Optical properties of Wannier excitons in the linear and weakly nonlinear regime

1990 ◽  
Vol 42 (5) ◽  
pp. 2959-2976 ◽  
Author(s):  
Jan R. Kuklinski ◽  
Shaul Mukamel
Keyword(s):  
Optical Properties ◽  
Nonlinear Regime ◽  
Weakly Nonlinear

The Linear and Weakly-Nonlinear Stability of a Core Annular Flow in a Corrugated Tube

2000 ◽  
Author(s):  
Hsien-Hung Wei ◽  
David S. Rumschitzki
Keyword(s):  
Thin Film ◽  
Nonlinear Stability ◽  
Annular Flow ◽  
Linear Instability ◽  
Base Flow ◽  
Nonlinear Regime ◽  
Weakly Nonlinear ◽  
Corrugated Tube

Abstract Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the limit of thin film and small corrugation are examined. Asymptotic techniques are used to derive the corrugated base flow and corresponding linear and weakly nonlinear stability equations. Interesting features show that the corrugation interaction can excite linear instability, but the nonlinearity still can suppress such instability in the weakly nonlinear regime.

scholarly journals Steep capillary-gravity waves in oscillatory shear-driven flows

2009 ◽  
Vol 640 ◽  
pp. 131-150 ◽  
Author(s):  
SHREYAS V. JALIKOP ◽  
ANNE JUEL
Keyword(s):  
Surface Tension ◽  
Gravity Waves ◽  
Pitchfork Bifurcation ◽  
Nonlinear Regime ◽  
Radius Of Curvature ◽  
Square Root ◽  
Capillary Length ◽  
Weakly Nonlinear ◽  
Gravitational Forces ◽  
Steep Waves

We study steep capillary-gravity waves that form at the interface between two stably stratified layers of immiscible liquids in a horizontally oscillating vessel. The oscillatory nature of the external forcing prevents the waves from overturning, and thus enables the development of steep waves at large forcing. They arise through a supercritical pitchfork bifurcation, characterized by the square root dependence of the height of the wave on the excess vibrational Froude number (W, square root of the ratio of vibrational to gravitational forces). At a critical valueWc, a transition to a linear variation inWis observed. It is accompanied by sharp qualitative changes in the harmonic content of the wave shape, so that trochoidal waves characterize the weakly nonlinear regime, but ‘finger’-like waves form forW≥Wc. In this strongly nonlinear regime, the wavelength is a function of the product of amplitude and frequency of forcing, whereas forW<Wc, the wavelength exhibits an explicit dependence on the frequency of forcing that is due to the effect of viscosity. Most significantly, the radius of curvature of the wave crests decreases monotonically withWto reach the capillary length forW=Wc, i.e. the lengthscale for which surface tension forces balance gravitational forces. ForW<Wc, gravitational restoring forces dominate, but forW≥Wc, the wave development is increasingly defined by localized surface tension effects.

Elliptic instability of a stratified fluid in a rotating cylinder

2010 ◽  
Vol 660 ◽  
pp. 240-257 ◽  
Author(s):  
D. GUIMBARD ◽  
S. LE DIZÈS ◽  
M. LE BARS ◽  
P. LE GAL ◽  
S. LEBLANC
Keyword(s):  
Stratified Fluid ◽  
Angular Frequency ◽  
Nonlinear Regime ◽  
Finite Cylinder ◽  
Linear Growth Rate ◽  
Small Eccentricity ◽  
Weakly Nonlinear ◽  
Instability Modes ◽  
Centrifugal Instability ◽  
New Type

In this paper, we analyse the characteristics of the elliptic instability in a finite cylinder in the presence of both background rotation and axial stratification. A general formula for the linear growth rate of the stationary sinuous modes is derived including viscous and detuning effects in the limit of small eccentricity. This formula is discussed and compared to experimental results which are obtained in a cylinder filled with salted water for two different eccentricities by varying the stratification, the background rotation and the cylinder rotation. A good agreement with the theory concerning the domain of instability of the sinuous modes is demonstrated. Other elliptic instability modes, oscillating at the cylinder angular frequency are also evidenced together with a new type of instability mode, which could be connected to a centrifugal instability occurring during the experimental phase of spin-up. The nonlinear regime of the elliptic instability is also documented. In contrast with the homogeneous case, no cycle involving growth, breakdown and re-laminarization is observed in the presence of strong stratification. The elliptic instability in a stratified fluid seems to yield either a persistent turbulent state or a weakly nonlinear regime.

scholarly journals Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime

2015 ◽  
Vol 22 (11) ◽  
pp. 112112 ◽  
Author(s):  
Wanhai Liu ◽  
Yulian Chen ◽  
Changping Yu ◽  
Xinliang Li
Keyword(s):  
Taylor Instability ◽  
Nonlinear Regime ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

The nonlinear evolution of zonally symmetric equatorial inertial instability

2003 ◽  
Vol 474 ◽  
pp. 245-273 ◽  
Author(s):  
STEPHEN D. GRIFFITHS
Keyword(s):  
Long Memory ◽  
Initial Conditions ◽  
Zonal Flow ◽  
Nonlinear Regime ◽  
Mean Flow ◽  
Coriolis Parameter ◽  
Weakly Nonlinear ◽  
Flow Change ◽  
Inertial Instability ◽  
The Mean

The inertial instability of equatorial shear flows is studied, with a view to understanding observed phenomena in the Earth's stratosphere and mesosphere. The basic state is a zonal flow of stratified fluid on an equatorial β-plane, with latitudinal shear. The simplest self-consistent model of the instability is used, so that the basic state and the disturbances are zonally symmetric, and a vertical diffusivity provides the scale selection. We study the interaction between the inertial instability, which takes the form of periodically varying disturbances in the vertical, and the mean flow, where ‘mean’ is a vertical mean.The weakly nonlinear regime is investigated analytically, for flows with an arbitrary dependence on latitude. An amplitude equation of the form dA/dt = A−k2A∫[mid ]A[mid ]2dt is derived for the disturbances, and the evolving stability properties of the mean flow are discussed. In the final steady state, the disturbances vanish, but there is a persistent mean flow change that stabilizes the flow. However, the magnitude of the mean flow change depends strongly on the initial conditions, so that the system has a long memory. The analysis is extended to include the effects of Rayleigh friction and Newtonian cooling, destroying the long-memory property.A more strongly nonlinear regime is investigated with the help of numerical simulations, extending the results up to the point where the instability leads to density contour overturning. The instability is shown to lead to a homogenization of fQ¯ around the initially unstable region, where f is the Coriolis parameter, and Q¯ is the vertical mean of the potential vorticity. As the instability evolves, the line of zero Q¯ moves polewards, rather than equatorwards as might be expected from a simple self-neutralization argument.

Sign in / Sign up

Export Citation Format

Share Document