A one-dimensional gravity wave spectrum

The one-dimensional gravity wave model (GWM) is the result of ignoring the convection term in the Saint-Venant Equations (SVEs), and has the characteristics of fast numerical calculation and low stability requirements. To study its performances and limitations in 1D dam-break flood, this paper verifies the model using a dam-break experiment. The experiment was carried out in a large-scale flume with depth ratios (initial downstream water depth divided by upstream water depth) divided into 0 and 0.1~0.4. The data were collected by image processing technology, and the hydraulic parameters, such as water depth, flow discharge, and wave velocity, were selected for comparison. The experimental results show that the 1D GWM performs an area with constant hydraulic parameters, which is quite different from the experimental results in the dry downstream case. For a depth ratio of 0.1, the second weak discontinuity point, which is connected to the steady zone in the 1D GWM, moves upstream, which is contrary to the experimental situation. For depth ratios of 0.2~0.4, the moving velocity of the second weak discontinuity point is faster than the experimental value, while the velocity of the shock wave is slower. However, as the water depth ratio increases, the hydraulic parameters calculated by 1D GWM in the steady zone gradually approach the experimental value.

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Evolution of a gravity wave spectrum through a current gradient

Journal of Geophysical Research Atmospheres ◽

10.1029/jc095ic12p22141 ◽

1990 ◽

Vol 95 (C12) ◽

pp. 22141 ◽

Cited By ~ 12

Author(s):

Gerd N. Trulsen ◽

Kristian B. Dysthe ◽

Jan Trulsen

Keyword(s):

Gravity Wave ◽

Wave Spectrum ◽

A Current

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Spin-Wave Spectrum in the Sinusoidal Superlattice with Amplitude and Phase Inhomogeneities

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.215.385 ◽

2014 ◽

Vol 215 ◽

pp. 385-388

Author(s):

Valter A. Ignatchenko ◽

Denis S. Tsikalov

Keyword(s):

Spin Wave ◽

Density Of States ◽

Wave Spectrum ◽

The Self ◽

One Dimensional ◽

Consistent Approximation ◽

Self Consistent ◽

Greens Function ◽

The One ◽

Spin Wave Spectrum

Effects of both the phase and the amplitude inhomogeneities of different dimensionalities on the Greens function and on the one-dimensional density of states of spin waves in the sinusoidal superlattice have been studied. Processes of multiple scattering of waves from inhomogeneities have been taken into account in the self-consistent approximation.

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On the Nonlinear Transfer of Energy in the Peak of a Gravity Wave Spectrum

Turbulent Fluxes Through the Sea Surface, Wave Dynamics, and Prediction ◽

10.1007/978-1-4612-9806-9_21 ◽

1978 ◽

pp. 319-334 ◽

Cited By ~ 1

Author(s):

M. J. H. Fox

Keyword(s):

Gravity Wave ◽

Wave Spectrum ◽

Nonlinear Transfer

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

Journal of the Atmospheric Sciences ◽

10.1175/jas3905.1 ◽

2007 ◽

Vol 64 (5) ◽

pp. 1509-1529 ◽

Cited By ~ 10

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.

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Numerical Evaluation of Energy Transfers in Internal Gravity Wave Spectra of the Ocean

Journal of Physical Oceanography ◽

10.1175/jpo-d-18-0075.1 ◽

2019 ◽

Vol 49 (3) ◽

pp. 737-749 ◽

Cited By ~ 6

Author(s):

Carsten Eden ◽

Friederike Pollmann ◽

Dirk Olbers

Keyword(s):

Fine Structure ◽

Gravity Wave ◽

Numerical Evaluation ◽

Weak Interactions ◽

Wave Spectrum ◽

Internal Gravity Wave ◽

Spectral Energy ◽

Spectral Slope ◽

Energy Transfers ◽

Mixing Rates

AbstractSpectral energy transfers by internal gravity wave–wave interactions for given empirical energy spectra are evaluated numerically from the kinetic equation that is derived from the assumption of weak interactions. Wave spectrum parameters, such as bandwidth, spectral slope, and Coriolis frequency f, are varied, as is the spectral resolution. In agreement with previous studies, we find in all cases a forward energy cascade toward smaller vertical and horizontal wavelengths. Energy sinks due to the transfers are predominantly at frequencies between 2f and 3f. While the mechanism of the energy transfer differs partly from findings of previous studies, a parameterization for internal wave dissipation—which is used in the fine structure parameterization to estimate dissipation and mixing rates from observations—agrees well with the numerical evaluation of the energy transfers. We also find a dependency of the energy transfers on the spectral slope, offering the possibility to decrease the bias of the fine structure parameterization by improving the knowledge about the spatial variations of this (and other) spectral parameter.

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On the non-linear energy transfer in a gravity-wave spectrum. Part 3. Evaluation of the energy flux and swell-sea interaction for a Neumann spectrum

Journal of Fluid Mechanics ◽

10.1017/s002211206300032x ◽

1963 ◽

Vol 15 (3) ◽

pp. 385-398 ◽

Cited By ~ 124

Author(s):

K. Hasselmann

Keyword(s):

Energy Transfer ◽

Gravity Wave ◽

Wave Spectrum ◽

Low Frequency ◽

Low Frequencies ◽

Frequency Peak ◽

Non Linear ◽

Gain Energy ◽

Rate Of Decay ◽

Linear Interactions

The energy transfer due to non-linear interactions between the components of a gravity-wave spectrum discussed in Parts 1 and 2 of this paper is evaluated for a fully and partially developed Neumann spectrum with various spreading factors. The characteristic time scales of the energy transfer are found to be typically of the order of a few hours. In all cases the high frequencies and the low-frequency peak are found to gain energy from an intermediate range of frequencies. The transfer of energy to very low frequencies and to waves travelling at large angles to the main propagation direction of the spectrum is negligible. Computations are presented also for the rate of decay of swell interacting with local wind-generated seas (represented by a Neumann spectrum). An appreciable decay is found only for swell frequencies in the same range as those of the local sea.

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