On the neutral stability of cross‐waves

1989 ◽  
Vol 1 (7) ◽  
pp. 1128-1132 ◽  
Author(s):  
E. Kit ◽  
L. Shemer
Keyword(s):  
Neutral Stability ◽  
Cross Waves

The mode number dependence of neutral stability of cross-waves

1990 ◽  
Vol 9 (3) ◽  
pp. 148-152 ◽  
Author(s):  
L. Shemer ◽  
S. Lichter
Keyword(s):  
Mode Number ◽  
Neutral Stability ◽  
Cross Waves

scholarly journals Modulated, frequency-locked, and chaotic cross-waves

1991 ◽  
Vol 225 ◽  
pp. 371-394 ◽  
Author(s):  
William B. Underhill ◽  
Seth Lichter ◽  
Andrew J. Bernoff
Keyword(s):  
Modulational Instability ◽  
Rectangular Channel ◽  
Wave Structure ◽  
Mode Analysis ◽  
Spanwise Direction ◽  
Neutral Stability ◽  
Coupled Mode ◽  
Weakly Coupled ◽  
Arnold Tongues ◽  
Cross Waves

Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by the circle-map theory describing weakly coupled oscillators. Some of the observed tongues are apparently folded by a subcritical bifurcation, with the tips of the tongues lying on the unstable manifold folded under the observed stable manifold. Near the intersection of the neutral stability curves for two adjacent modes, a standing wave localized on one side of the tank was observed in agreement with the coupled-mode analysis of Ayanle, Bernoff & Lichter (1990). At large cross-wave amplitudes, the spanwise wave structure apparently breaks up, because of modulational instability, into coherent soliton-like structures that propagate in the spanwise direction and are reflected by the sidewalls.

scholarly journals Analysis of the unstable Tollmien–Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

2009 ◽  
Vol 623 ◽  
pp. 167-185
Author(s):  
M. R. TURNER ◽  
P. W. HAMMERTON
Keyword(s):  
Asymptotic Theory ◽  
Free Stream ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
S Wave ◽  
Stability Equation ◽  
Stability Point ◽  
Tollmien Schlichting

The interaction between free-stream disturbances and the boundary layer on a body with a rounded leading edge is considered in this paper. A method which incorporates calculations using the parabolized stability equation in the Orr–Sommerfeld region, along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalized to bodies with an inviscid slip velocity which tends to a constant far downstream. We present results for the position of the lower branch neutral stability point and the magnitude of the unstable Tollmien–Schlichting (T-S) mode at this point for both a parabolic body and the Rankine body. For the Rankine body, which has an adverse pressure gradient along its surface far from the nose, we find a double maximum in the T-S wave amplitude for sufficiently large Reynolds numbers.

Stability Analysis of Thermocapillary Convection of B2O3/Sapphire Melt in an Annular Pool

2021 ◽  
Vol 1036 ◽  
pp. 175-184
Author(s):  
Dong Ming Mo
Keyword(s):  
Stability Analysis ◽  
Temperature Distribution ◽  
Thermocapillary Convection ◽  
Silicone Oil ◽  
Liquid Interface ◽  
Sapphire Crystal ◽  
Neutral Stability ◽  
Unstable Flow ◽  
Fluid Layers ◽  
Lower Fluid

Aiming at the thermocapillary convection stability of sapphire crystal grown by liquid-encapsulated Czochralski method, by non-linear numerical simulation, obtained the flow function and temperature distribution of R-Z cross section, as well as the velocity and temperature distribution at liquid-liquid interface and monitoring point of B2O3/sapphire melt in annular two liquid system, covered with solid upper wall and in microgravity. By means of linear stability analysis, obtained the neutral stability curve and critical stability parameters of the system, and revealed the temperature fluctuation of the liquid-liquid interface. The calculated results of B2O3/sapphire melt were compared with 5cSt silicone oil/HT-70. The results show that under the same geometrical conditions, the flow of B2O3/sapphire melt system is more unstable than 5cSt silicone oil/HT-70, there are two unstable flow patterns, radial three-dimensional steady flow cell and hydrothermal waves near the hot wall. The larger the ratio of Pr number of upper and lower fluid layers is, the better the effect of restraining the flow of lower fluid layers is.

scholarly journals How significant is the usual assumption of neutral stability in evapotranspiration estimating models?

1999 ◽  
Vol 6 (2) ◽  
pp. 155-158 ◽  
Author(s):  
M Anadranistakis ◽  
P Kerkides ◽  
A Liakatas ◽  
S Alexandris ◽  
A Poulovasilis
Keyword(s):  
Neutral Stability ◽  
Usual Assumption

scholarly journals Surface Stress and Atmospheric Boundary Layer Response to Mesoscale SST Structure in Coupled Simulations of the Northern California Current System

2019 ◽  
Vol 148 (1) ◽  
pp. 259-287
Author(s):  
R. M. Samelson ◽  
L. W. O’Neill ◽  
D. B. Chelton ◽  
E. D. Skyllingstad ◽  
P. L. Barbour ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Wind Stress ◽  
Current System ◽  
California Current ◽  
Heat Fluxes ◽  
Neutral Stability ◽  
Northern California ◽  
Coupling Coefficients ◽  
California Current System ◽  
Northern California Current

Abstract The influence of mesoscale sea surface temperature (SST) variations on wind stress and boundary layer winds is examined from coupled ocean–atmosphere numerical simulations and satellite observations of the northern California Current System. Model coupling coefficients relating the divergence and curl of wind stress and wind to downwind and crosswind SST gradients are generally smaller than observed values and vary by a factor of 2 depending on planetary boundary layer (PBL) scheme, with values larger for smoothed fields on the 0.25° observational grid than for unsmoothed fields on the 12-km model grid. Divergence coefficients are larger than curl coefficients on the 0.25° grid but not on the model grid, consistent with stronger scale dependence for the divergence response than for curl in a spatial cross-spectral analysis. Coupling coefficients for 10-m equivalent neutral stability winds are 30%–50% larger than those for 10-m wind, implying a correlated effect of surface-layer stability variations. Crosswind surface air temperature and SST gradients are more strongly coupled than downwind gradients, while the opposite is true for downwind and crosswind heat flux and SST gradients. Midlevel boundary layer wind coupling coefficients show a reversed response relative to the surface that is predicted by an analytical model; a predicted second reversal with height is not seen in the simulations. The relative values of coupling coefficients are consistent with previous results for the same PBL schemes in the Agulhas Return Current region, but their magnitudes are smaller, likely because of the effect of mean wind on perturbation heat fluxes.

Stability Analysis of a Thin Pseudoplastic Fluid with Condensation Effects Flowing on a Rotating Circular Disk

2013 ◽  
Vol 699 ◽  
pp. 413-421
Author(s):  
Ming Che Lin
Keyword(s):  
Linear Stability ◽  
Kinematic Model ◽  
Circular Disk ◽  
Vital Role ◽  
Linear Growth Rate ◽  
Flow Index ◽  
Neutral Stability ◽  
Pseudoplastic Fluid ◽  
Linear Solution ◽  
By Products

This paper investigates the linear stability of a thin axisymmetric pseudoplastic fluid with condensation effects flowing on a rotating circular disk. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The method of normal mode is applied to study the linear stability. The neutral stability curve and the linear growth rate are obtained subsequently as the by-products of linear solution. The study reveals that the rotation number generates a destabilizing effect in pseudoplastic fluid. The degree of the flow index n plays a vital role in stabilizing the film flow.

scholarly journals Neutral Stability, Rate Propagation, and Critical Branching in Feedforward Networks

2013 ◽  
Vol 25 (7) ◽  
pp. 1768-1806 ◽  
Author(s):  
N. Alex Cayco-Gajic ◽  
Eric Shea-Brown
Keyword(s):  
Neural Networks ◽  
Markov Chain ◽  
Mean Field ◽  
Neutral Stability ◽  
Feedforward Networks ◽  
Firing Rates ◽  
Wide Range ◽  
Complex Models ◽  
Dynamical Properties ◽  
Parameter Ranges

Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing patterns. We seek the simplest setting in which these properties emerge, clarifying their origin and relationship in random, feedforward networks of McCullochs-Pitts neurons. Two key parameters are the thresholds at which neurons fire spikes and the overall level of feedforward connectivity. When neurons have low thresholds, we show that there is always a connectivity for which the properties in question all occur, that is, these networks preserve overall firing rates from layer to layer and produce broad distributions of activity in each layer. This fails to occur, however, when neurons have high thresholds. A key tool in explaining this difference is the eigenstructure of the resulting mean-field Markov chain, as this reveals which activity modes will be preserved from layer to layer. We extend our analysis from purely excitatory networks to more complex models that include inhibition and local noise, and find that both of these features extend the parameter ranges over which networks produce the properties of interest.

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