摘要:

We investigate the development of two-dimensional turbulence in a temporally-growing shear layer. This is accomplished through the application of numerical simulation techniques in computational domains which accommodate many wavelengths of the primary Kelvin-Helmholtz instability. Both homogeneous and density-stratified flows are considered. Spreading rates of homogeneous and stratified shear layers are computed and compared with the results of laboratory experiments. We show that shear-driven vortex mergers generate downscale enstrophy cascades through filamentation, as do the mergers which occur in the isotropic case. In the long-time limit, homogeneous shear layers are dominated by a single coherent vortex. The addition of even a slight degree of stratification alters the vortex dynamics dramatically. Vortex filaments which are generated and stabilized by the straining deformations between adjacent large vortices are reinforced by the baroclinic torque. As a result, these structures ultimately dominate the vorticity field in weakly-stratified flows. In strongly-stratified cases, pairing instability is suppressed and the flow relaxes quickly to a stable parallel state.

ISSN:0309-1929    

DOI:10.1080/03091929308203572

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A primitive equation numerical model is used to study the generation of internal lee waves in a steady, rotating, uniformly stratified flow past an isolated seamount. We find that large-amplitude internal lee waves can form over the seamount even when the imposed steady flow is too weak to support the internal lee waves away from the seamount (i.e. low Froude and Rossby numbers). These internal lee waves are trapped over the flank of the seamount where nonlinear advection of momentum leads to a large local acceleration of the flow. As the flow decelerates downstream of the seamount, the internal lee wave amplitude and wavelength are reduced to the point where parameterized subgridscale mixing quickly dissipates the waves. This contrasts with the traditional case of internal lee waves in rapid background flows where the local acceleration over the seamount is relatively unimportant and the waves continue well downstream of the seamount. The model results also indicate that the trapped internal lee waves form within a few days following flow initiation, suggesting that they may be excited by more realistic temporally varying oceanic flows.

ISSN:0309-1929    

DOI:10.1080/03091929308203573

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A closure model is used to study the statistical equilibria achieved when flows are forced over random topography by an external momentum source. Especially we examine the correlation between vorticity and underlying topography, and the resulting topographic stress. This is done by solving a set of closure equations for stationary solutions. Theoretical results are compared with ensemble averages from direct numerical simulations for parameters relevant to midlatitude deep ocean environment.

ISSN:0309-1929    

DOI:10.1080/03091929308203574

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Finite-amplitude solutions are sought to the Barotropic Vorticity Equation (BVE) on a sphere in the presence of realistic zonal flows. The new solutions are characterized by multivalued (q, Ψ) relationships, and can be constructed analytically. The resulting zonal flows and the (q, Ψ) scatter plots can be very close to climatology. Many observed flow features of the persistent anomalies, like the midlatitude westerly jetstreams and splits as well as the well-known dipole-blocking structures can be well described in terms of these new solutions. It is suggested that the observed persistent anomalies in the atmosphere may be a manifestation of these solutions being resonantly excited through thermal forcing.

ISSN:0309-1929    

DOI:10.1080/03091929308203575

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor numberTa=106and Prandtl numberPr=1 and with increasing Rayleigh numberR, convection undergoes a series of bifurcations from onset of steadily propagating motions SP atR=Rc= 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained atR= 1.3Rc,R= 1.7Rc,R= 2Rc, andR= 5Rc, respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave numbermof the convection pattern oscillates amongm= 3,4,5, and 6; the convection pattern near the outer shell has largermthan that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts inmfor the NP state atR= 5Rc, whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained atR= 50Rc. At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases exceptR= 50Rc, at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.

ISSN:0309-1929    

DOI:10.1080/03091929308203576

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The study of MHD instabilities in Earth's fluid core is simplified by making the usual assumptions that the fluid is uniform, inviscid, incompressible, and electrically-conducting (conductivity, [sgrave]). It is also supposed that it is in a state of rapid, and nearly solid-body rotation about the polar axis, Oz; in that frame, the prevailing velocity,V0, is slow and, like the magnetic field,B0, is nearly azimuthal. In an ideal fluid (defined as one in which [sgrave] is infinite), an important class of instabilities arise, namely Acheson'sfield gradientmodes. In the case considered here, in whichV0= 0, these arise when thes-gradient of (B0/s)2, wheresis the distance from the axis of rotation, is sufficiently large. Commonly (and here), these instabilities are studied using a simple model in whichB0is a function ofsalone, and in which the fluid fills a cylindrical annulussi≤s≤s0.

ISSN:0309-1929    

DOI:10.1080/03091929308203577

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Hydrodynamic and hydromagnetic stability problems often reduce to solving the eigenvalue problem Ax =px, where Re(p) is the growth rate and Im(p) is the frequency of the instability. The Lanczos method is a means of reducing a diagonalisable matrixAto an equivalent tridiagonal matrixT(whose eigenvalues can easily be found). The method can take full advantage of the sparsity ofA, so, with given computer memory, it can deal with much larger matrices than more traditional methods of finding all the eigenvalues of a matrix. In practice, the Lanczos method is best suited to findingsomeof the eigenvalues of a large sparse matrix. The Lanczos method is well established in the numerical linear algebra literature and has been applied to problems in particle physics and plasma physics, for example. The method does not appear to be well known in the Geophysical and Astrophysical Fluid Dynamics community, so we take the opportunity here to briefly review the method, its strengths and its weaknesses, before describing our experience of applying it to magnetic stability problems.

ISSN:0309-1929    

DOI:10.1080/03091929308203578

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We have studied the fine-structure introduced by thermal conduction across the magnetic field lines in the linear phase of the thermal instability. This fine-structure assumes the form of (a large number of) field-aligned “threads”. It is shown that for the most unstable solutions in the normal mode spectrum, the size of these threads corresponds at least in order of magnitude with values reported in prominence observations. We conclude therefore that perpendicular thermal conduction may be responsible for the formation of prominence fine-structure.

ISSN:0309-1929    

DOI:10.1080/03091929308203579

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We show for a wide class of unbounded domains, that minimizing the magnetic energy subject to prescribed helicity or relative helicity, does not lead to non-trivial force-free fields. Instead, we show by an explicit construction that all minimizing sequences satisfying the helicity constraint, converge to a vacuum field.

ISSN:0309-1929    

DOI:10.1080/03091929308203580

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

We show that Moffat's formula for the helicity of linked flux tubes is valid for arbitrary field line structure provided that helicity is replaced by mutual helicity, i.e. if self-helicities are excluded. We use Arnold's recent notion of asymptotic linking number to derive our result.

ISSN:0309-1929    

DOI:10.1080/03091929308203581

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor