摘要:

The stability of the wind-driven ocean circulation to finite amplitude perturbations is explored. Sufficient conditions for stability, in the kinetic energy norm, are determined for steady solutions of the quasi-geostrophic barotropic vorticity equation on a midlatitude β-plane. In addition, the spatial pattern of the perturbation which is able to extract energy from the flow just above criticality is determined (the most energetic disturbance). The energy stability bounds are computed numerically, by using a continuation method to follow branches of steady states in parameter space, energy identities and calculus of variations. It is found that wind-driven single gyre flows are more stable than double gyre flows. For zero bottom friction and slip meridional boundaries, the most energetic disturbance is a single cell basin-wide flow. No-slip conditions at the meridional boundaries stabilize the double gyre flow and modify the structure of the most energetic disturbance to a multicellular one. Bottom friction further stabilizes the flows and its presence may strongly localize the spatial pattern of the most energetic disturbance.

ISSN:0309-1929    

DOI:10.1080/03091929608213640

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Two modulated vortex methods for the study of large scale atmospheric or oceanic flow are presented. In particular the methods discussed are based on the equations for the conservation of potential vorticity. The point vortex method is shown to be first order accurate in frequency and second order accurate in group velocity. The blob method presented is shown to be second order accurate in frequency and group velocity. Although the blob method is more accurate it is less efficient than the point vortex method. Currently fast methods exist for the point vortex method but not for the blob vortex method. A methodology for choosing the blob radius is given. These methods are used to calculate the behavior of a modon.

ISSN:0309-1929    

DOI:10.1080/03091929608213641

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The effect of topographic wave radiation on isolated eddies is modelled by anf-plane modon propagating parallel to an infinitely long escarpment. It is assumed that the lengthscale of the modon is much smaller than the lengthscale on which the topographic waves evolve. This enables the linearised equations of motion to be solved and the asymptotic (far-field, large-time) behaviour of the topographic wave field is subsequently described. A steady wave-like response is found when the modon moves within the range of possible topographic wave phase speeds. An anomalous case exists when the modon speed is the same as the long topographic wave group speed. This implies that energy cannot escape from the vicinity of the modon and consequently the response eventually becomes nonlinear. It is shown that the appropriate equation to describe the evolution of topographic waves in this case is a forced KdV equation.

ISSN:0309-1929    

DOI:10.1080/03091929608213642

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The effects of high Rayleigh number convection for temperature-dependent viscosity at infinite Prandtl number are studied with three-dimensional direct numerical simulations (using a fully spectral method) in a wide box with dimensions 5 × 5 × 1. The form of the temperature-dependent viscosity decreases exponentially with the temperature. Solutions for an volumetrically averaged Rayleigh numbers up to 6.25 × 106have been obtained for a viscosity contrast of 25. Both models with and without viscous dissipation and adiabatic heatings have been considered. There is a distinct difference in the plume dynamics between models with a dissipation numberD= 0 andD= 0.3. At zero dissipation number the hot plumes extend up to the top, while plumes atD= 0.3 are cooled due to adiabatic expansion and do not extend throughout the entire layer. The cold descending flows occur in sheets and they form longer wavelength networks and can reach the bottom, regardless of the value ofD.A time-varying depth-dependent mean horizontal flow is produced from the correlation between the laterally varying viscosity field and the velocity gradients. At high Rayleigh number there is also a change in the surface toroidal velocity field to a coherent network of river-like structures and compact vortices. Viscous dissipation is found to increase with the Rayleigh number and is particularly strong in regions of downwelling flows. In the context of mantle convection, these localized heat sources are observed to be strong with local magnitudes in some places exceeding what Earth-like radioactive heating would be by more than an order of magnitude.

ISSN:0309-1929    

DOI:10.1080/03091929608213643

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A theory of the non-diffusive anisotropic kinetic alpha-effect (“Γ-effect”) for densitystratified rotating turbulent fluids is developed. No limitations on the rotation rate are imposed and the fully nonlinear dependence of the Γ-effect on the angular velocity is studied. When the Coriolis number, ω* = 2τ ω, is small the dimensionless “dynamo number”, Cτ, characterising the power of the Γ-effect, grows with ω*. The dependence, however, reaches a maximum for ω* ∼ 2. For still higher rotation rates CΛdecreases as 1/ω*. In opposition, the corresponding number, Cx, of the hydromagnetic α2-dynamo problems remains finite for very large ω*. Hence, for fast rotation the hydrodynamic Γ-effect is small while the hydromagnetic α-effect remains large. In consequence, the large-scale magnetic and velocity structures are expected to be generated with roughly equal power in slowly rotating objects. In the rapid rotators, however, generation of the large-scale flows is problematic.

ISSN:0309-1929    

DOI:10.1080/03091929608213644

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This paper considers force-free equilibria in twisted magnetic flux tubes with helical symmetry. Such symmetry simplifies the force-free field condition to a pair of equations which are generalisations of the Grad-Shafranov equations. A simple linear solution is given analytically in terms of a Heun function, which exhibits several important aspects of twisted flux tubes. The equilibrium equations impose a functional relation between the axial field component and the flux function for the other two components, which can be used to establish current-sheet formation when certain classes of flux tubes are twisted together. Implications for magnetic energy release in the solar corona are discussed.

ISSN:0309-1929    

DOI:10.1080/03091929608213645

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor