Internal gravity wave resonance of thermal convection fields in rectangular cavities with heat-flux vibration (effects of aspect ratio on the fields)

2007 ◽  
Vol 36 (3) ◽  
pp. 158-171 ◽  
Author(s):  
Shota Matsumura ◽  
Hideshi Ishida ◽  
Kazunari Momose ◽  
Genta Kawahara
Keyword(s):  
Heat Flux ◽  
Aspect Ratio ◽  
Gravity Wave ◽  
Thermal Convection ◽  
Internal Gravity Wave ◽  
Wave Resonance

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

2019 ◽  
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 linearly 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.

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.

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