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Thierry Penduff - One of the best experts on this subject based on the ideXlab platform.
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geostrophic turbulence in the frequency Wavenumber domain eddy driven low frequency variability
Journal of Physical Oceanography, 2014Co-Authors: Brian K Arbic, Malte Muller, James G Richman, Jay F Shriver, Andrew J Morten, Robert B Scott, Guillaume Serazin, Thierry PenduffAbstract:AbstractMotivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–Wavenumber domain. Frequency–Wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low Wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged Wavenumbers. Low-frequency, low-Wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean mod...
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geostrophic turbulence in the frequency Wavenumber domain eddy driven low frequency variability
Journal of Physical Oceanography, 2014Co-Authors: Brian K Arbic, Malte Muller, James G Richman, Jay F Shriver, Andrew J Morten, Robert B Scott, Guillaume Serazin, Thierry PenduffAbstract:Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–Wavenumber domain. Frequency–Wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low Wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged Wavenumbers. Low-frequency, low-Wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low Wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.
C. Glorieux - One of the best experts on this subject based on the ideXlab platform.
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On the unwrapping of dispersion curves in the irreducible Brillouin zone by means of a spatial Fourier transform approach
International Journal of Solids and Structures, 2020Co-Authors: N.b. Roozen, L. Labelle, C. GlorieuxAbstract:Using Bloch-Floquet boundary conditions implies a periodicity in both the spatial and Wavenumber domains, causing the numerically computed Wavenumbers to be folded or aliased within the Brillouin zone. A methodology is presented to unwrap the Wavenumber spectrum to extended Brillouin zones using a Fourier transform method in the spatial domain, thus providing new insights on the physical meaning and relative amplitudes of aliased wave components. In addition, a procedure is presented to identify out-of-plane (Lamb wave type) components, which are usually of interest for thin structures. The proposed methodologies were applied to finite element based simulations of a 2D periodic reticulated structure consisting of interconnected rectangular struts with orthorombic symmetry. This reticulated structure was used as a toy model for the skeleton in porous media, focusing on the out-of-plane waves. Laser ultrasonic experiments were conducted to verify the numerical results. Both the simulations and measurement results indicate that, in spite of bandgap features induced by the periodicity of the structure, the dispersion behavior of the out of plane Lamb wave modes in the considered type of structure is similar to the one of the Lamb waves of a homogeneous plate with thickness equal to the one of the struts, both for Wavenumbers within and outside the Irreducible Brillouin Zone.
Mimi Dai - One of the best experts on this subject based on the ideXlab platform.
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kolmogorov s dissipation number and the number of degrees of freedom for the 3d navier stokes equations
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2019Co-Authors: Alexey Cheskidov, Mimi DaiAbstract:Kolmogorov's theory of turbulence predicts that only Wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional (3D) fluid flow. A determining Wavenumber, first introduced by Foias and Prodi for the 2D Navier–Stokes equations, is a mathematical analogue of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining Wavenumber for the 3D Navier–Stokes equations whose time average is bounded by Kolmogorov's dissipation Wavenumber for all solutions on the global attractor whose intermittency is not extreme.
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kolmogorov s dissipation number and the number of degrees of freedom for the 3d navier stokes equations
arXiv: Analysis of PDEs, 2015Co-Authors: Alexey Cheskidov, Mimi DaiAbstract:Kolmogorov's theory of turbulence predicts that only Wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional fluid flow. A determining Wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes equations, is a mathematical analog of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining Wavenumber for the 3D Navier-Stokes equations whose time average is bounded by Kolmogorov's dissipation Wavenumber for all solutions on the global attractor whose intermittency is not extreme.
Brian K Arbic - One of the best experts on this subject based on the ideXlab platform.
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geostrophic turbulence in the frequency Wavenumber domain eddy driven low frequency variability
Journal of Physical Oceanography, 2014Co-Authors: Brian K Arbic, Malte Muller, James G Richman, Jay F Shriver, Andrew J Morten, Robert B Scott, Guillaume Serazin, Thierry PenduffAbstract:AbstractMotivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–Wavenumber domain. Frequency–Wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low Wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged Wavenumbers. Low-frequency, low-Wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean mod...
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geostrophic turbulence in the frequency Wavenumber domain eddy driven low frequency variability
Journal of Physical Oceanography, 2014Co-Authors: Brian K Arbic, Malte Muller, James G Richman, Jay F Shriver, Andrew J Morten, Robert B Scott, Guillaume Serazin, Thierry PenduffAbstract:Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–Wavenumber domain. Frequency–Wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low Wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged Wavenumbers. Low-frequency, low-Wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low Wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.
Ian R. Young - One of the best experts on this subject based on the ideXlab platform.
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The form of the asymptotic depth-limited wind-wave spectrum part III: directional spreading
Coastal Engineering, 2010Co-Authors: Ian R. YoungAbstract:Abstract The directional spreading of both the Wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the Wavenumber and frequency forms are narrowest at the spectral peak and broaden at Wavenumbers (frequencies) both above and below the peak. The directional spreading of the Wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the Wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of Wavenumber spectra, rather than frequency spectra.
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the form of the asymptotic depth limited wind wave spectrum part ii the Wavenumber spectrum
Coastal Engineering, 2009Co-Authors: Ian R. Young, Alexander V BabaninAbstract:Abstract Data from a spatial array of wave gauges is analysed using the Wavelet Directional Method (WDM) to directly determine the Wavenumber spectrum. The data shows that the asymptotic depth-limited Wavenumber spectrum can be represented as a two-parameter form, which is far simpler than the corresponding frequency spectrum. The WDM analysis shows that there are significant nonlinear processes active in the finite depth water, which results in energy being “smeared” across a range of Wavenumbers and frequencies around the standard dispersion shell. As a result, the Wavenumber spectrum has much less peak enhancement than seen in the frequency spectrum obtained with standard Fourier analysis. In addition, the Wavenumber spectrum does not have the clear harmonic previously observed in the finite depth frequency spectrum. This result demonstrates that the harmonic is nonlinearly phase-locked to the spectral peak.
