摘要:

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

ISSN:0309-1929    

DOI:10.1080/03091929008219847

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

In this note it is shown that Andrews’ theorem, which states that Arnol'd stability implies symmetry, is not special to fluid mechanics, but holds in the general context of classical mechanics with symmetry. More importantly, we emphasise that in Andrews’ theorem one should consider stability modulo the symmetry group or solution class. We do this by using the energy-Casimir method to prove the stability of two-dimensional ABC flows, even though they arenotsymmetric.

ISSN:0309-1929    

DOI:10.1080/03091929008219848

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The acceptability of zero potential vorticity models as approximations for natural systems of small, but finite, potential vorticity is studied for bounded frontal flows of arbitrary profile. It is demonstrated that all (infinitely) long-wave solutions of the zero potential vorticity front are asymptotic limits for some (not necessarily long-wave) solutions of the small potential vorticity front. In contrast, for downstream-varying solutions there is no simple way of demonstrating this property. These findings suggest that the use of zero potential vorticity models should be carefully examined in other, non-frontal, problems as well. Finally we show that the longwave solutions of the zero potential vorticity flow are at most neutral (quasi-stable).

ISSN:0309-1929    

DOI:10.1080/03091929008219849

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

Fluid of a lower density and viscosity can buoyantly rise through a viscous fluid through conduits that support simple pipe flows. The conduits also support solitary waves which exhibit near soliton behavior. Laboratory experiments on the characteristics of the solitary waves and their interactions have been conducted and compared with theory. The observations of shape and phase speed of individual waves show good agreement with the theoretical predictions. Large amplitude waves traveled slightly faster than the theoretical predictions. The discrepancy is probably due to higher order effects associated with wave slope not accounted for in the theory. Individual wave characteristics (shape, amplitude and speed) were very nearly preserved after collision with another wave. A phase jump of each wave was the main consequence of an interaction. The larger (faster) waves increased in amplitude by an average of 5 percent after collision and their phase speeds decreased by an average of 4 percent. The small wave was unchanged. Numerical solutions overpredicted the magnitude of the observed phase jumps by about 40 percent when compared to the experiments.

ISSN:0309-1929    

DOI:10.1080/03091929008219850

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

ISSN:0309-1929    

DOI:10.1080/03091929008219851

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

Using a contour dynamical algorithm, we have found rotating tripolar V-state solutions for the inviscid Euler equations in two-dimensions. We have studied their geometry as a function of their physical parameters. Their stability was investigated with the aid of contour surgery, and most of the states were found to be stable. Under finite-amplitude perturbations, tripoles are shown to either fission into two asymmetric dipoles or to evolve into a shielded axisymmetric vortex, demonstrating the existence of two new ‘‘reversible transitions'’ between topologically distinct coherent vortex structures. These dynamical results are confirmed by pseudo-spectral simulations, with which we also show how continuous tripolar long-lived coherent vortex structures can be generated in a variety of ways.

ISSN:0309-1929    

DOI:10.1080/03091929008219852

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

An open boundary condition is constructed for three dimensional primitive equation ocean circulation models. The boundary condition utilises dominant balances in the governing equations to assist calculations of variables at the boundary. The boundary condition can be used in two forms. Firstly as a passive one in which there is no forcing at the boundary and phenomena generated within the domain of interest can propagate outwards without distorting the interior. Secondly as an active condition where a model is forced by the boundary condition. Three simple idealised tests are performed to verify the open boundary condition, (1) a passive condition to test the outflow of free Kelvin waves, (2) an active condition during the spin up phase of an ocean, (3) finally an example of the use of the condition in a tropical ocean.

ISSN:0309-1929    

DOI:10.1080/03091929008219853

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

A unified analysis is given of the critical conditions for the onset of stratification due to either a vertical or a horizontal buoyancy flux, with tidal or wind stirring.

ISSN:0309-1929    

DOI:10.1080/03091929008219854

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The long wave equations governing the flow in alluvial rivers and channels are considered. The linearized equations are re-cast in the form of a single equation of wave hierarchy type as discussed by Whitham (1974). The dynamic and kinematic waves are of third and second order respectively. Behaviour at the wave fronts is considered and a roll-wave type instability is revealed.

ISSN:0309-1929    

DOI:10.1080/03091929008219855

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

Small amplitude two-dimensional Boussinesq convection in a plane layer with stress-free boundaries rotating uniformly about the vertical is studied. A horizontally unbounded layer is modelled by periodic boundary conditions. When the centrifugal force is balanced by an appropriate pressure gradient the resulting equations are translation invariant, and overstable convection can take the form of travelling waves. In the Prandtl number regime 0.53 < [sgrave] < 0.68 such solutions are preferred over the more usual standing waves. For [sgrave] < 0.53, travelling waves are stable provided the Taylor number is sufficiently large.

ISSN:0309-1929    

DOI:10.1080/03091929008219856

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor