摘要:

A mechanism which may lead to algebraic growth, followed by exponential decay, of small nonaxisymmetric disturbances in pipe flow is considered. The mechanism is interpreted as a direct resonance between the perturbations of the pressure and the streamwise velocity. The eigenvalue problems for the pressure and the velocity modes have been solved numerically for complex streamwise wave number, and 36 resonances have been investigated. A plot of the propagation speed versus the damping rate shows that the resonances follow certain sequences as the azimuthal wave number increases. The largest propagation speed is found to be ≈ 0.69 times the centerline velocity. No lowest speed is obtained, and as the azimuthal wave number increases the propagation speed decreases. The effects of changing the Reynolds number have also been investigated. It is found that the streamwise wave number and the damping rate are proportional to 1/RasR→ ∞. The complex phase speed and the propagation speed become independent ofRin the same

ISSN:0022-2526    

DOI:10.1002/sapm198980295

年代:1989

数据来源: WILEY

摘要:

The solutions of the equationare discussed in the limitρ→ 0. The solutions which oscillate about − |t| ast→ ∞ have asymptotic expansions whose leading terms arewhereÃ+, ,Ã−, and are constants. The connection problem is to determine the asymptotic expansion at + ∞. In other words, we wish to find (Ã+, ) as functions ofÃ−and The nonlinear solutions withñnot small are analyzed by using the method of averaging. It is shown that this method breaks down for small amplitudes. In this case a solution can be obtained on [0, ∞) as a small amplitude perturbation about the exact nonoscillating solutionW(t) whose asymptotic expansion isThis is a solution of (1) which corresponds toÃ+≡ 0 in (2). A quantity which determines the scale of the small amplitude response is −W'(0). This quantity is found to be exponentially small. The determination of this constant is shown to reduce to a solution of the equation for the first Painlevé transcendent. The asymptotic behavior of the required solution is determined by

ISSN:0022-2526    

DOI:10.1002/sapm1989802109

年代:1989

数据来源: WILEY

摘要:

The model equations describing two‐dimensional convection in a fluid system driven by three diffusing components are studied. For such a model Griffiths found the state of pure conduction could become unstable to simultaneous steady and oscillatory convection. When the diffusing agents are temperature, salt, and angular velocity, Arneodo et al. found five instabilities of the rest state, including three multiple instabilities. In this paper we return to the model introduced by Griffiths, and, identifying his multiple instability as one of those found by Arneodo et al., we use dynamical systems theory to derive and study the evolution equations for the amplitudes of convection close to bifurcatio

ISSN:0022-2526    

DOI:10.1002/sapm1989802137

年代:1989

数据来源: WILEY

摘要:

A theory for soliton automata is developed and applied to the analysis and prediction of patterns in their behavior. A complete characterization and method of construction of 1‐periodic particles is given. A general evolution theorem (GET) is obtained which provides significant information for a state in terms of preceding states. Application of this theorem yields several interesting results predicting periodicity and solitonic collisions. The GET explains and is based on a fundamental property of soliton automata, observed and analyzed in this paper, namely that pieces of information are lost on the left and reappear on the righ

ISSN:0022-2526    

DOI:10.1002/sapm1989802165

年代:1989

数据来源: WILEY