scholarly journals Testing Lagrangian Theories of Internal Wave Spectra. Part II: Varying the Number of Waves

2009 ◽  
Vol 66 (5) ◽  
pp. 1101-1125 ◽  
Author(s):  
G. P. Klaassen
Keyword(s):  
Internal Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Spectrum ◽  
Doppler Spread ◽  
Wave Spectra ◽  
Single Wave ◽  
Wave Fields ◽  
Large Numbers ◽  
Lagrangian Frame

Abstract It has been proposed by Allen and Joseph, Hines, and Chunchuzov that the kinematic advection produced by superpositions of sinusoidal Lagrangian gravity waves confined to lower vertical wavenumbers m provides an explanation for the quasi-universal m−3 Eulerian spectral tails commonly found at higher m in the oceans and the atmosphere. In support of these theories, Hines has proposed a prototype wave spectrum claimed to meet criteria for Lagrangian linearity and the production of m−3 Eulerian spectra. Although the shape of the Lagrangian spectrum is claimed not to play a major role in this process, Hines has argued that moderately large numbers of waves are required to ensure quasilinear behavior in the Lagrangian frame. The present results demonstrate that, for amplitudes consistent with measurements of saturated waves in the middle atmosphere and for wavenumbers consistent with Hines’ prototype, adiabatic excesses do not diminish with increasing numbers of waves; in contrast, consistency with adiabatic constraints is only achieved in the limit of a single wave, for which the advective nonlinearity u · ∇ vanishes. Moreover, fields with strong singularities yield Eulerian tail slopes as large as −1.6, whereas those with lesser violations of adiabatic constraints yield Eulerian spectral tail slopes that are much steeper (more strongly negative) than −3. The implications for theories based on superpositions of Lagrangian sinusoidal waves, for the Hines quasilinear criteria, and for the Hines Doppler-spread theory and parameterization are addressed. The results are also relevant for experimentalists interested in spectral analysis of internal wave fields.

scholarly journals Testing Lagrangian Theories of Internal Wave Spectra. Part I: Varying the Amplitude and Wavenumbers

2009 ◽  
Vol 66 (5) ◽  
pp. 1077-1100 ◽  
Author(s):  
G. P. Klaassen
Keyword(s):  
Gravity Waves ◽  
Middle Atmosphere ◽  
Three Dimensional ◽  
Small Scale ◽  
Wave Spectra ◽  
Wave Fields ◽  
Turbulent Eddies ◽  
Stretching Deformation ◽  
Hydrostatic Balance ◽  
Field Approaches

Abstract A growing body of literature has been built on the premise that kinematic advection produced by linear superpositions of sinusoidal Lagrangian gravity waves confined to lower vertical wavenumbers can provide an explanation for quasi-universal Eulerian spectral tails commonly found in the oceans and the atmosphere. Recently, Hines has established criteria delineating the circumstances in which Eulerian and Lagrangian spectra differ. For conditions in which Hines claims Lagrangian linearity and the production of quasi-universal Eulerian m−3 spectra, a kinematic advection model based on ensembles of seven nonstanding Lagrangian waves reveals the presence of gross violations of continuity and adiabaticity as well as severe departures from hydrostatic balance. Similar infractions are found for other seven-wave ensembles having a broad range of amplitudes and wavenumbers typical of saturated wave fields in the middle atmosphere. Furthermore, m−3 spectra are found only as the Lagrangian wave field approaches a singular state. The singularities in the Lagrangian to Eulerian transformation are induced by stretching deformation fields that form during the superposition of sinusoidal waves with nonparallel wave vectors. Such deformation fields are known to be unstable with respect to three-dimensional vortices. The results strongly suggest that saturated middle atmosphere wave fields are frequently accompanied by small-scale turbulent eddies.

scholarly journals Consistent Scale Interaction of Gravity Waves in the Doppler Spread Parameterization

2009 ◽  
Vol 66 (5) ◽  
pp. 1434-1449 ◽  
Author(s):  
Erich Becker ◽  
Charles McLandress
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
General Circulation ◽  
Middle Atmosphere ◽  
Wave Spectrum ◽  
Upper Atmosphere ◽  
Doppler Spread ◽  
Vertical Diffusion ◽  
Wave Damping ◽  
Scale Interaction

Abstract The standard Doppler spread parameterization of gravity waves, which was proposed by C.-O. Hines and has been applied in a number of middle atmosphere general circulation models, is extended by the inclusion of all effects associated with vertical diffusion. Here the Wentzel–Kramers–Brillouin (WKB) approximation is employed to calculate the vertical propagation of the wave spectrum in the presence of wave damping. According to the scale interaction between quasi-stationary turbulence and the larger nonturbulent flow, all vertical diffusion applied to the resolved flow should damp the parameterized gravity waves as well. Hence, the unobliterated part of the gravity wave spectrum is subject to diffusive damping by the following processes: 1) the background diffusion derived from the model’s boundary layer vertical diffusion scheme, which may extend into the middle atmosphere, 2) molecular diffusion, and 3) the turbulent diffusion resulting from the truncation of the gravity wave spectrum by Doppler spreading, which thus feeds back on the unobliterated gravity waves. The extended Doppler spread parameterization is examined using perpetual July simulations performed with a mechanistic general circulation model. For reasonable parameter settings, the convergence of the potential temperature flux cannot be neglected in the sensible heat budget, especially in the thermosphere. Less gravity wave flux enters the model thermosphere when vertical diffusion is included, thus avoiding the need for artificial means to control the parameterized gravity waves in the upper atmosphere. The zonal wind in the tropical middle and upper atmosphere is found to be especially sensitive to gravity wave damping by diffusion.

scholarly journals Interaction Features of Internal Wave Breathers in a Stratified Ocean

Fluids ◽  
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.

scholarly journals On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere

2009 ◽  
Vol 27 (11) ◽  
pp. 4105-4124 ◽  
Author(s):  
I. P. Chunchuzov
Keyword(s):  
Wave Field ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Spectrum ◽  
Broad Band ◽  
Internal Gravity Waves ◽  
Wave Number ◽  
Band Spectrum ◽  
Relative Temperature ◽  
Lagrangian Variables

Abstract. The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.

scholarly journals Internal Wave Radiation through Surface Mixed Layer Turbulence

2019 ◽  
Vol 49 (7) ◽  
pp. 1827-1844
Author(s):  
Lars Czeschel ◽  
Carsten Eden
Keyword(s):  
Internal Wave ◽  
Mixed Layer ◽  
Gravity Waves ◽  
Transition Layer ◽  
Wave Spectrum ◽  
Internal Gravity Waves ◽  
Heat Fluxes ◽  
Wave Radiation ◽  
Substantial Part ◽  
Surface Mixed Layer

AbstractIn a series of large-eddy simulations with different forcing, we study the generation of internal gravity waves at the base of the surface mixed layer. If turbulent eddies act as obstacles and undulate the base of the mixed layer, horizontal velocities associated with inertial oscillations and Ekman dynamics can move the obstacles relative to the stratified interior, exciting internal gravity waves similar to lee waves. We find strong evidence that the “obstacle mechanism” is able to excite large parts of the internal wave spectrum, including near inertial waves. The high-frequency part of the excited wave spectrum is filtered by the increased stratification in the transition layer between the mixed layer and lower stratified interior, but a substantial part of the wave spectrum is able to overcome this barrier, hence contributing to interior mixing. The magnitude of the downward-radiated energy below the transition layer depends on the source of turbulence, but we show that the obstacle mechanism, especially under destabilizing heat fluxes, has the potential to contribute considerably to the internal wave energy in the interior ocean.

scholarly journals Dynamics of Orographic Gravity Waves Observed in the Mesosphere over the Auckland Islands during the Deep Propagating Gravity Wave Experiment (DEEPWAVE)

2016 ◽  
Vol 73 (10) ◽  
pp. 3855-3876 ◽  
Author(s):  
Stephen D. Eckermann ◽  
Dave Broutman ◽  
Jun Ma ◽  
James D. Doyle ◽  
Pierre-Dominique Pautet ◽  
...  
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Breaking ◽  
Large Amplitude ◽  
Middle Atmosphere ◽  
Three Dimensional ◽  
Surface Flow ◽  
Heating Rates ◽  
Wave Fields ◽  
Wave Experiment

Abstract On 14 July 2014 during the Deep Propagating Gravity Wave Experiment (DEEPWAVE), aircraft remote sensing instruments detected large-amplitude gravity wave oscillations within mesospheric airglow and sodium layers at altitudes z ~ 78–83 km downstream of the Auckland Islands, located ~1000 km south of Christchurch, New Zealand. A high-altitude reanalysis and a three-dimensional Fourier gravity wave model are used to investigate the dynamics of this event. At 0700 UTC when the first observations were made, surface flow across the islands’ terrain generated linear three-dimensional wave fields that propagated rapidly to z ~ 78 km, where intense breaking occurred in a narrow layer beneath a zero-wind region at z ~ 83 km. In the following hours, the altitude of weak winds descended under the influence of a large-amplitude migrating semidiurnal tide, leading to intense breaking of these wave fields in subsequent observations starting at 1000 UTC. The linear Fourier model constrained by upstream reanalysis reproduces the salient aspects of observed wave fields, including horizontal wavelengths, phase orientations, temperature and vertical displacement amplitudes, heights and locations of incipient wave breaking, and momentum fluxes. Wave breaking has huge effects on local circulations, with inferred layer-averaged westward flow accelerations of ~350 m s−1 h−1 and dynamical heating rates of ~8 K h−1, supporting recent speculation of important impacts of orographic gravity waves from subantarctic islands on the mean circulation and climate of the middle atmosphere during austral winter.

Interharmonics in internal gravity waves generated by tide-topography interaction

2008 ◽  
Vol 611 ◽  
pp. 61-95 ◽  
Author(s):  
ALEXANDER S. KOROBOV ◽  
KEVIN G. LAMB
Keyword(s):  
Internal Wave ◽  
Gravity Waves ◽  
Wave Spectrum ◽  
Tidal Flow ◽  
Internal Gravity Waves ◽  
Wave Band ◽  
Wave Interactions ◽  
Highly Nonlinear ◽  
Tidal Frequency ◽  
Forced Waves

The dynamics and spectrum of internal gravity waves generated in a linearly stratified fluid by tidal flow over a flat-topped ridge are investigated at five different latitudes using an inviscid two-dimensional numerical model. The resulting wave field includes progressive freely propagating waves which satisfy the dispersion relation, and forced waves which are trapped non-propagating oscillations with frequencies outside the internal wave band. The flow is largely stable with respect to shear instabilities, and, throughout the runs, there is a negligibly small amount of overturning which is confined to the highly nonlinear regions along the sloping topography and where tidal beams reflect from the boundaries. The wave spectrum exhibits a self-similar structure with prominent peaks at tidal harmonics and interharmonics, whose magnitudes decay exponentially with frequency. Two strong subharmonics are generated by an instability of tidal beams which is particularly strong for near-critical latitudes where the Coriolis frequency is half the tidal frequency. When both subharmonics are within the free internal wave range (as in cases 0°–20° N), they form a resonant triad with the tidal harmonic. When at least one of the two subharmonics is outside of the range (as in cases 30°–40° N) the observed instability is no longer a resonant triad interaction. We argue that the two subharmonics are generated by parametric subharmonic instability that can produce both progressive and forced waves. Other interharmonics are produced through wave–wave interactions and are not an artefact of Doppler shifting as assumed by previous authors. As the two subharmonics are, in general, not proper fractions of the tidal frequency, the wave–wave interactions are capable of transferring energy to a continuum of frequencies.

scholarly journals Momentum and Energy Transport by Gravity Waves in Stochastically Driven Stratified Flows. Part II: Radiation of Gravity Waves from a Gaussian Jet

2008 ◽  
Vol 65 (7) ◽  
pp. 2308-2325 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Brian F. Farrell
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Energy Transport ◽  
Middle Atmosphere ◽  
Wave Spectrum ◽  
Flux Divergence ◽  
Stochastic Forcing ◽  
Forced Waves ◽  
Horizontal Wavelength ◽  
Wave Momentum

Abstract Interaction between the midlatitude jet and gravity waves is examined, focusing on the nonnormality of the underlying linear dynamics, which plays an essential role in processing the wave activity and selecting structures that dominate wave momentum and energy transport. When the interior of a typical midlatitude jet is stochastically forced, waves with short horizontal wavelength are trapped inside the jet and deposit momentum and energy at jet interior critical levels. Longer waves transport momentum and energy away from the jet, and the resulting momentum flux divergence produces a significant deceleration of the tropospheric and lower-stratospheric jet. This induced drag is found to depend on the shape of the jet and on the horizontal wavelength of the excited waves, reaching a maximum at wavelength λx = 20 km and leading to a deceleration O(1) m s−1 day−1 for a stochastic forcing rate of 0.1 W m−2 distributed over the height of the jet. This deceleration is robust to changes in static stability but is reduced when the stochastic forcing is correlated over too long a time. Implications of gravity wave absorption for middle-atmosphere circulation are discussed, focusing on differences implied for acceleration of the winter and summer midlatitude upper-stratospheric jets. The tropospheric flow is found not only to passively filter transiting waves, but also to amplify portions of the wave spectrum in conjunction with the distributed forcing, leading to enhanced gravity wave momentum and energy fluxes in agreement with observations linking middle-atmosphere enhanced variance with regions of high jet velocities.

Evaluation of Directional Analysis Methods for Low-Frequency Waves to Predict LNGC Motion Response in Nearshore Areas

2013 ◽  
Author(s):  
Sanne van Essen ◽  
Arne van der Hout ◽  
René Huijsmans ◽  
Olaf Waals
Keyword(s):  
Shallow Water ◽  
Wave Field ◽  
Wave Spectrum ◽  
Low Frequency ◽  
Wave Frequency ◽  
Stochastic Methods ◽  
Wave Spectra ◽  
Wave Fields ◽  
Free Wave

Because LNG terminals are located increasingly close to shore, the importance of shallow-water effects associated with low-frequency (LF) waves increases as well. The LF wave spectrum in these areas is generally complex, with multiple frequency peaks and/or directional peaks due to LF wave interaction with the shore. Both free and bound LF waves at the same frequency can be present. Since LF waves are potentially very significant for moored vessel motions, it is important to include their effect in an early stage of the terminal design. This requires an efficient and relatively simple tool able to estimate the LF wave spectrum in nearshore areas. The benefit of such a procedure with respect to state-of-the-art response methods is the ability to include the LF free wave distribution in a local wave field in the vessel response calculation. The objectives of the present study are to identify such a tool, and to evaluate the use of its output as input for a vessel motion calculation. Three methods, designed for the determination of wave spectra of free wave-frequency (WF) waves, were applied to artificial LF wave fields for comparison of their performance. Two stochastic methods, EMEP (Hashimoto et al., 1994) and BDM (Hashimoto et al., 1987) and one deterministic method, r-DPRA (De Jong and Borsboom, 2012) were selected for this comparison. The foreseen application is beyond the formal capabilities for which these three methods were intended. However, in this study we have investigated how far we can take these existing methods for the determination of directional LF wave spectra. Sensitivity analyses showed that the EMEP method is the most suitable method of the three for a range of LF wave fields. The reconstructed LF wave spectra using EMEP resembled the input spectra most closely over the whole range of water depths and frequencies, although its performance deteriorated with increasing water depth and wave frequency. Subsequently, a first effort was made to use the information in the reconstructed EMEP LF wave spectrum of a representative shallow-water wave field for a first estimate of the motions of a moored LNG carrier. The results were acceptable. This is a first indication that EMEP output might be used to calculate the motions of an LNG carrier moored in shallow water.

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