摘要:

An analytical method for computing the classical problem of a light (or heavy) water source feeding the ocean near the coast is proposed. The nonlinear model includes two active layers; the width of the basin in which the outflow spreads is taken to be finite. Friction is neglected but the motions near the source are not constrained to be quasi-geostrophic. The velocity and pressure fields are computed by taking into account the flow forces to the left and right (looking off-shore) of the source, without assuming a hydrostatic pressure along the front and tail. This procedure leads to a set of five algebraic equations (with five unknowns) which can be solved analytically.

ISSN:0309-1929    

DOI:10.1080/03091928808208824

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Coupled equations describing the nonlinear evolution of a disturbance in a two-layer coastal current with a surface front are derived by assuming that the alongshore scale of the disturbance is much longer than the current width, the lower layer is much thicker than the upper layer and the potential vorticity in the upper layer is zero. Linear stability and the characteristics of the cnoidal wave and soliton solutions governed by these equations are examined analytically, and the nonlinear evolution of disturbance is discussed using numerical methods. The main results are as follows. (1) The current is linearly stable when the current speed is greater than a certain critical value. (2) Even in such a situation, there is no stable nonlinear solution whose amplitude lies between certain critical values,acanda′c, which are functions of the wavelength and the basic flow speed. (3) A solitary disturbance whose amplitude lies betweenacanda′cgrows with an eddy-pair-like structure in the lower layer. After its amplitude exceedsa′c, a soliton with a large amplitude separates from the eddy-pair-like structure and propagates by itself. (4) In the linearly unstable case, a wave-like perturbation with small amplitude grows. However, this unstable mode does not grow indefinitely but reaches a maximum amplitude, having exceeded the critical amplitude,a′c. Its amplitude then oscillates with time. (5) When several unstable waves have been given as the initial condition, the unstable waves interact nonlinearly with each other and solitary disturbances are produced. These solitary disturbances also repeat the growth and decay, and a turbulence-like phenomenon occurs.

ISSN:0309-1929    

DOI:10.1080/03091928808208825

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flowU0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear,U0γ20/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.

ISSN:0309-1929    

DOI:10.1080/03091928808208826

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Severe unidirectional Fourier truncation of the equations for 2-D incompressible flow leads to a system of three coupled PDEs in one space dimension with the same quadratic invariants as the original set (i.e. energy and enstrophy). Numerically generated equilibria for inviscid, truncated versions of the reduced system are well approximated by Kraichnan's energy-enstrophy equipartition spectra. Viscous calculations for decaying turbulence at moderate resolution (1024 degrees of freedom) also appear to be consistent with a direct,k−3, enstrophy cascading inertial range when the dissipation is small. Dissipation range intermittency in the form of spatially intermittent enstrophy dissipation with occasional strong bursts producing linear phase locking is also observed. In contrast to full 2-D simulations, no tendency towards the emergence of isolated, coherent vorticity structures is observed. The model consequently mimics some, but not all, of the properties of the full 2-D set.

ISSN:0309-1929    

DOI:10.1080/03091928808208827

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We study the problem of the coalescence of twisted flux tubes by assuming that the azimuthal field lines reconnect at a current sheet during the coalescence process and everywhere else the magnetic field is frozen in the fluid. We derive relations connecting the topology of the coalesced flux tube with the topologies of the initial flux tubes, and then obtain a structure equation for calculating the field configuration of the coalesced flux tube from the given topology. Some solutions for the two extreme cases of low-β plasma and high-β plasma are discussed. The coalesced flux tube has less twist than the initial flux tube. Magnetic helicity is found to be exactly conserved during the coalescence, but the assumptions in the model put a constraint on the energy dissipation so that we do not get a relaxation to the minimum-energy Taylor state in the low-β case. It is pointed out that the structure equation connecting the topology and the equilibrium configuration is quite general and can be of use in many two-dimensional flux tube problems.

ISSN:0309-1929    

DOI:10.1080/03091928808208828

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The heating by resistive turbulence of solar coronal magnetic fields is evaluated by means of the Taylor-Heyvaerts hypothesis, which enables one to calculate the evolution of the magnetic helicity and magnetic field in the corona in response to prescribed motions of the photospheric footpoints. The relationship between the photospheric velocity field and the helicity generation rate is considered for a coronal arcade and the energy release is proved to be positive definite in general. Also, the evolution and dissipation is determined for the axisymmetric magnetic field above a single sunspot which is being twisted up from below.

ISSN:0309-1929    

DOI:10.1080/03091928808208829

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor