Resonance of internal gravity wave by a bottom-wall oscillation in a square cavity

2002 ◽  
Author(s):  
Seo Young Kim ◽  
Sung Ki Kim ◽  
Byung Ha Kang
Keyword(s):  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Bottom Wall ◽  
Square Cavity ◽  
Wall Oscillation

On parametric instabilities of finite-amplitude internal gravity waves

1982 ◽  
Vol 119 ◽  
pp. 367-377 ◽  
Author(s):  
J. Klostermeyer
Keyword(s):  
Gravity Wave ◽  
Internal Gravity Wave ◽  
Maximum Growth ◽  
Numerical Approach ◽  
Internal Gravity Waves ◽  
Resonant Interaction ◽  
Finite Amplitude ◽  
Interaction Diagram ◽  
Parametric Instabilities ◽  
Boussinesq Fluid

The equations describing parametric instabilities of a finite-amplitude internal gravity wave in an inviscid Boussinesq fluid are studied numerically. By improving the numerical approach, discarding the concept of spurious roots and considering the whole range of directions of the Floquet vector, Mied's work is generalized to its full complexity. In the limit of large disturbance wavenumbers, the unstable disturbances propagate in the directions of the two infinite curve segments of the related resonant-interaction diagram. They can therefore be classified into two families which are characterized by special propagation directions. At high wavenumbers the maximum growth rates converge to limits which do not depend on the direction of the Floquet vector. The limits are different for both families; the disturbance waves propagating at the smaller angle to the basic gravity wave grow at the larger rate.

scholarly journals Global, Non-Parametric, Non-Iterative Optimization of Time-Averaged Quantities under Small, Time-Varying Forcing: An Application to a Thermal Convection Field

2018 ◽  
Author(s):  
Hideshi Ishida ◽  
Shiho Ihara ◽  
Chiharu Okema ◽  
Shohei Yamada ◽  
Genta Kawahara
Keyword(s):  
Thermal Convection ◽  
Internal Gravity Wave ◽  
Mean Value ◽  
Small Time ◽  
Time Varying ◽  
Square Cavity ◽  
Iterative Optimization ◽  
Wave Resonance ◽  
Ordinary Differential Equation Systems ◽  
Non Parametric

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

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

2019 ◽  
Vol 49 (3) ◽  
pp. 737-749 ◽  
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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