radar‐B Experiment

Imagery of ocean surface waves obtained from synthetic aperture radar (SAR) provides a unique two‐dimensional fine‐resolution view of the ocean wave field which has been long thought to be of considerable value for studying air‐sea inter‐action, wave generation and propagation, and wave‐current refraction. Wave spectra from SAR have also been thought to be extremely useful for updating and verifying global wave forecast models. Such promise prompted a SAR to be placed on Seasat, an oceanographic satellite which operated in a rather glorious mode for only a little over 3 months in 1978. This imagery has been well studied and indeed has demonstrated the feasibility of acquiring useful directional wave spectra from space [e.g., Vesecky and Stewart, 1982].

Acoustic detection in the weak scattering region of an oceanic internal wave field

The coherent pressure field of an acoustic harmonic point source is gradually transformed into an incoherent pressure field as a function of propagation distance through the oceanic internal wave field. A receiver located in the weak scattering region would measure a fluctuating acoustic pressure with a Gaussianly distributed logarithmic amplitude and phase. The consequence is a biased estimate for the conventional maximum likelihood estimate of pressure or intensity and subsequently a biased detection criteria. It is proposed that detection performance may be improved in this case by logarithmically transforming the pressure prior to detection processing. An analysis and discussion will be presented using the Garrett and Munk internal wave field model. [Work supported by NUSC IR/IED.]

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.

The upper ocean internal wave field: Influence of the surface and mixed layer

A model is developed to calculate the upper ocean internal wave spectrum as modified by the surface boundary and mixed layer. The Garrett‐Munk spectrum is assumed to describe the deep ocean wave field. The main effect of the surface and mixed layer is to align the vertical structure of the waves forming vertically standing waves locally; this contrasts with the assumption of random alignment in the Garrett‐Munk model. Model spectra and coherences are calculated for idealized buoyancy frequency profiles and compared with the Garrett‐Munk model. Measurements in the upper 200 m from the Mixed Layer Dynamics Experiment in the northeast Pacific in 1983 are also compared with the model results. The most striking success of the model is predicting the observed high coherence and 180° phase difference across the mixed layer of horizontal velocity.

Nonlinear interactions among internal gravity waves

This paper reviews the nonlinear interaction calculations for the internal gravity wave field in the deep ocean. The nonlinear interactions are a principal part of the dynamics of internal waves and are an important link in the overall energy cascade from large to small scales. Four approaches have been taken for their analysis: the evaluation of the transfer integral describing weakly and resonantly interacting waves, the application of closure hypotheses from turbulence theories to more strongly interacting waves, the integration of the eikonal or ray equations describing the propagation of small‐scale internal waves in a background of large‐scale internal waves, and the direct numerical simulation of the basic hydrodynamic equations of motion. The weak resonant interaction calculations have provided most of the conventional wisdom. Specific interaction processes and their role in shaping the internal wave spectrum have been unveiled and a comprehensive inertial range theory developed. The range of validity of the resonant interaction approximation, however, is not known and must be seriously doubted for high‐wave number, high‐frequency waves. The turbulence closure calculations and the direct numerical modeling are not yet in a state to be directly applicable to the oceanic internal wave field. The closure models are too complex and rest on conjectures that are not demonstrably justified. Numerical modeling can treat strongly interacting waves and buoyant turbulence, but is severely limited by finite computer resolutions. Extensive suites of experiments have only been carried out for two‐dimensional flows. The eikonal calculations provide an efficient and versatile tool to study the interaction of small‐scale internal waves, but it is not clear to what extent the scale‐separated interactions with larger‐scale internal waves compete with and might be overwhelmed by interactions among like scales. The major shortcoming of all four approaches is that they neglect the interaction with the vortical (=potential vorticity carrying) mode of motion that must be expected to exist in addition to internal waves at small scales. This interaction is intrinsically neglected in all Lagrangian‐based studies and in the non‐rotating two‐dimensional simulations. The most promising approach for the future that can handle both arbitrarily strong interactions and the interaction with the vortical mode is numerical modeling once the resolution problem is overcome.

Energy and action flow through the internal wave field: An eikonal approach

The energy and action flow through the small‐scale part of the oceanic internal wave field is modeled by use of the eikonal technique, which is not subject to a weak interaction assumption. Both Monte Carlo calculations and a simplified model are presented and found to agree. It is found that the action flows toward slightly higher frequency (and thus the waves gain energy), in striking contrast to weak interaction predictions of a strong frequency decrease. The energy dissipation scales with depth as N2 cosh−1 (N/f), in agreement with measurements. The overall level is, however, a factor of 4 smaller than measurements. Possible sources of this discrepancy are discussed. A comparison is made with previous theoretical approaches for the depth dependence of dissipation.

Observations and modeling of seafloor microseisms

The seismic noise level on the deep seafloor has been essentially unknown at periods longer than 10 s and poorly known at shorter periods. We present data obtained with two new types of seafloor instrumentation: a differential pressure gauge and an antenna which measures a horizontal component of the electric field. The electric field is closely related to the horizontal ground motion. The observed spectra can be divided into three frequency bands. At periods longer than 40 s surface gravity waves produce velocity and pressure fluctuations which are felt at the deep seabed and dominate other sources. This signal is expected to be uniform throughout the ocean basins and will make detecting small seismic waves at periods longer than 40 s difficult. At periods between 10 and 40 s the spectrum is much quieter and may approach the background observed at quiet land stations. The pressure signal in this band may be at least partially caused by very low frequency acoustic waves in the atmosphere. The electric field spectrum is much noisier, suggesting that horizontal motions may be larger than vertical motions. At periods slightly shorter than 10 s the pressure spectrum rises sharply 45 dB into the microseism peak. Many studies of microseisms have established a clear relationship between the ocean surface gravity wave field and microseisms. We have found close agreement between the theory of microseism generation and observations obtained while a small storm moved over a seafloor instrument. The microseism spectrum evolved in concert with the changing wind wave field. We found that plausible estimates of the directionality of the wind wave field as a function of frequency could be derived from the microseism observations. The structure of the microseism peak in frequency is also related to the properties of surface waves trapped in the upper layers of sediment. Our calculations of the forcing of microseisms by a distributed pressure field at the surface elucidate this relationship and allow a partial determination of sediment structure at an instrument site from the microseism observations.

Estimation of ocean wave wavenumber and propagation direction from limited synthetic aperture radar data

A method for estimating wavenumber and propagation direction for the dominant wave component in an ocean wave field from a few scans of synthetic aperture radar data is described and analyzed. The use of just a few radar scans rather than a complete image reduces data storage requirements significantly. The analysis shown uses actual synthetic aperture radar data and provides parameter tradeoffs and statistical performance results. While reasonable estimates of wavenumber and propagation direction are achieved in some cases, the estimates are not sufficiently consistent to be satisfactory over a wide range of cases. The primary problem is one of low signal-to-noise ratio of the radar scan data.

Models of the oceanic internal wave field

In recent years, considerable progress has been made in internal wave research by a fruitful combination of experiment and theory. Kinematical models of the wave field appear to be well established, and dynamical models are evolving toward a stage of understanding the energetics and the interrelations of the waves within the oceanic field of motion. This review presents kinematical models of the wave field in terms of vertically progressive waves (WKB waves) as well as standing modes. Some emphasis is attributed to critical layer effects. Spectral models have been successfully developed for the wave field in the main thermocline. This appears to be in a stationary universal state with respect to spectral shape and level, whereas the upper ocean wave field shows considerable temporal and regional variability. Several approaches for separating the internal wave contribution from turbulence and other contaminations in observations have been proposed. This problem is of particular relevance in the transition region between waves and small‐scale turbulence at small vertical wavelengths. An accurate identification of reversible (wave induced) fine structure and irreversible fine structure is needed to determine the dissipation rate of the wave field and the mixing rates of the ocean. The search for dynamical relations of the wave field to environmental conditions has been extensive. The lack of dynamical correspondences between the wave spectrum and possible forcing fields in observations suggests that forcing is weak. Theoretical models of wave generation show that many mechanisms may contribute with equal efficiency. In concert with the observed low dissipation rates in the deep ocean, these results point toward the conclusion that there is no dominant source of energy but weak forcing by many different sources and weak dissipation. Under such conditions the interrelation between forcing and dissipation as well as the spectral form is controlled by internal transfer by wave‐wave interactions which are very efficient in relaxing spectral distortions to the observed universal form.

The response of Antarctic icebergs to ocean waves

The heave, tilt, and strain responses of three Antarctic tabular icebergs to ocean waves were measured during a 1980–1981 cruise of HMS Endurance to the South Atlantic. The three icebergs, located near the South Sandwich and South Orkney islands, were instrumented with accelerometers, tiltmeters, and wire strainmeters, while a Waverider buoy was used to record the ocean wave field. The thickness of the icebergs was surveyed by a helicopter‐borne radio echo sounder. The heave response occurred mainly at the swell period but with outbreaks of bobbing which lasted for a few cycles at a resonant period (about 40 s), which agreed well with the predictions of a numerical finite element model. The roll response occurred mainly at a long resonant period (40–50 s), which again agreed well with the model, but there was also a significant response at ocean wave periods (5–20 s), which exceeded predictions. The strain response had a component at very long periods, which is unexplained by theory, while the surface strain at ocean wave periods agreed with the simple analytical model of Goodman et al. (1980). Using this model it is possible to predict a wave height and period that will cause breakup of the icebergs, and we conclude that swell‐induced breakup is likely to occur during major storms in the open southern ocean.

Internal waves in the ocean: A review

This review documents the advances in our knowledge of the oceanic internal wave field during the past quadrennium. Emphasis is placed on studies that deal most directly with the measurement and modeling of internal waves as they exist in the ocean. Progress has come by realizing that specific physical processes might behave differently when embedded in the complex, omnipresent sea of internal waves. To understand fully the dynamics of the internal wave field requires knowledge of the simultaneous interactions of the internal waves with other oceanic phenomena as well as with themselves.

Southern ocean mean monthly waves and surface winds for winter 1978 by Seasat radar altimeter

Data acquired by the SEASAT radar altimeter during the 3 month satellite lifetime are analyzed in a study of the sea state of the southern hemisphere oceans. The lifetime of the SEASAT satellite, July 7 to October 10, 1978, corresponds to the Antarctic winter. Mean monthly maps of wind speed, significant wave height, and swell have been generated from the altimeter measurements along the satellite tracks. These maps delineate spatial and temporal differences of these parameters in the Atlantic, Indian, and Pacific oceans. Several features of the Southern Ocean wind and wave fields agree with conventional descriptions. For example, the principle zonal wind regimes established by the Southeast Trades and Westerlies are clearly evident in the monthly averages. Significant wave height and swell also exhibit minima near the Doldrums at low latitudes with steady increases southward to the latitudes of the Westerlies. However, superimposed on these general patterns is significant variability with horizontal scales as small as 1000 km. The maps also document a gradual migration of the region of absolute maximum wind and wave from the Atlantic eastward to the Indian Ocean and finally into the Pacific.

Measurements of Sea-State Variations Across Oceanic Fronts Using Laser Profilometry

Abstract As part of the Grand Banks Experiment in May 1979, airborne laser profilometer measurements of the ocean wave field were made across a large cold-water extrusion situated over the Newfoundland Ridge. The feature is actually an extension of the Labrador Current which is bordered on the west side by the Gulf Stream and on the east side by the North Atlantic Current. Star-shaped flight patterns were flown over the fronts on each side of the cold-water feature. A graphic technique was applied to the apparent wavenumber spectra in order to determine the changes in wave energy, wavelength and direction of propagation of the dominant wind-wave and swell components as they move across the fronts. At the western front, the sea state increased abruptly and the results indicate that wave-current interactions were the most important mechanism for wave modification although boundary-layer effects were present and increased wave breaking was observed. At the eastern front, changes in the swell are compared to ...

Modeling of microseismic surface wave sources

In a recent paper by Szelwis (1980) microseismic surface waves were inverted with respect to modal contribution and direction of approach. Array cross spectra of two observational runs were analyzed. The microseismic energy peaking in a frequency range of about 0.13 Hz to0.17 Hz was found to be essentially transported in the two lowest Rayleigh modes and the fundamental Love mode, approaching from one directional interval. In the present paper, the direction mode structure is related to the sources of microseisms. The Rayleigh waves are attributed to ocean wave interactions at the Norwegian coast. This is verified on the basis of Hasselmann's (1963) theoretical concept of the generation of microseisms, by estimating the corresponding source spectrum in two different ways. On the one hand, it is computed from the mode structure observed and a model of the wave‐carrying medium including refraction and attenuation. On the other hand, it is computed from a model of the ocean wave field subject to specular reflection from a planar coast. The ocean wave model is taken from sea wave generation research, the input parameters—wind velocity and fetch—are read from the weather charts. The two source spectrum estimates agree within reasonable limits of the model parameters, thus supporting the assumed Rayleigh wave generation mechanism. The Love waves appear to be coupled to the Rayleigh waves, as (1) both wave types approach from the same directions, and (2) their modal spectra relative to the subsurface transfer functions show a high frequency‐by‐frequency correlation, implying corresponding peak frequencies. A common origin, examined in terms of the spectra of one source, is not compatible with the underlying models.