Gravity waves on shear flows

2001 ◽  
Vol 443 ◽  
pp. 293-299 ◽  
Author(s):  
JOHN MILES
Keyword(s):  
Eigenvalue Problem ◽  
Gravity Waves ◽  
Wave Speed ◽  
Upper And Lower Bounds ◽  
Wave Approximation ◽  
Long Wave ◽  
Running Wave ◽  
Long Wave Approximation ◽  
Variational Formulations ◽  
Critical Wavenumber

The eigenvalue problem for gravity waves on a shear flow of depth h and non-inflected velocity profile U(y) (typically parabolic) is revisited, following Burns (1953) and Yih (1972). Complementary variational formulations that provide upper and lower bounds to the Froude number F as a function of the wave speed c and wavenumber k are constructed. These formulations are used to improve Burns's long-wave approximation and to determine Yih's critical wavenumber k∗, for which the wave is stationary (c = 0) and to which k must be inferior for the existence of an upstream running wave.

Long-Wave Approximation to the 3-D Capillary-Gravity Waves

2012 ◽  
Vol 44 (4) ◽  
pp. 2920-2948 ◽  
Author(s):  
Mei Ming ◽  
Ping Zhang ◽  
Zhifei Zhang
Keyword(s):  
Gravity Waves ◽  
Wave Approximation ◽  
Long Wave ◽  
Long Wave Approximation

Nonlinear dispersion hyperbolic models of continuous media

2007 ◽  
Vol 5 ◽  
pp. 273-278
Author(s):  
V.Yu Liapidevskii
Keyword(s):  
Boussinesq Equations ◽  
Nonlinear Dispersion ◽  
Order Of Accuracy ◽  
Flow Models ◽  
Wave Approximation ◽  
Long Wave ◽  
Primary Model ◽  
Nonequilibrium Flows ◽  
Internal Inertia ◽  
Long Wave Approximation

Nonequilibrium flows of an inhomogeneous liquid in channels and pipes are considered in the long-wave approximation. Nonlinear dispersion hyperbolic flow models are derived allowing taking into account the influence of internal inertia during the relative motion of phases upon the structure of nonlinear wave fronts. The asymptotic derivation of dispersion hyperbolic models is shown on the example of classical Boussinesq equations. It is shown that the hyperbolic approximation of the equations has the same order of accuracy as the primary model.

scholarly journals NUMERICAL MODELS OF HUGE TSUNAMIS OFF THE SANRIKU COAST

1976 ◽  
Vol 1 (15) ◽  
pp. 61
Author(s):  
Toshio Iwasaki
Keyword(s):  
Numerical Models ◽  
Source Model ◽  
Wave Source ◽  
Sanriku Coast ◽  
Wave Approximation ◽  
Long Wave ◽  
Small Wave ◽  
Wave Heights ◽  
Deep Region ◽  
Long Wave Approximation

Although numerical computations of the generation and propagation of tsunamis are successfully achieved in recent years, modeling of their wave sources is still a big problem. Three kinds of, wave source model, that is statistical, oceanographic and fault model, are studied in this paper. It is found that the first model gives reasonable wave heights as shown in the previous paper, the second one presents roughly one half of those for the first model and the last one produces too small wave heights. Based on the analysis of computed results, nature of undulations off from the shore boundary, directivity of wave propagation and the spindle shaped leading part are discussed. Comparing magnitude of various wave parameters for the leading wave along the minor axis of the wave source, it is shown that the long wave approximation modified by the slope effect illustrates the tsunamis in deep region of the sea and the slope effect is most dominant in shallow region.

Nonlinear dynamics of electrostatic Faraday instability in thin films

2018 ◽  
Vol 855 ◽  
Author(s):  
Dipin S. Pillai ◽  
R. Narayanan
Keyword(s):  
Thin Films ◽  
Standing Waves ◽  
Gas Holdup ◽  
Conducting Liquid ◽  
Mode Instability ◽  
Wave Approximation ◽  
Long Wave ◽  
Faraday Instability ◽  
Unstable Configuration ◽  
Long Wave Approximation

The nonlinear evolution of an interface between a perfect conducting liquid and a perfect dielectric gas subject to periodic electrostatic forcing is studied under the long-wave approximation. It is shown that inertial thin films become unstable to finite-wavelength Faraday modes at the onset, prior to the long-wave pillaring instability reported in the lubrication limit. It is further shown that the pillaring-mode instability is subcritical in nature, with the interface approaching either the top or the bottom wall, depending on the liquid–gas holdup. On the other hand, the Faraday modes exhibit subharmonic or harmonic oscillations that nonlinearly saturate to standing waves at low forcing amplitudes. Unlike the pillaring mode, wherein the interface approaches the wall, Faraday modes may exhibit saturated standing waves when the instability is subcritical. At higher forcing amplitudes, the interface may approach either wall, again depending on the liquid–gas holdup. It is also shown that a gravitationally unstable configuration of such thin films, under the long-wave approximation, cannot be stabilized by periodic electrostatic forcing, unlike mechanical Faraday forcing. In this case, it is observed that the interface exhibits oscillatory sliding behaviour, approaching the wall in an ‘earthworm-like’ motion.

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