摘要:

Baroclinically unstable Eady waves representing solutions of a two-dimensional, uniform potential vorticity, semigeostrophic model are considered. These semigeostrophic waves are expressed as linear solutions in geostrophic coordinate space (X,Z,T), but they satisfy a nonlinear advection equation in physical space (x,z,t). The transformation of the velocityv(X,Z,T) into a physical space solutionv(x,z,t) is accomplished by an approximate technique that represents a truncation at second-order in the Rossby number. Two nonlinear processes are delineated: there is nonlinearity inherent in the transformation (X,Z,T)→(x,z,t), and there are nonlinear interactions between the waves. Solutions, representing the interaction of two semigeostrophic waves, are determined for initial conditions that span a range of wave-numbers. Under these conditions both single and double frontal structures (one or two concentrated cyclonic shear zones) can develop. The most significant nonlinear interactions between the unstable waves are primarily associated with these concentrated regions of cyclonic shear, and the magnitude of the shear may either be enhanced or diminished by the interacting wave disturbances. The unstable growth rate may vary with time and, in all cases examinedv(x,z,t) develops an infinite slope in a finite timetc. It is shown that two interacting semigeostrophic waves are characterized by a minus eight-third power law spectrum at timetc, a result previously established by Andrews and Hoskins (1978) for one wave. The present results are not significantly altered by the inclusion of an Ekman layer, in which the unstable waves propagate at different phase speeds.

ISSN:0309-1929    

DOI:10.1080/03091928608208795

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

At the short-wave boundary of the instability region, the nonlinearity plays a stabilizing role irrespective of the value of the parameter β, and this includes the region in which the neutral curve has a maximum (β=4.3−3/2for the flowu=tanhy). At the long-wave boundary, there exists a range of wave numbers for which the nonlinearity has a destabilizing effect.

ISSN:0309-1929    

DOI:10.1080/03091928608208796

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The kinematic dynamo problem is investigated for the class of flows u=(Asinz+Ccosy,Bsinx+Acosz,Csiny+Bcosx) which in general have chaotic streamlines. Numerical results are reported for magnetic Reynolds numbersRmup to 450 and various choices ofA,BandC. ForA=B=C=1 dynamo action is present in at least two windows inRm, the first extending from ≈9 to ≈17.5 and the second beyond ≈27. certain symmetries implied by the flow are preserved in the lower window but are broken in the upper. The fastest growing mode shows concentrated cigar-like structures centered on stagnation points in the flow. WhenA,BandCare varied, windows of dynamo action may or may not be present. When one of the coefficients vanishes, the flow becomes two-dimensional and non-chaotic, but with three-dimensional magnetic fields, dynamo action is still possible and has been investigated forRmup to 1500. In the two-dimensional example studied the growth rate achieved a maximum nearRm=300 and then behaved in a way appropriate for a slow dynamo (one whose growth rate tends to zero asRm∞). It is not clear yet whether or not in the three-dimensional case the opposite can happen (fast dynamo). The α-effect that is produced by these helical flows acting on very large-scale magnetic fields is calculated. Surprisingly, it can remain finite even when dynamo action is present at the scale of the flow, as long as certain symmetries are not broken.

ISSN:0309-1929    

DOI:10.1080/03091928608208797

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor