共查询到20条相似文献，搜索用时 621 毫秒
1.
Abstract 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. 相似文献
2.
The problem of the onset of thermal convection is considered, firstly when a uniform tilted magnetic field is present, and secondly in a frame rotating about an oblique axis. If up–down symmetry is broken we expect to find only bifurcations that lead to travelling waves. Numerical studies show, however, that in a Boussinesq fluid the spectrum of eigenvalues can be symmetrical about the real axis, even when the boundary conditions are asymmetrical. Here we show analytically that this symmetry property indeed holds for a wide range of boundary conditions and hence that both steady solutions and standing waves are allowed. 相似文献
3.
R. L. Jennings 《地球物理与天体物理流体动力学》2013,107(1-4):147-189
Abstract An idealized nonlinear αω-dynamo is investigated. Emphasis is placed upon the different spatial symmetries, and the asymmetries that arise after secondary bifurcations. On varying the main control parameter D (the dynamo number), many transitions are found involving solutions without an equatorial symmetry, and solutions with quasiperiodic time dependence, but no chaos. Instead of a cascade to smaller spatial scales when D is highly supercritical it is found that additional asymmetries are introduced at tertiary bifurcations. Our complete bifurcation diagrams allow us to follow in detail how stability is passed from one solution to another as D varies. In these diagrams there are typically multiple stable solutions at any value of D, which suggests that similar stars can have different magnetic patterns. 相似文献
4.
Using the data set of about 1 Hz Lg amplitudes from 80 stations in the six eastern provinces of China, the ratios of horizontal
to vertical amplitude of Lg waves,H/Z are determined. The mean lg(H/Z)-value is equal to 0.13. For the station bases of soft deposit,granite and sedimentary rock, lg(H/Z)-values average 0.55, 0.04 and 0.10, respectively. For the three kinds of station bases, the station terms of horizontal
amplitude,C
h
average 0.65, −0.09 and 0.00; that of vertical amplitude,C
z
average 0.32, −0.04 and 0.00, respectively. There are the relations betweenC
h
,C
z
and lg(H/Z):C
h
=0.01+2.10C
z
andC
h
=−0.15+1.46 lg(H/Z).
The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 281–286, 1991.
Project sponsored by the Chinese Joint Seismological Science Foundation. 相似文献
5.
We investigate the parameter space of a Parker dynamo with a simple alpha quenching nonlinearity, taking as governing parameters the dynamo number D (D<0) and the ratio of diffusion times in the radial and latitudinal directions in the convective zone. The latter parameter, μ, is connected with the aspect ratio (dimensionless thickness) of the convective zone. We isolate two asymptotic configuration of the dynamo waves excited by the Parker dynamo in the limiting case of strong generation. Apart from the standard case with the solar type dynamo wave travelling from mid-latitudes to the equator, we describe a form of dynamo activity which is basically an anharmonic standing wave. The first situation occurs when μ increases with |D|. With μ fixed and |D| increasing, the second asymptotic configuration occurs. We discuss possibilities of identifying these asymptotic configurations with various types of stellar activity as traced by stellar CaII data. 相似文献
6.
Stefano Pierini 《地球物理与天体物理流体动力学》2013,107(1-4):97-108
Abstract In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL 2/h 3, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l 4 f 2/g)1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q? O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ?O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation. 相似文献
7.
Modelling sand wave migration in shallow shelf seas 总被引：5，自引：0，他引：5
Attila A. Nmeth Suzanne J. M. H. Hulscher Huib J. de Vriend 《Continental Shelf Research》2002,22(18-19)
Sand waves form a prominent regular pattern in the offshore seabed of sandy shallow seas. The positions of sand-wave crests and troughs slowly change in time. Sand waves are usually assumed to migrate in the direction of the residual current. This paper considers the physical mechanisms that may cause sand waves to migrate and methods to quantify the associated migration rates. We carried out a theoretical study based on the assumption that sand waves evolve as free instabilities of the system. A linear stability analysis was then performed on a 2DV morphological model describing the interaction between the vertically varying water motion and an erodible bed in a shallow sea. Here, we disrupted the basic tidal symmetry by choosing a combination of a steady current (M0) and a sinusoidal tidal motion (M2) as the basic flow. We allowed for two different physical mechanisms to generate the steady current: a sea surface wind stress and a pressure gradient. The results show that similar sand waves develop for both flow conditions and that these sand waves migrate slowly in the direction of the residual flow. The rates of migration and wavelengths found in this work agree with theoretical and empirical values reported in the literature. 相似文献
8.
N. O. Weiss 《地球物理与天体物理流体动力学》2013,107(1-4):229-247
Abstract Cowling investigated the effect of an imposed magnetic field on convection in order to explain the origin of sunspots. After summarizing the classical linear theory of Boussinesq magnetoconvection, this review proceeds to more recent nonlinear results. Weakly nonlinear theory is used to establish the relevant bifurcation structure, which involves steady, oscillatory and chaotic solutions. Behaviour found in numerical experiments can then be related to these analytical results. Thereafter, attention is focused on the astrophysically relevant problem of fully compressible magnetoconvection. Steady two-dimensional nonlinear solutions show two important effects: stratification introduces an asymmetry between rising and falling fluid, while compressibility leads to evacuated magnetic flux sheets. Time-dependent behaviour includes transitions between standing waves and travelling waves, as well as changes in horizontal scale, leading to the development of more complicated spatial structures. Work on three-dimensional models, which is now in progress, will lead to a better understanding of the structure of a sunspot. 相似文献
9.
Summary The waves generated by a steadily moving two-dimensional pressure distribution are examined using non-linear shallow water theory. The applied pressure is zero ahead of the disturbance, that is in the downstream direction, and is a constantP
0 in the upstream direction, these regions being joined smoothly by a cubic function.We consider here only the case of supercritical flow in both regions, the solution representing an asymmetric solitary wave travelling with the disturbance. The wave profiles are determined by an iterative method previously employed for non-linear waves. Wave amplitudes and profiles, and the wave drag, associated with each system are computed for various values ofP
0/Q g h, whereh is the undisturbed depth of water ahead of the wave.The solution obtained reduces to the classical solitary wave of finite amplitude when the applied pressure is everywhere zero.
Division of Numerical and Applied Mathematics, National Physical Laboratory. 相似文献
Résumé Nous avons calculé les expressions des profils d'ondes solitaires produites par une pression, qui se propagent sur la surface d'une couche d'eau peu profonde avec une vitesseU plus grande que (g h)1/2. La pression appliquée est nulle en avant de l'onde, elle est une constanteP 0 en arrière, et entre ces deux régions elle est representée par une fonction cubique. Les profils sont calculés par une methode iterative déjà employée pour des ondes non-linéaires. L'amplitude, le profil et la force ont été evalués pour diverses valeurs deP 0/Q g h, ouh est la profondeur en avant de l'onde.
Division of Numerical and Applied Mathematics, National Physical Laboratory. 相似文献
10.
ABSTRACTKnowledge of rainfall characteristics such as drop-size distribution is essential for the development of erosion-mitigation strategies and models. This research used an optical disdrometer to elucidate the relationships between raindrop-size distribution, median volume drop diameter (D50), kinetic energy and radar reflectivity (dBz) of simulated rainfall of different intensities. The D50 values were higher for the simulated rain than for natural rain at almost all rainfall intensities, perhaps due to variations in rainfall types and the turbulence in natural rain that breaks up large drops. The kinetic energy ranged from 26.67 to 5955.51 J m?2 h ?1, while the median volume drop diameter (D50) was in the range 1.94–7.25 mm, for intensities between 1.5 and 202.6 mm h?1. The relationship between radar reflectivity (Z) and the intensity (R) of the simulated rain was best described by a power law function (Z = aRb), with a and b coefficients in the ranges 162–706 and 0.94–2.46, respectively, throughout the range of rainfall intensities (1.5–202.6 mm h?1). 相似文献
11.
John W. Miles 《地球物理与天体物理流体动力学》2013,107(3-4):243-251
Abstract A variational approximation to the dispersion relation for trapped waves on a flat shelf of depth h 1, bounded internally by a vertical coast and externally by a semi-infinite ocean of depth h 2>h 1, is obtained through an integral-equation formulation that accounts for all of the non-propagated modes that are excited at the discontinuity in depth (the conventional formulation of the edge-wave problem allows only for the propagated mode on the shelf and the dominant, non-propagated mode in the deep water). Coriolis effects are neglected. The exact result in the limit ω2 h 2/g↓0 (ω = angular frequency) is obtained by conformal mapping and compared with the variational approximation, which proves to be quite accurate over the entire range 1>h 2/h 1>x. The effects of the higher-order, non-propagated modes are found to be small for the long waves observed over the Southern California shelf by Snodgrass, Munk and Miller (1962). 相似文献
12.
ABSTRACTIn this paper a universal multifractals comparison of the outputs of two types of collocated optical disdrometers installed on the roof of the Ecole des Ponts ParisTech is performed. A Campbell Scientific PWS100 which analyses the light scattered by the hydrometeors and an OTT Parsivel2 which analyses the portion of occluded light are deployed. Both devices provide a binned distribution of drops according to their size and velocity. Various fields are studied across a range of scales: rain rate (R), liquid water content (ρ), polarimetric weather radar quantities such the horizontal reflectivity (Zh) and the specific differential phase (Kdp), and drop size distribution (DSD) parameters such as the total drop concentration (Nt) and the mass-weighted diameter (Dm). For both devices, good scaling is retrieved on the whole range of available scales (2?h–30?s), except for the DSD parameters for which the scaling only holds down to few minutes. For R, the universal multifractal parameters are found to equal 1.5 and 0.2 for α and C1, respectively. Results are interpreted with the help of the classical Zh–R and R–Kdp radar relations.
Editor D. Koutsoyiannis; Associate editor E. Volpi 相似文献
13.
New equations and techniques for dealing with drop breakups are developed and applied to the modelling of the evolution of raindrop spectra in rainshafts. Breakup experiments byMcTaggart-Cowan andList (1975) served as data base.No matter what the original size distribution, the spectrum evolution will always lead to a Marshall-Palmer type equilibrium di tributionN=N
0e–D, with =constant andN
0 proportional to the rainfall rateR. (D stands for raindrop diameter.) ForR29 mm h–1 and an original Marshall-Palmer distribution, the required fall height to reach equilibrium is 2 km.The equilibrium distributions are characterized by linear relationships betweenR, the radar reflectivity factorZ, the liquid water content LWC and theN
0 of the Marshall-Palmer distribution. Possible explanations for the discrepancy with observations are given.The fact that the all-water processes cannot produce drops withD2.5 mm (as confirmed by observations) leads to the conclusion that observed large raindrops withD5 mm represent melted hailstones and have not yet reached an equilibrium distribution. These latter conclusions were reached within the original assumption of videspread, steady state precipitation. 相似文献
14.
Abstract A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context. 相似文献
15.
Using the data set of about 1 Hz Lg amplitudes from 80 stations in the six eastern provinces of China, the ratios of horizontal to vertical amplitude of Lg waves,H/Z are determined. The mean lg(H/Z)-value is equal to 0.13. For the station bases of soft deposit,granite and sedimentary rock, lg(H/Z)-values average 0.55, 0.04 and 0.10, respectively. For the three kinds of station bases, the station terms of horizontal amplitude,C h average 0.65, ?0.09 and 0.00; that of vertical amplitude,C z average 0.32, ?0.04 and 0.00, respectively. There are the relations betweenC h ,C z and lg(H/Z):C h =0.01+2.10C z andC h =?0.15+1.46 lg(H/Z). 相似文献
16.
A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents.
Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part i is related to their migration speed.
Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively).
The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration.
The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength.
Responsible Editor: Jens Kappenberg 相似文献
17.
Lszl Szarka 《Geophysical Prospecting》1997,45(5):763-774
In this paper the locations where ρapp = ρ1 and ? = π/4 and where these parameters reach an extreme value in two-layer magnetotelluric (MT) sounding curves are summarized in an extremely compact form. The key parameters over two-layer models with conductivities σ1, σ2 and upper layer thickness h are the real S and α, where S is the conductivity contrast and α is the distance between the observation site and the conductivity interface, normalized to the half skindepth in the first layer. If the impedance components, various resistivity definitions ( ρRe Z, ρIm Z and ρ|Z|, based on different parts of the complex impedance Z ) and the magnetotelluric phase ? are derived as a function of S and α, then the conditions for the apparent resistivity ρapp and the phase ? are that they either satisfy ρapp = ρ1 and ? = π/4 or attain extreme values which can be given in terms of simple algebraic equations between S and α. All equations are valid for observation sites at any depth 0 ≤ z ≤ h in the first layer. The set of equations, presented in a tabular form, may make it possible to determine a layer boundary from the short period part of the sounding curves, in particular the ρRe Z and the ?MT curves. 相似文献
18.
Olga Podvigina 《地球物理与天体物理流体动力学》2013,107(3):299-326
We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε2 being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k c . For waves, the largest growth rate is of the order ε4/3. In the case of Eckhaus instability the growth rate is of the order of α2. 相似文献
19.
Abstract We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD 0, and the other for |D| ? 1. Asymptotic solutions for |D—D 0| ? |D 0| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|?s) for |B| → ∞, we demonstrate that |B| = O(|D|1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified. 相似文献
20.
The results of a periodogramanalysis of the variations in the ionospheric parameters, measured using the vertical radio sounding method at midlatitude Irkutsk observatory (Eastern Siberia), are presented. The 1984–1986 period of observations was used. It has been indicated that the statistically significant oscillations with periods typical of planetary waves are present in the variations in f 0Es, f bEs, h′Es, f min, f 0F2, and h′F.
相似文献