scholarly journals Acoustic Bloch wave energy transport and group velocity

1991 ◽  
Vol 89 (4B) ◽  
pp. 1971-1971
Author(s):  
Charles E. Bradley ◽  
David T. Blackstock
Keyword(s):  
Group Velocity ◽  
Wave Energy ◽  
Energy Transport ◽  
Bloch Wave

scholarly journals Another Note on Rossby Wave Energy Flux

2020 ◽  
Vol 50 (2) ◽  
pp. 531-534
Author(s):  
Theodore S. Durland ◽  
J. Thomas Farrar
Keyword(s):  
Group Velocity ◽  
Energy Flux ◽  
Rossby Wave ◽  
Wave Energy ◽  
Energy Equation ◽  
Divergent Part ◽  
Pressure Work ◽  
Wave Energy Flux ◽  
The Difference ◽  
Definition Of

AbstractLonguet-Higgins in 1964 first pointed out that the Rossby wave energy flux as defined by the pressure work is not the same as that defined by the group velocity. The two definitions provide answers that differ by a nondivergent vector. Longuet-Higgins suggested that the problem arose from ambiguity in the definition of energy flux, which only impacts the energy equation through its divergence. Numerous authors have addressed this issue from various perspectives, and we offer one more approach that we feel is more succinct than previous ones, both mathematically and conceptually. We follow the work described by Cai and Huang in 2013 in concluding that there is no need to invoke the ambiguity offered by Longuet-Higgins. By working directly from the shallow-water equations (as opposed to the more involved quasigeostrophic treatment of Cai and Huang), we provide a concise derivation of the nondivergent pressure work and demonstrate that the two energy flux definitions are equivalent when only the divergent part of the pressure work is considered. The difference vector comes from the nondivergent part of the geostrophic pressure work, and the familiar westward component of the Rossby wave group velocity comes from the divergent part of the geostrophic pressure work. In a broadband wave field, the expression for energy flux in terms of a single group velocity is no longer meaningful, but the expression for energy flux in terms of the divergent pressure work is still valid.

scholarly journals Momentum and Energy Transport by Gravity Waves in Stochastically Driven Stratified Flows. Part I: Radiation of Gravity Waves from a Shear Layer

2007 ◽  
Vol 64 (5) ◽  
pp. 1509-1529 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Petros J. Ioannou
Keyword(s):  
Shear Flow ◽  
Shear Layer ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Energy ◽  
Energy Transport ◽  
Wave Spectrum ◽  
Internal Gravity Waves ◽  
Wave Interference ◽  
Wide Range

Abstract In this paper, the emission of internal gravity waves from a local westerly shear layer is studied. Thermal and/or vorticity forcing of the shear layer with a wide range of frequencies and scales can lead to strong emission of gravity waves in the region exterior to the shear layer. The shear flow not only passively filters and refracts the emitted wave spectrum, but also actively participates in the gravity wave emission in conjunction with the distributed forcing. This interaction leads to enhanced radiated momentum fluxes but more importantly to enhanced gravity wave energy fluxes. This enhanced emission power can be traced to the nonnormal growth of the perturbations in the shear region, that is, to the transfer of the kinetic energy of the mean shear flow to the emitted gravity waves. The emitted wave energy flux increases with shear and can become as large as 30 times greater than the corresponding flux emitted in the absence of a localized shear region. Waves that have horizontal wavelengths larger than the depth of the shear layer radiate easterly momentum away, whereas the shorter waves are trapped in the shear region and deposit their momentum at their critical levels. The observed spectrum, as well as the physical mechanisms influencing the spectrum such as wave interference and Doppler shifting effects, is discussed. While for large Richardson numbers there is equipartition of momentum among a wide range of frequencies, most of the energy is found to be carried by waves having vertical wavelengths in a narrow band around the value of twice the depth of the region. It is shown that the waves that are emitted from the shear region have vertical wavelengths of the size of the shear region.

scholarly journals The Hybrid Kelvin–Edge Wave and Its Role in Tidal Dynamics

2010 ◽  
Vol 40 (12) ◽  
pp. 2757-2767 ◽  
Author(s):  
Ziming Ke ◽  
Alexander E. Yankovsky
Keyword(s):  
Group Velocity ◽  
Wave Energy ◽  
Numerical Experiments ◽  
Tidal Energy ◽  
Ocean Modeling ◽  
Edge Wave ◽  
Kelvin Wave ◽  
Regional Ocean Modeling System ◽  
Offshore Wave ◽  
Zero Group

Abstract A full set of long waves trapped in the coastal ocean over a variable topography includes a zero (fundamental) mode propagating with the coast on its right (left) in the Northern (Southern) Hemisphere. This zero mode resembles a Kelvin wave at lower frequencies and an edge wave (Stokes mode) at higher frequencies. At the intermediate frequencies this mode becomes a hybrid Kelvin–edge wave (HKEW), as both rotational effects and the variable depth become important. Furthermore, the group velocity of this hybrid mode becomes very small or even zero depending on shelf width. It is found that in midlatitudes a zero group velocity occurs at semidiurnal (tidal) frequencies over wide (∼300 km), gently sloping shelves. This notion motivated numerical experiments using the Regional Ocean Modeling System in which the incident HKEW with a semidiurnal period propagates over a wide shelf and encounters a narrowing shelf so that the group velocity becomes zero at some alongshore location. The numerical experiments have demonstrated that the wave energy increases upstream of this location as a result of the energy flux convergence while farther downstream the wave amplitude is substantially reduced. Instead of propagating alongshore, the wave energy radiates offshore in the form of Poincaré modes. Thus, it is concluded that the shelf areas where the group velocity of the HKEW becomes zero are characterized by an increased tidal amplitude and (consequently) high tidal energy dissipation, and by offshore wave energy radiation. This behavior is qualitatively consistent with the dynamics of semidiurnal tides on wide shelves narrowing in the direction of tidal wave propagation, including the Patagonia shelf and the South China Sea.

scholarly journals Wave energy attenuation in fields of colliding ice floes – Part 2: A laboratory case study

2019 ◽  
Vol 13 (11) ◽  
pp. 2901-2914 ◽  
Author(s):  
Agnieszka Herman ◽  
Sukun Cheng ◽  
Hayley H. Shen
Keyword(s):  
Sea Ice ◽  
Wave Energy ◽  
Energy Transport ◽  
Video Recording ◽  
Wave Model ◽  
Expansion Method ◽  
Element Model ◽  
Substantial Contribution ◽  
Elastic Plates ◽  
Dissipative Processes

Abstract. This work analyses laboratory observations of wave energy attenuation in fragmented sea ice cover composed of interacting, colliding floes. The experiment, performed in a large (72 m long) ice tank, includes several groups of tests in which regular, unidirectional, small-amplitude waves of different periods were run through floating ice with different floe sizes. The vertical deflection of the ice was measured at several locations along the tank, and video recording was used to document the overall ice behaviour, including the presence of collisions and overwash of the ice surface. The observational data are analysed in combination with the results of two types of models: a model of wave scattering by a series of floating elastic plates, based on the matched eigenfunction expansion method (MEEM), and a coupled wave–ice model, based on discrete-element model (DEM) of sea ice and a wave model solving the stationary energy transport equation with two source terms, describing dissipation due to ice–water drag and due to overwash. The observed attenuation rates are significantly larger than those predicted by the MEEM model, indicating substantial contribution from dissipative processes. Moreover, the dissipation is frequency dependent, although, as we demonstrate in the example of two alternative theoretical attenuation curves, the quantitative nature of that dependence is difficult to determine and very sensitive to assumptions underlying the analysis. Similarly, more than one combination of the parameters of the coupled DEM–wave model (restitution coefficient, drag coefficient and overwash criteria) produce spatial attenuation patterns in good agreement with observed ones over a range of wave periods and floe sizes, making selection of “optimal” model settings difficult. The results demonstrate that experiments aimed at identifying dissipative processes accompanying wave propagation in sea ice and quantifying the contribution of those processes to the overall attenuation require simultaneous measurements of many processes over possibly large spatial domains.

scholarly journals The propagation and absorption of spiral density waves

1970 ◽  
Vol 38 ◽  
pp. 323-325 ◽  
Author(s):  
F. H. Shu
Keyword(s):  
Angular Momentum ◽  
Group Velocity ◽  
Wave Energy ◽  
Radial Direction ◽  
Wave Action ◽  
Spiral Waves ◽  
Stellar Disk ◽  
Density Waves ◽  
Spiral Density Waves

An ‘anti-spiral theorem’ holds with limited validity for the neutral modes of oscillation in a stellar disk - namely, whenever the effects of stellar resonances can be ignored. In the regions between Lindblad resonances, a group of spiral waves will propagate in the radial direction with the group velocity found by Toomre. This propagation occurs with the conservation of ‘wave action’, wave energy, and wave angular momentum.

scholarly journals Energy exchange and wave action conservation for magnetohydrodynamic (MHD) waves in a general, slowly varying medium

2014 ◽  
Vol 32 (12) ◽  
pp. 1495-1510 ◽  
Author(s):  
A. D. M. Walker
Keyword(s):  
Ray Tracing ◽  
Wave Energy ◽  
Energy Exchange ◽  
Energy Transport ◽  
Wave Action ◽  
Mhd Equations ◽  
Alfven Wave ◽  
Mhd Waves ◽  
Sound Waves ◽  
Uniform Compression

Abstract. Magnetohydrodynamic (MHD) waves in the solar wind and magnetosphere are propagated in a medium whose velocity is comparable to or greater than the wave velocity and which varies in both space and time. In the approximation where the scales of the time and space variation are long compared with the period and wavelength, the ray-tracing equations can be generalized and then include an additional first-order differential equation that determines the variation of frequency. In such circumstances the wave can exchange energy with the background: wave energy is not conserved. In such processes the wave action theorem shows that the wave action, defined as the ratio of the wave energy to the frequency in the local rest frame, is conserved. In this paper we discuss ray-tracing techniques and the energy exchange relation for MHD waves. We then provide a unified account of how to deal with energy transport by MHD waves in non-uniform media. The wave action theorem is derived directly from the basic MHD equations for sound waves, transverse Alfvén waves, and the fast and slow magnetosonic waves. The techniques described are applied to a number of illustrative cases. These include a sound wave in a medium undergoing a uniform compression, an isotropic Alfvén wave in a steady-state shear layer, and a transverse Alfvén wave in a simple model of the magnetotail undergoing compression. In each case the nature and magnitude of the energy exchange between wave and background is found.

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