Doppler Sonar Observations of Internal Waves, Wave-Field Structure

The paper is concerned with analytical study of inertia-gravity waves in rotating density-stratified ideal fluid confined in a spherical shell. It primarily aims at clarifying the possible role of these motions in deep ocean mixing. Recently, it was found that on the ‘non-traditional’ β-plane inertia-gravity internal waves can propagate polewards beyond their inertial latitude, where the wave frequency equals the local Coriolis parameter, by turning into subinertial modes trapped in the narrowing waveguides around the local minima of buoyancy frequency N. The behaviour of characteristics was established: wave horizontal and vertical scales decrease as the wave advances polewards and tend to zero at a latitude corresponding to an attractor of characteristics. However, the basic questions about wave evolution, its quantitative description and the possibility of its reflection from the critical latitude remain open. The present work addresses these issues by studying the linear inviscid evolution of finite bandwidth wavepackets on the ‘non-traditional’ β-plane past the inertial latitude for generic oceanic stratification. Beyond the inertial latitude, the wave field is confined in narrowing waveguides of three distinct generic types around different local minima of the buoyancy frequency. In the oceanic context, the widest is adjacent to the flat bottom, the thinnest is the upper mixed layer, and the middle one is located between the seasonal and main thermocline. We find explicit asymptotic solutions describing the wave field in the WKB approximation. As a byproduct, the conservation of wave action principle is explicitly formulated for all types of internal waves on the ‘non-traditional’ β-plane. The wave velocities and vertical shear tend to infinity and become singular at the attractor latitude or its vicinity for both monochromatic and finite bandwidth packets. We call this phenomenon singular focusing. These WKB solutions are shown to remain valid up to singularity for the bottom and mid-ocean waveguides. The main conclusion is that even in the inviscid setting the wave evolution towards smaller and smaller horizontal and vertical scales is irreversible: there is no reflection. For situations typical of deep ocean, a simultaneous increase in wave amplitude and decrease of vertical scale causes a sharp increase of vertical shear, which may lead to wave breaking and increased mixing.

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Internal Waves and Mixing near the Kerguelen Plateau

Journal of Physical Oceanography ◽

10.1175/jpo-d-15-0055.1 ◽

2015 ◽

Vol 46 (2) ◽

pp. 417-437 ◽

Cited By ~ 9

Author(s):

Amelie Meyer ◽

Kurt L. Polzin ◽

Bernadette M. Sloyan ◽

Helen E. Phillips

Keyword(s):

Internal Wave ◽

Wave Field ◽

Internal Waves ◽

Large Scale ◽

Polar Front ◽

Frontal Region ◽

Small Scale ◽

Kerguelen Plateau ◽

Flow Strength ◽

Internal Wave Field

AbstractIn the stratified ocean, turbulent mixing is primarily attributed to the breaking of internal waves. As such, internal waves provide a link between large-scale forcing and small-scale mixing. The internal wave field north of the Kerguelen Plateau is characterized using 914 high-resolution hydrographic profiles from novel Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. Altogether, 46 coherent features are identified in the EM-APEX velocity profiles and interpreted in terms of internal wave kinematics. The large number of internal waves analyzed provides a quantitative framework for characterizing spatial variations in the internal wave field and for resolving generation versus propagation dynamics. Internal waves observed near the Kerguelen Plateau have a mean vertical wavelength of 200 m, a mean horizontal wavelength of 15 km, a mean period of 16 h, and a mean horizontal group velocity of 3 cm s−1. The internal wave characteristics are dependent on regional dynamics, suggesting that different generation mechanisms of internal waves dominate in different dynamical zones. The wave fields in the Subantarctic/Subtropical Front and the Polar Front Zone are influenced by the local small-scale topography and flow strength. The eddy-wave field is influenced by the large-scale flow structure, while the internal wave field in the Subantarctic Zone is controlled by atmospheric forcing. More importantly, the local generation of internal waves not only drives large-scale dissipation in the frontal region but also downstream from the plateau. Some internal waves in the frontal region are advected away from the plateau, contributing to mixing and stratification budgets elsewhere.

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Bispectral Analysis of Energy Transfer within the Two-Dimensional Oceanic Internal Wave Field

Journal of Physical Oceanography ◽

10.1175/jpo2816.1 ◽

2005 ◽

Vol 35 (11) ◽

pp. 2104-2109 ◽

Cited By ~ 26

Author(s):

Naoki Furuichi ◽

Toshiyuki Hibiya ◽

Yoshihiro Niwa

Keyword(s):

Internal Wave ◽

Wave Field ◽

Internal Waves ◽

Internal Tide ◽

Energy Cascade ◽

Minor Role ◽

Two Dimensional ◽

Bispectral Analysis ◽

Internal Wave Field ◽

Oceanic Internal Wave

Abstract Bispectral analysis of the numerically reproduced spectral responses of the two-dimensional oceanic internal wave field to the incidence of the low-mode semidiurnal internal tide is performed. At latitudes just equatorward of 30°, the low-mode semidiurnal internal tide dominantly interacts with two high-vertical-wavenumber diurnal (near inertial) internal waves, forming resonant triads of parametric subharmonic instability (PSI) type. As the high-vertical-wavenumber near-inertial energy level is raised by this interaction, the energy cascade to small horizontal and vertical scales is enhanced. Bispectral analysis thus indicates that energy in the low-mode semidiurnal internal tide is not directly transferred to small scales but via the development of high-vertical-wavenumber near-inertial current shear. In contrast, no noticeable energy cascade to high vertical wavenumbers is recognized in the bispectra poleward of ∼30° as well as equatorward of ∼25°. A new finding is that, although PSI is possible equatorward of ∼30°, the efficiency drops sharply as the latitude falls below ∼25°. At all latitudes, another resonant interaction suggestive of induced diffusion is found to occur between the low-mode semidiurnal internal tide and two high-frequency internal waves, although bispectral analysis shows that this interaction plays only a minor role in cascading the low-mode semidiurnal internal tide energy.

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Experimental Study of Ship Internal Waves—The Supersonic Case

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2920081 ◽

1993 ◽

Vol 115 (1) ◽

pp. 16-22 ◽

Cited By ~ 2

Author(s):

H. Ma ◽

M. P. Tulin

Keyword(s):

Experimental Study ◽

Internal Wave ◽

Wave Field ◽

Experimental Method ◽

Internal Waves ◽

Measured Data ◽

Density Distributions ◽

Wave Patterns ◽

Wave Profiles ◽

Theoretical Results

Internal waves produced by a ship traveling faster than the fastest internal waves (supersonic case) were investigated experimentally in our laboratory in a wide tank using averaging conductivity wave gages developed for this investigation. The wave gage is similar to the conductivity probe, but has space-averaging electrodes. An array of seven such gages was used in a wave tank with dimensions 12 ft length, 8 ft width, 2 ft depth. The water in the tank was stratified with salt to obtain desired density distributions. A spheroid, split vertically, was towed against and along a sidewall to simulate a moving ship. Simultaneous wave profiles at various distances normal to the track of the ship were obtained for different Froude numbers and density distributions. The internal wave patterns were calculated from the measured data and compared with theoretical results. The amplitude on the first crest of the internal wave field is also plotted against the distance from the ship, and a limited comparison with theory is made. The experimental method developed for this study is sensitive, simple and reliable. It may serve to obtain a data base for ship-generated internal waves under a variety of conditions.

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Asymptotic Representations of the Solution of the Problem on the Wave Field Structure Formed by the Plane Wave Incidence on a Semitransparent Ingomogeneous Plasma Layer (a Model Problem)

Journal of Communications Technology and Electronics ◽

10.1134/s1064226921010071 ◽

2021 ◽

Vol 66 (1) ◽

pp. 14-22

Author(s):

E. A. Palkin ◽

A. A. Petrovich

Keyword(s):

Plane Wave ◽

Wave Field ◽

Model Problem ◽

Plasma Layer ◽

Field Structure ◽

Asymptotic Representations ◽

Wave Incidence ◽

Plane Wave Incidence

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Variability in the Internal Wave Field Induced by the Atlantic Deep Western Boundary Current at 16°N

Journal of Physical Oceanography ◽

10.1175/jpo-d-13-010.1 ◽

2014 ◽

Vol 44 (2) ◽

pp. 492-516 ◽

Cited By ~ 6

Author(s):

Janna Köhler ◽

Christian Mertens ◽

Maren Walter ◽

Uwe Stöber ◽

Monika Rhein ◽

...

Keyword(s):

Internal Wave ◽

Wave Field ◽

Continental Slope ◽

Internal Waves ◽

Vertical Mixing ◽

Low Frequency ◽

Western Boundary Current ◽

Western Boundary ◽

Boundary Current ◽

Deep Western Boundary Current

Abstract Five years of continuous mooring data combined with conductivity–temperature–depth (CTD)/lowered acoustic Doppler current profiler (LADCP) measurements from five cruises are used to investigate the influence of the deep western boundary current (DWBC) on the internal wave field and associated vertical mixing at the continental slope at 16°N in the western Atlantic. The mooring data include 2-hourly rotor current-meter measurements and temperature/conductivity time series with a high temporal resolution of 5–20 min. Thus, the data resolve time scales ranging from the low-frequency variability of the large-scale DWBC that generates internal waves due to interactions with the topography to frequencies greater than that of internal waves that are associated with vertical mixing. Estimates of the vertical mixing induced by the breaking of the observed internal waves show elevated diapycnal diffusivities of up to 10−3 ± 0.4 × 10−3 m2 s−1 in the bottommost 1500 m during times of a strong DWBC (maximum velocities at the mooring site up to 50 cm s−1) whereas vertical mixing rates are about an order of magnitude lower (1.6 × 10−4 ± 0.6 × 10−4 m2 s−1) during weak flow. During periods of a strong DWBC, spectra of horizontal velocity and internal wave available potential energy change substantially at depths below 1200 m and show a strong increase in variance particularly in the near-inertial frequency band. Low-frequency, near-inertial waves generated by topography/DWBC interaction on the slope to the west of the moorings can potentially cause this observed wave intensification; ray paths estimated for these waves agree well with the observed spectral changes at different depths. Variability in the high-frequency range, considered as a proxy for turbulent mixing, is significantly correlated with the DWBC strength above the continental slope.

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Can barotropic tide–eddy interactions excite internal waves?

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.1 ◽

2013 ◽

Vol 721 ◽

pp. 1-27 ◽

Cited By ~ 8

Author(s):

M.-P. Lelong ◽

E. Kunze

Keyword(s):

Internal Wave ◽

Wave Field ◽

Internal Waves ◽

Tidal Current ◽

Deep Ocean ◽

Wave Excitation ◽

Barotropic Tide ◽

Internal Wave Field ◽

Flow Components ◽

Internal Wave Generation

AbstractThe interaction of barotropic tidal currents and baroclinic geostrophic eddies is considered theoretically and numerically to determine whether energy can be transferred to an internal wave field by this process. The eddy field evolves independently of the tide, suggesting that it acts catalytically in facilitating energy transfer from the barotropic tide to the internal wave field, without exchanging energy with the other flow components. The interaction is identically zero and no waves are generated when the barotropic tidal current is horizontally uniform. Optimal internal wave generation occurs when the scales of tide and eddy fields satisfy resonant conditions. The most efficient generation is found if the tidal current horizontal scale is comparable to that of the eddies, with a weak maximum when the scales differ by a factor of two. Thus, this process is not an effective mechanism for internal wave excitation in the deep ocean, where tidal current scales are much larger than those of eddies, but it may provide an additional source of internal waves in coastal areas where horizontal modulation of the tide by topography can be significant.

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Coupling of surface and internal gravity waves: a mode coupling model

Journal of Fluid Mechanics ◽

10.1017/s0022112076001195 ◽

1976 ◽

Vol 77 (1) ◽

pp. 185-208 ◽

Cited By ~ 48

Author(s):

Kenneth M. Watson ◽

Bruce J. West ◽

Bruce I. Cohen

Keyword(s):

Energy Transfer ◽

Surface Wave ◽

Internal Wave ◽

Surface Waves ◽

Wave Field ◽

Internal Waves ◽

Wave Spectrum ◽

Coupled Model ◽

Internal Gravity Waves ◽

Growth Time

A surface-wave/internal-wave mode coupled model is constructed to describe the energy transfer from a linear surface wave field on the ocean to a linear internal wave field. Expressed in terms of action-angle variables the dynamic equations have a particularly useful form and are solved both numerically and in some analytic approximations. The growth time for internal waves generated by the resonant interaction of surface waves is calculated for an equilibrium spectrum of surface waves and for both the Garrett-Munk and two-layer models of the undersea environment. We find energy transfer rates as a function of undersea parameters which are much faster than those based on the constant Brunt-ViiisSila model used by Kenyon (1968) and which are consistent with the experiments of Joyce (1974). The modulation of the surface-wave spectrum by internal waves is also calculated, yielding a ‘mottled’ appearance of the ocean surface similar to that observed in photographs taken from an ERTS1 satellite (Ape1 et al. 1975b).

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Revisiting the Generation of Internal Waves by Resonant Interaction with Surface Waves

Journal of Physical Oceanography ◽

10.1175/jpo-d-15-0064.1 ◽

2016 ◽

Vol 46 (8) ◽

pp. 2335-2350 ◽

Cited By ~ 7

Author(s):

Dirk Olbers ◽

Carsten Eden

Keyword(s):

Internal Wave ◽

Surface Waves ◽

Wave Field ◽

Internal Waves ◽

Mixed Layer ◽

High Frequency ◽

Transfer Rate ◽

Ocean Model ◽

Interaction Process ◽

Internal Wave Field

AbstractTwo surface waves can interact to produce an internal gravity wave by nonlinear resonant coupling. The process has been called spontaneous creation (SC) because it operates without internal waves being initially present. Previous studies have shown that the generated internal waves have high frequency close to the local Brunt–Väisälä frequency and wavelengths that are much larger than those of the participating surface waves, and that the spectral transfer rate of energy to the internal wave field is small compared to other generation processes. The aim of the present analysis is to provide a global map of the energy transfer into the internal wave field by surface–internal wave interaction, which is found to be about 10−3 TW in total, based on a realistic wind-sea spectrum (depending on wind speed), mixed layer depths, and stratification below the mixed layer taken from a state-of-the-art numerical ocean model. Unlike previous calculations of the spectral transfer rate based on a vertical mode decomposition, the authors use an analytical framework that directly derives the energy flux of generated internal waves radiating downward from the mixed layer base. Since the radiated waves are of high frequency, they are trapped and dissipated in the upper ocean. The radiative flux thus feeds only a small portion of the water column, unlike in cases of wind-driven near-inertial waves that spread over the entire ocean depth before dissipating. The authors also give an estimate of the interior dissipation and implied vertical diffusivities due to this process. In an extended appendix, they review the modal description of the SC interaction process, completed by the corresponding counterpart, the modulation interaction process (MI), where a preexisting internal wave is modulated by a surface wave and interacts with another one. MI establishes a damping of the internal wave field, thus acting against SC. The authors show that SC overcomes MI for wind speeds exceeding about 10 m s−1.

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