The First Integrals of Nonlinear Acoustic Gravity Wave Equations

2000 ◽  
Vol 61 (5) ◽  
pp. 526-526 ◽  
Author(s):  
Zhaonan Liu
Keyword(s):  
Gravity Wave ◽  
Wave Equations ◽  
First Integrals ◽  
Acoustic Gravity Wave ◽  
Nonlinear Acoustic

scholarly journals Time-Reversal Analogy by Nonlinear Acoustic–Gravity Wave Triad Resonance

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 91 ◽  
Author(s):  
Usama Kadri
Keyword(s):  
Wave Packet ◽  
Gravity Wave ◽  
Time Reversal ◽  
Sudden Change ◽  
Wave Theory ◽  
Acoustic Mode ◽  
Acoustic Gravity Wave ◽  
Surface Gravity Wave ◽  
Energy Pumping ◽  
Nonlinear Acoustic

Time reversal of free-surface water (gravity) waves due to a sudden change in the effective gravity has been extensively studied in recent years. Here, we show that an analogy to time-reversal can be obtained using nonlinear acoustic-gravity wave theory. More specifically, we present a mathematical model for the evolution of a time-reversed gravity wave packet from a nonlinear resonant triad perspective. We show that the sudden appearance of an acoustic mode in analogy to a sudden vertical oscillation of the liquid film, can resonate effectively with the original gravity wave packet causing energy pumping into an oppositely propagating (time-reversed) surface gravity wave of an almost identical shape.

Influence of the upper atmosphere inhomogeneity on acoustic gravity wave propagation

2012 ◽  
Vol 18 (4(77)) ◽  
pp. 30-36 ◽  
Author(s):  
Y.I. Kryuchkov ◽  
◽  
O.K. Cheremnykh ◽  
A.K. Fedorenko ◽  
◽  
...  
Keyword(s):  
Wave Propagation ◽  
Gravity Wave ◽  
Upper Atmosphere ◽  
Acoustic Gravity Wave

Acoustic gravity wave propagation past the antipode

1974 ◽  
Vol 55 (S1) ◽  
pp. S75-S75
Author(s):  
Wayne A. Kinney ◽  
Christopher Y. Kapper ◽  
Allan D. Pierce
Keyword(s):  
Wave Propagation ◽  
Gravity Wave ◽  
Acoustic Gravity Wave

Amplification of energy flux of nonlinear acoustic waves in a gas-filled tube under an axial temperature gradient

2002 ◽  
Vol 456 ◽  
pp. 377-409 ◽  
Author(s):  
N. SUGIMOTO ◽  
K. TSUJIMOTO
Keyword(s):  
Boundary Layer ◽  
Temperature Gradient ◽  
Energy Flux ◽  
Acoustic Waves ◽  
Wave Equations ◽  
Main Flow ◽  
Nonlinear Wave Equations ◽  
Axial Temperature Gradient ◽  
Axial Temperature ◽  
Nonlinear Acoustic

This paper considers nonlinear acoustic waves propagating unidirectionally in a gas-filled tube under an axial temperature gradient, and examines whether the energy flux of the waves can be amplified by thermoacoustic effects. An array of Helmholtz resonators is connected to the tube axially to avoid shock formation which would otherwise give rise to nonlinear damping of the energy flux. The amplification is expected to be caused by action of the boundary layer doing reverse work, in the presence of the temperature gradient, on the acoustic main flow outside the boundary layer. By the linear theory, the velocity at the edge of the boundary layer is given in terms of the fractional derivatives of the axial velocity of the gas in the acoustic main flow. It is clearly seen how the temperature gradient controls the velocity at the edge. The velocity is almost in phase with the heat flux into the boundary layer from the wall. With effects of both the boundary layer and the array of resonators taken into account, nonlinear wave equations for unidirectional propagation in the tube are derived. Assuming a constant temperature gradient along the tube, the evolution of compression pulses is solved numerically by imposing the initial profiles of both an acoustic solitary wave and of a square pulse. It is revealed that when a positive gradient is imposed, the excess pressure decreases while the particle velocity increases and that the total energy flux can indeed be amplified if the gradient is suitable.

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