Propagation of small-scale gravity waves through large-scale internal wave fields: Eikonal effects at low-frequency approximation critical levels

Abstract A heuristic model is used to study the synoptic response to mountain gravity waves (GWs) absorbed at directional critical levels. The model is a semigeostrophic version of the Eady model for baroclinic instability adapted by Smith to study lee cyclogenesis. The GWs exert a force on the large-scale flow where they encounter directional critical levels. This force is taken into account in the model herein and produces potential vorticity (PV) anomalies in the midtroposphere. First, the authors consider the case of an idealized mountain range such that the orographic variance is well separated between small- and large-scale contributions. In the absence of tropopause, the PV produced by the GW force has a surface impact that is significant compared to the surface response due to the large scales. For a cold front, the GW force produces a trough over the mountain and a larger-amplitude ridge immediately downstream. It opposes somehow to the response due to the large scales of the mountain range, which is anticyclonic aloft and cyclonic downstream. For a warm front, the GW force produces a ridge over the mountain and a trough downstream; hence it reinforces the response due to the large scales. Second, the robustness of the previous results is verified by a series of sensitivity tests. The authors change the specifications of the mountain range and of the background flow. They also repeat some experiments by including baroclinic instabilities, or by using the quasigeostrophic approximation. Finally, they consider the case of a small-scale orographic spectrum representative of the Alps. The significance of the results is discussed in the context of GW parameterization in the general circulation models. The results may also help to interpret the complex PV structures occurring when mountain gravity waves break in a baroclinic environment.

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

International Journal of Geophysics ◽

10.1155/2012/863792 ◽

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.

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Evaluating the Global Internal Wave Model IDEMIX Using Finestructure Methods

Journal of Physical Oceanography ◽

10.1175/jpo-d-16-0204.1 ◽

2017 ◽

Vol 47 (9) ◽

pp. 2267-2289 ◽

Cited By ~ 16

Author(s):

Friederike Pollmann ◽

Carsten Eden ◽

Dirk Olbers

Keyword(s):

Internal Wave ◽

Gravity Waves ◽

Wave Energy ◽

Turbulent Mixing ◽

Large Scale ◽

Internal Gravity Waves ◽

Small Scale ◽

Radiation Balance ◽

Dissipation Rates ◽

Ocean Models

AbstractSmall-scale turbulent mixing affects large-scale ocean processes such as the global overturning circulation but remains unresolved in ocean models. Since the breaking of internal gravity waves is a major source of this mixing, consistent parameterizations take internal wave energetics into account. The model Internal Wave Dissipation, Energy and Mixing (IDEMIX) predicts the internal wave energy, dissipation rates, and diapycnal diffusivities based on a simplification of the spectral radiation balance of the wave field and can be used as a mixing module in global numerical simulations. In this study, it is evaluated against finestructure estimates of turbulent dissipation rates derived from Argo float observations. In addition, a novel method to compute internal gravity wave energy from finescale strain information alone is presented and applied. IDEMIX well reproduces the magnitude and the large-scale variations of the Argo-derived dissipation rate and energy level estimates. Deficiencies arise with respect to the detailed vertical structure or the spatial extent of mixing hot spots. This points toward the need to improve the forcing functions in IDEMIX, both by implementing additional physical detail and by better constraining the processes already included in the model. A prominent example is the energy transfer from the mesoscale eddies to the internal gravity waves, which is identified as an essential contributor to turbulent mixing in idealized simulations but needs to be better understood through the help of numerical, analytical, and observational studies in order to be represented realistically in ocean models.

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Parametric instability of internal gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112075000547 ◽

1975 ◽

Vol 67 (4) ◽

pp. 667-687 ◽

Cited By ~ 61

Author(s):

A. D. McEwan ◽

R. M. Robinson

Keyword(s):

Internal Wave ◽

Large Scale ◽

Wave Spectrum ◽

Parametric Instability ◽

Mathieu Equation ◽

Internal Gravity Waves ◽

Small Scale ◽

Preliminary Calculation ◽

Theoretical Predictions ◽

Oceanic Internal Wave

A continuously stratified fluid, when subjected to a weak periodic horizontal acceleration, is shown to be susceptible to a form of parametric instability whose time dependence is described, in its simplest form, by the Mathieu equation. Such an acceleration could be imposed by a large-scale internal wave field. The growth rates of small-scale unstable modes may readily be determined as functions of the forcing-acceleration amplitude and frequency. If any such mode has a natural frequency near to half the forcing frequency, the forcing amplitude required for instability may be limited in smallness only by internal viscous dissipation. Greater amplitudes are required when boundaries constrain the form of the modes, but for a given bounding geometry the most unstable mode and its critical forcing amplitude can be defined.An experiment designed to isolate the instability precisely confirms theoretical predictions, and evidence is given from previous experiments which suggest that its appearance can be the penultimate stage before the traumatic distortion of continuous stratifications under internal wave action.A preliminary calculation, using the Garrett & Munk (197%) oceanic internal wave spectrum, indicates that parametric instability could occur in the ocean at scales down to that of the finest observed microstructure, and may therefore have a significant role to play in its formation.

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Internal tide energy flux over a ridge measured by a co-located ocean glider and moored ADCP

10.5194/os-2019-15 ◽

2019 ◽

Author(s):

Rob Hall ◽

Barbara Berx ◽

Gillian Damerell

Keyword(s):

Energy Flux ◽

Large Scale ◽

Low Frequency ◽

Internal Tide ◽

Small Scale ◽

Potential Density ◽

The North ◽

Model Study ◽

Continental Shelves ◽

Alternative Approach

Abstract. Internal tide energy flux is an important diagnostic for the study of energy pathways in the ocean, from large-scale input by the surface tide, to small-scale dissipation by turbulent mixing. Accurate calculation of energy flux requires repeated full-depth measurements of both potential density (ρ) and horizontal current velocity (u) over at least a tidal cycle and over several weeks to resolve the internal spring-neap cycle. Typically, these observations are made using full-depth oceanographic moorings that are vulnerable to being fished-out by commercial trawlers when deployed on continental shelves and slopes. Here we test an alternative approach to minimise these risks, with u measured by a low-frequency ADCP moored near the seabed and ρ measured by an autonomous ocean glider holding station by the ADCP. The method is used to measure the M2 internal tide radiating from the Wyville Thompson Ridge in the North Atlantic. The observed energy flux (4.2 ± 0.2 kW m−1) compares favourably with historic observations and a previous numerical model study. Error in the energy flux calculation due to imperfect co-location of the glider and ADCP is estimated by sub-sampling potential density in an idealised internal tide field along pseudorandomly distributed glider paths. The error is considered acceptable (

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Interaction Features of Internal Wave Breathers in a Stratified Ocean

Fluids ◽

10.3390/fluids5040205 ◽

2020 ◽

Vol 5 (4) ◽

pp. 205

Author(s):

Ekaterina Didenkulova ◽

Efim Pelinovsky

Keyword(s):

Internal Wave ◽

Internal Waves ◽

Gravity Waves ◽

Fourth Order ◽

Numerical Experiments ◽

Vries Equation ◽

Internal Gravity Waves ◽

Wave Fields ◽

Tidal Waves ◽

Stratified Ocean

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.

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Modulation of Internal Gravity Waves in a Multiscale Model for Deep Convection on Mesoscales

Journal of the Atmospheric Sciences ◽

10.1175/2010jas3269.1 ◽

2010 ◽

Vol 67 (8) ◽

pp. 2504-2519 ◽

Cited By ~ 7

Author(s):

Daniel Ruprecht ◽

Rupert Klein ◽

Andrew J. Majda

Keyword(s):

Gravity Waves ◽

Large Scale ◽

Energy Transport ◽

Deep Convection ◽

Potential Temperature ◽

Internal Gravity Waves ◽

Small Scale ◽

Closed Model ◽

Large Scale Flow ◽

Effective Stability

Abstract Starting from the conservation laws for mass, momentum, and energy together with a three-species bulk microphysics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multiscale asymptotic techniques. From the leading-order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime on which the analysis is based. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy. A two-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and microscale up- and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and nonsaturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: (i) it reduces vertical energy transport by waves, (ii) it increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) it introduces a new lower horizontal cutoff wavenumber in addition to the well-known high wavenumber cutoff, and (iv) moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime.

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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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Unsteady Structure Measurement of Cloud Cavitation on a Foil Section Using Conditional Sampling Technique

Journal of Fluids Engineering ◽

10.1115/1.3243624 ◽

1989 ◽

Vol 111 (2) ◽

pp. 204-210 ◽

Cited By ~ 130

Author(s):

A. Kubota ◽

H. Kato ◽

H. Yamaguchi ◽

M. Maeda

Keyword(s):

High Speed ◽

Large Scale ◽

Laser Doppler Anemometry ◽

Low Frequency ◽

Sampling Technique ◽

Experimental Result ◽

Small Scale ◽

Conditional Sampling ◽

Cloud Cavitation ◽

Structure Of Flow

The structure of flow around unsteady cloud cavitation on a stationary two-dimensional hydrofoil was investigated experimentally using a conditional sampling technique. The unsteady flow velocity around the cloud cavitation was measured by a Laser Doppler Anemometry (LDA) and matched with the unsteady cavitation appearance photographed by a high-speed camera. This matching procedure was performed using data from pressure fluctuation measurements on the foil surface. The velocities were divided into two components using a digital filter, i.e., large-scale (low-frequency) and small-scale (high frequency) ones. The large-scale component corresponds with the large-scale unsteady cloud cavitation motion. In this manner, the unsteady structure of the cloud cavitation was successfully measured. The experimental result showed that the cloud cavitation observed at the present experiment had a vorticity extremum at its center and a cluster containing many small cavitation bubbles. The convection velocity of the cavitation cloud was much lower than the uniform velocity. The small-scale velocity fluctuation was not distributed uniformly in the cavitation cloud, but was concentrated near its boundary.

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Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment.

10.5194/egusphere-egu2020-9374 ◽

2020 ◽

Author(s):

Costanza Rodda ◽

Uwe Harlander

Keyword(s):

Gravity Waves ◽

Large Scale ◽

Small Scale ◽

Turbulent Regime ◽

Weakly Nonlinear ◽

Geostrophic Flows ◽

Balanced Flow ◽

Energy And Momentum ◽

Open Question ◽

Inertia Gravity Waves

Inertia-gravity waves (IGWs) are known to play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when they propagate upwards. An open question is to which extent nearly linear IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale. In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes k-3 for the large scales and k-5/3 for smaller scales. By separating the spectra into a vortex and wave part, it emerges that at the largest scales in the mesoscale range the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition towards a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.

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