摘要:

In this paper an analytical method to study the hydrodynamic stability of simple barotropic, non-divergent flows is discussed. The method is based on the variational approach introduced by Arnold and derived from the Lyapunov stability criteria. In this context, the sufficient condition for the stability of a steady barotropic flow ψ(x,y) is obtained whendP(ψ)/dPψ = ψ, the derivative of the absolute vorticityP(ψ), is positive definite. In this case, we discuss the effect of higher derivativesdnP(ψ)/dψnψψ = ψon the non-linear stability. Then we show that some classical examples of oceanic non-divergent flows (i.e. lee waves downstream an Island, steady flows through a Strait, the Fofonoff gyre) are stable to finite-amplitude perturbations.

ISSN:0309-1929    

DOI:10.1080/03091928408219260

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The characteristics of the free stream motion in a two meter wide by ten meter long rotating free surface flow facility are discussed. Experiments on the flow past a right circular cylinder whose axis is parallel to the rotation axis are presented for the following parameter ranges: 2,500≦Re≦37,500; Ro≧1.43; 0.33≦R/H≦1.67; and 0.05≦R/S≦0.25 where Re is the Reynolds number, Ro, the Rossby number,R/H, the cylinder aspect ratio andR/S, the channel blockage factor.

ISSN:0309-1929    

DOI:10.1080/03091928408219261

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo numberD=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. ForD>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for allDand the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.

ISSN:0309-1929    

DOI:10.1080/03091928408219262

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The Lortz dynamo with helical symmetry is re-examined. It is shown that by imposing appropriate boundary conditions the set of possible solutions can be broken down into various classes characterized by the behavior of the mean magnetic field. It is found that, as the cylindrical radius, s, tends to zero, <BΦ> ∼ 0(sj), <Bz> ∼ const + 0(sj−i), where j>5. It is proved that the azimuthal wavenumber associated with the j=5 class is necessarily equal to 2. The existence of at least one cylindrical surface inside which the dynamo is self-sustained is demonstrated. A new simple explicit solution is obtained. The topology the magnetic field is studied and three-dimensional pictures of the magnetic field lines are exhibited. Finally, a criterion for reversal of the magnetic field as a function of radius is ohtained and is applied to our solution.

ISSN:0309-1929    

DOI:10.1080/03091928408219263

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor