Wavenumber transport: scattering of small-scale internal waves by large-scale wavepackets

1995 ◽  
Vol 289 ◽  
pp. 379-405 ◽  
Author(s):  
David L. Bruhwiler ◽  
Tasso J. Kaper
Keyword(s):  
Internal Waves ◽  
High Frequency ◽  
Large Scale ◽  
Wave Interaction ◽  
Initial Distribution ◽  
Small Scale ◽  
Theoretic Model ◽  
Frequency Interval ◽  
Crossing Theory ◽  
Invariance Theory

In this work, we treat the problem of small-scale, small-amplitude, internal waves interacting nonlinearly with a vigorous, large-scale, undulating shear. The amplitude of the background shear can be arbitrarily large, with a general profile, but our analysis requires that the amplitude vary on a length scale longer than the wavelength of the undulations. In order to illustrate the method, we consider the ray-theoretic model due to Broutman & Young (1986) of high-frequency oceanic internal waves that trap and detrap in a near-inertial wavepacket as a prototype problem. The near-inertial wavepacket tends to transport the high-frequency test waves from larger to smaller wavenumber, and hence to higher frequency. We identify the essential physical mechanisms of this wavenumber transport, and we quantify it. We also show that, for an initial ensemble of test waves with frequencies between the inertial and buoyancy frequencies and in which the number of test waves per frequency interval is proportional to the inverse square of the frequency, a single nonlinear wave–wave interaction fundamentally alters this initial distribution. After the interaction, the slope on a log-log plot is nearly flat, whereas initially it was -2. Our analysis captures this change in slope. The main techniques employed are classical adiabatic invariance theory and adiabatic separatrix crossing theory.

scholarly journals Bottom-pressure observations of deep-sea internal hydrostatic and non-hydrostatic motions

2013 ◽  
Vol 714 ◽  
pp. 591-611 ◽  
Author(s):  
Hans van Haren
Keyword(s):  
Hydrostatic Pressure ◽  
High Resolution ◽  
Internal Waves ◽  
High Frequency ◽  
Large Scale ◽  
Temperature Data ◽  
Large Reynolds Number ◽  
Small Scale ◽  
Bottom Pressure ◽  
Sloping Bottom

AbstractIn the ocean, sloping bottom topography is important for the generation and dissipation of internal waves. Here, the transition of such waves to turbulence is demonstrated using an accurate bottom-pressure sensor that was moored with an acoustic Doppler current profiler and high-resolution thermistor string on the sloping side of the ocean guyot ‘Great Meteor Seamount’ (water depth 549 m). The site is dominated by the passage of strong frontal bores, moving upslope once or twice every tidal period, with a trail of high-frequency internal waves. The bore amplitude and precise timing of bore passage vary every tide. A bore induces mainly non-hydrostatic pressure, while the trailing waves induce mainly internal hydrostatic pressure. These separate (internal wave) pressure terms are independently estimated using current and temperature data, respectively. In the bottom-pressure time series, the passage of a bore is barely visible, but the trailing high-frequency internal waves are. A bore is obscured by higher-frequency pressure variations up to ${\sim} 4{\times} 1{0}^{3} ~\mathrm{cpd} \approx 80N$ (cpd, cycles per day; $N$, the large-scale buoyancy frequency). These motions dominate the turbulent state of internal tides above a sloping bottom. In contrast with previous bottom-pressure observations in other areas, infra-gravity surface waves contribute little to these pressure variations in the same frequency range. Here, such waves do not incur observed pressure. This is verified in a consistency test for large-Reynolds-number turbulence using high-resolution temperature data. The high-frequency quasi-turbulent internal motions are visible in detailed temperature and acoustic echo images, revealing a nearly permanently wave-turbulent tide going up and down the bottom slope. Over the entire observational period, the spectral slope and variance of bottom pressure are equivalent to internal hydrostatic pressure due to internal waves in the lower 100 m above the bottom, by non-hydrostatic pressure due to high-frequency internal waves and large-scale overturning. The observations suggest a transition between large-scale internal waves, small-scale internal tidal waves residing on thin (${{\sim} }1~\mathrm{m} $) stratified layers and turbulence.

scholarly journals Internal Waves and Mixing near the Kerguelen Plateau

2015 ◽  
Vol 46 (2) ◽  
pp. 417-437 ◽  
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.

Upscale Energy Transfer by the Vortical Mode and Internal Waves

2014 ◽  
Vol 44 (9) ◽  
pp. 2446-2469 ◽  
Author(s):  
Anne-Marie E. G. Brunner-Suzuki ◽  
Miles A. Sundermeyer ◽  
M.-Pascale Lelong
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Internal Waves ◽  
Numerical Experiments ◽  
Large Scale ◽  
Vertical Shear ◽  
Small Scale ◽  
Driving Mechanism ◽  
Vortex Interaction ◽  
Vertical Scale

Abstract Diapycnal mixing in the ocean is sporadic yet ubiquitous, leading to patches of mixing on a variety of scales. The adjustment of such mixed patches can lead to the formation of vortices and other small-scale geostrophic motions, which are thought to enhance lateral diffusivity. If vortices are densely populated, they can interact and merge, and upscale energy transfer can occur. Vortex interaction can also be modified by internal waves, thus impacting upscale transfer. Numerical experiments were used to study the effect of a large-scale near-inertial internal wave on a field of submesoscale vortices. While one might expect a vertical shear to limit the vertical scale of merging vortices, it was found that internal wave shear did not disrupt upscale energy transfer. Rather, under certain conditions, it enhanced upscale transfer by enhancing vortex–vortex interaction. If vortices were so densely populated that they interacted even in the absence of a wave, adding a forced large-scale wave enhanced the existing upscale transfer. Results further suggest that continuous forcing by the main driving mechanism (either vortices or internal waves) is necessary to maintain such upscale transfer. These findings could help to improve understanding of the direction of energy transfer in submesoscale oceanic processes.

scholarly journals The wave instability pathway to turbulence

2013 ◽  
Vol 724 ◽  
pp. 1-4 ◽  
Author(s):  
Bruce R. Sutherland
Keyword(s):  
Internal Waves ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Wave Beam ◽  
Small Scale ◽  
Monochromatic Wave ◽  
Wave Instability ◽  
Analysis Techniques ◽  
Parametric Subharmonic Instability ◽  
The Waves

AbstractOne way that large-scale oceanic internal waves transfer their energy to small-scale mixing is through parametric subharmonic instability (PSI). But there is a disconnect between theory, which assumes the waves are periodic in space and time, and reality, in which waves are transient and localized. The innovative laboratory experiments and analysis techniques of Bourget et al. (J. Fluid Mech., vol. 723, 2013, pp. 1–20) show that theory can be applied to interpret the generation of subharmonic disturbances from a quasi-monochromatic wave beam. Their methodology and results open up new avenues of investigation into PSI through experiments, simulations and observations.

High‐resolution crosswell imaging of a west Texas carbonate reservoir: Part 1—Project summary and interpretation

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 667-681 ◽  
Author(s):  
Jerry M. Harris ◽  
Richard C. Nolen‐Hoeksema ◽  
Robert T. Langan ◽  
Mark Van Schaack ◽  
Spyros K. Lazaratos ◽  
...  
Keyword(s):  
High Resolution ◽  
High Frequency ◽  
Large Scale ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Small Scale ◽  
Observation Well ◽  
Traveltime Tomography ◽  
Seismic Profiling ◽  
West Texas

A carbon dioxide flood pilot is being conducted in a section of Chevron’s McElroy field in Crane County, west Texas. Prior to [Formula: see text] injection, two high‐frequency crosswell seismic profiles were recorded to investigate the use of seismic profiling for high‐resolution reservoir delineation and [Formula: see text] monitoring. These preinjection profiles provide the baseline for time‐lapse monitoring. Profile #1 was recorded between an injector well and an offset observation well at a nominal well‐to‐well distance of 184 ft (56 m). Profile #2 was recorded between a producing well and the observation well at a nominal distance of 600 ft (183 m). The combination of traveltime tomography and stacked CDP reflection amplitudes demonstrates how high‐frequency crosswell seismic data can be used to image both large and small scale heterogeneity between wells: Transmission traveltime tomography is used to image the large scale velocity variations; CDP reflection imaging is then used to image smaller scale impedance heterogeneities. The resolution capability of crosswell data is clearly illustrated by an image of the Grayburg‐San Andres angular unconformity, seen in both the P‐wave and S‐wave velocity tomograms and the reflection images. In addition to the imaging study, cores from an observation well were analyzed to support interpretation of the crosswell images and assess the feasibility of monitoring changes in [Formula: see text] saturation. The results of this integrated study demonstrate (1) the use of crosswell seismic profiling to produce a high‐resolution reservoir delineation and (2) the possibility for successful monitoring of [Formula: see text] in carbonate reservoirs. The crosswell data were acquired with a piezoelectric source and a multilevel hydrophone array. Both profiles, nearly 80 000 seismic traces, were recorded in approximately 80 hours using a new acquisition technique of shooting on‐the‐fly. This paper presents the overall project summary and interpretation of the results from the near‐offset profile.

scholarly journals Generation of Internal Waves by Eddies Impinging on the Western Boundary of the North Atlantic

2016 ◽  
Vol 46 (4) ◽  
pp. 1067-1079 ◽  
Author(s):  
L. Clément ◽  
E. Frajka-Williams ◽  
K. L. Sheen ◽  
J. A. Brearley ◽  
A. C. Naveira Garabato
Keyword(s):  
Internal Waves ◽  
North Atlantic ◽  
High Frequency ◽  
Large Scale ◽  
Acoustic Doppler Current Profiler ◽  
Relative Vorticity ◽  
Western Boundary ◽  
The North ◽  
Current Profiler ◽  
The North Atlantic

AbstractDespite the major role played by mesoscale eddies in redistributing the energy of the large-scale circulation, our understanding of their dissipation is still incomplete. This study investigates the generation of internal waves by decaying eddies in the North Atlantic western boundary. The eddy presence and decay are measured from the altimetric surface relative vorticity associated with an array of full-depth current meters extending ~100 km offshore at 26.5°N. In addition, internal waves are analyzed over a topographic rise from 2-yr high-frequency measurements of an acoustic Doppler current profiler (ADCP), which is located 13 km offshore in 600-m deep water. Despite an apparent polarity independence of the eddy decay observed from altimetric data, the flow in the deepest 100 m is enhanced for anticyclones (25.2 cm s−1) compared with cyclones (−4.7 cm s−1). Accordingly, the internal wave field is sensitive to this polarity-dependent deep velocity. This is apparent from the eddy-modulated enhanced dissipation rate, which is obtained from a finescale parameterization and exceeds 10−9 W kg−1 for near-bottom flows greater than 8 cm s−1. The present study underlines the importance of oceanic western boundaries for removing the energy of low-mode westward-propagating eddies to higher-mode internal waves.

Ritual Frequency, Emotionality, and Modes of Religiosity

2021 ◽  
pp. 53-81
Author(s):  
Harvey Whitehouse
Keyword(s):  
High Frequency ◽  
Large Scale ◽  
Low Frequency ◽  
New Guinea ◽  
Small Scale ◽  
Complex Societies ◽  
High Arousal ◽  
The World ◽  
Hierarchical Groups ◽  
To Come

Collective rituals tend to come in two kinds: frequently performed but relatively lowkey; rarely enacted but emotionally intense. According to the theory of modes of religiosity, high-frequency but low-arousal rituals produce large-scale hierarchical groups (the doctrinal mode), while low-frequency but high-arousal rituals produce small-scale highly cohesive groups (the imagistic mode). This chapter describes how that theory was first developed while carrying out fieldwork in the New Guinea rainforest. But then the author realized it could help to explain how groups throughout the world take shape and spread, and it could also help to explain how complex societies evolved.

scholarly journals Investigation of High-Frequency Internal Wave Interactions with an Enveloped Inertia Wave

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
B. Casaday ◽  
J. Crockett
Keyword(s):  
Internal Wave ◽  
High Frequency ◽  
Wave Breaking ◽  
Large Scale ◽  
Critical Level ◽  
Low Frequency ◽  
Small Scale ◽  
Wave Interactions ◽  
Frequency Wave ◽  
Action Density

Using ray theory, we explore the effect an envelope function has on high-frequency, small-scale internal wave propagation through a low-frequency, large-scale inertia wave. Two principal interactions, internal waves propagating through an infinite inertia wavetrain and through an enveloped inertia wave, are investigated. For the first interaction, the total frequency of the high-frequency wave is conserved but is not for the latter. This deviance is measured and results of waves propagating in the same direction show the interaction with an inertia wave envelope results in a higher probability of reaching that Jones' critical level and a reduced probability of turning points, which is a better approximation of outcomes experienced by expected real atmospheric interactions. In addition, an increase in wave action density and wave steepness is observed, relative to an interaction with an infinite wavetrain, possibly leading to enhanced wave breaking.

scholarly journals Deep-sea turbulence evolution observed by multiple closely spaced instruments

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chu-Fang Yang ◽  
Wu-Cheng Chi ◽  
Hans van Haren
Keyword(s):  
Kinetic Energy ◽  
Internal Waves ◽  
Deep Sea ◽  
Large Scale ◽  
Time Derivative ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Ocean Bottom ◽  
Seafloor Topography

AbstractTurbulent mixing in the deep ocean is not well understood. The breaking of internal waves on sloped seafloor topography can generate deep-sea turbulence. However, it is difficult to measure turbulence comprehensively due to its multi-scale processes, in addition to flow–flow and flow–topography interactions. Dense, high-resolution spatiotemporal coverage of observations may help shed light on turbulence evolution. Here, we present turbulence observations from four broadband ocean bottom seismometers (OBSs) and a 200-m vertical thermistor string (T-string) in a footprint of 1 × 1 km to characterize turbulence induced by internal waves at a depth of 3000 m on a Pacific continental slope. Correlating the OBS-calculated time derivative of kinetic energy and the T-string-calculated turbulent kinetic energy dissipation rate, we propose that the OBS-detected signals were induced by near-seafloor turbulence. Strong disturbances were detected during a typhoon period, suggesting large-scale inertial waves breaking with upslope transport speeds of 0.2–0.5 m s−1. Disturbances were mostly excited on the downslope side of the array where the internal waves from the Pacific Ocean broke initially and the turbulence oscillated between < 1 km small-scale ridges. Such small-scale topography caused varying turbulence-induced signals due to localized waves breaking. Arrayed OBSs can provide complementary observations to characterize deep-sea turbulence.

Interaction between small-scale surface waves and large-scale internal waves

1978 ◽  
Vol 21 (11) ◽  
pp. 1900 ◽  
Author(s):  
Magdi H. Rizk ◽  
Denny R. S. Ko
Keyword(s):  
Surface Waves ◽  
Internal Waves ◽  
Large Scale ◽  
Small Scale ◽  
Scale Surface
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