Parametric instability of internal gravity waves

1975 ◽  
Vol 67 (4) ◽  
pp. 667-687 ◽  
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.

scholarly journals Evaluating the Global Internal Wave Model IDEMIX Using Finestructure Methods

2017 ◽  
Vol 47 (9) ◽  
pp. 2267-2289 ◽  
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.

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

2010 ◽  
Vol 67 (8) ◽  
pp. 2504-2519 ◽  
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.

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.

scholarly journals The study of the effect of small-scale turbulence on internal gravity waves propagation in a pycnocline

2013 ◽  
Vol 20 (6) ◽  
pp. 977-986 ◽  
Author(s):  
O. A. Druzhinin ◽  
L. A. Ostrovsky ◽  
S. S. Zilitinkevich
Keyword(s):  
Internal Wave ◽  
Internal Gravity Waves ◽  
Small Scale ◽  
Main Attention ◽  
Random Forcing ◽  
Damping Rate ◽  
Waves Propagation ◽  
Scale Turbulence ◽  
Comparison Of The Results ◽  
Semi Empirical

Abstract. This paper presents the results of modeling the interaction between internal waves (IWs) and turbulence using direct numerical simulation (DNS). Turbulence is excited and supported by a random forcing localized in a vertical layer separated from the pycnocline. The main attention is paid to the internal wave damping due to turbulence and comparison of the results with those obtained theoretically by using the semi-empirical approach. It is shown that the IW damping rate predicted by the theory agrees well with the DNS results when turbulence is sufficiently strong to be only weakly perturbed by the internal wave; however, the theory overestimates the damping rate of IWs for a weaker turbulence. The DNS parameters are matched to the parameters of the laboratory experiment, and an extrapolation to the oceanic scales is also provided.

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 Global Characterization of the Ocean’s Internal Wave Spectrum

2020 ◽  
Vol 50 (7) ◽  
pp. 1871-1891 ◽  
Author(s):  
Friederike Pollmann
Keyword(s):  
Internal Wave ◽  
Gravity Wave ◽  
Spectral Characteristics ◽  
Wave Spectrum ◽  
Internal Gravity Wave ◽  
Ocean Dynamics ◽  
Small Scale ◽  
Northwest Pacific ◽  
Spatial And Temporal Variability ◽  
Spectral Parameters

AbstractA key ingredient of energetically consistent ocean models is the parameterized link between small-scale turbulent mixing, an important energy source of large-scale ocean dynamics, and internal gravity wave energetics. Theory suggests that this link depends on the wave field’s spectral characteristics, but because of the paucity of suitable observations, its parameterization typically relies on a model spectrum [Garrett–Munk (GM)] with constant parameters. Building on the so-called “finestructure method,” internal gravity wave spectra are derived from vertical strain profiles obtained from Argo floats to provide a global estimate of the spatial and temporal variability of the GM model’s spectral parameters. For spectral slopes and wavenumber scales, the highest variability and the strongest deviation from the model’s canonical parameters are observed in the North Atlantic, the northwest Pacific, and the Southern Ocean. Internal wave energy levels in the upper ocean are well represented by the GM model value equatorward of approximately 50°, while they are up to two orders of magnitude lower poleward of this latitude. The use of variable spectral parameters in the energy level calculation hides the seasonal cycle in the northwest Pacific that was previously observed for constant parameters. The global estimates of how the GM model’s spectral parameters vary in space and time are hence expected to add relevant detail to various studies on oceanic internal gravity waves, deepening the understanding of their energetics and improving parameterizations of the mixing they induce.

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

1976 ◽  
Vol 77 (1) ◽  
pp. 185-208 ◽  
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).

scholarly journals Effective Diffusivity in Baroclinic Flow

2014 ◽  
Vol 71 (3) ◽  
pp. 972-984 ◽  
Author(s):  
Eric M. Leibensperger ◽  
R. Alan Plumb
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Effective Diffusivity ◽  
Static Stability ◽  
Small Scale ◽  
Tracer Transport ◽  
Theoretical Predictions ◽  
Diffusive Processes ◽  
Theoretical Developments

Abstract Large-scale chaotic stirring stretches tracer contours into filaments containing fine spatial scales until small-scale diffusive processes dissipate tracer variance. Quantification of tracer transport in such circumstances is possible through the use of Nakamura’s “effective diffusivity” diagnostics, which make clear the controlling role of stirring, rather than small-scale dissipation, in large-scale transport. Existing theory of effective diffusivity is based on a layerwise approach, in which tracer variance is presumed to cascade via horizontal (or isentropic) stirring to small-scale horizontal (or isentropic) diffusion. In most geophysical flows of interest, however, baroclinic shear will tilt stirred filamentary structures into almost-horizontal sheets, in which case the thinnest dimension is vertical; accordingly, it will be vertical (or diabatic) diffusion that provides the ultimate dissipation of variance. Here new theoretical developments define effective diffusivity in such flows. In the frequently relevant case of isentropic stirring, it is shown that the theory is, in most respects, unchanged from the case of isentropic diffusion: effective isentropic diffusivity is controlled by the isentropic stirring and, it is argued, largely independent of the nature of the ultimate dissipation. Diabatic diffusion is not amplified by the stirring, although it can be modestly enhanced through eddy modulation of static stability. These characteristics are illustrated in numerical simulations of a stratospheric flow; in regions of strong stirring, the theoretical predictions are well supported, but agreement is less good where stirring is weaker.

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