About some very small harmonics which are present in the tide of the Pacific

Summary Over 85% of the harmonic components of the tide along the west coast of Mexico have amplitudes smaller than 2 cm. Yet they are fully resolvable from the noise back-ground so that cotidal charts could be drawn for minor components such asQ ₁ andT ₂ . A cotidal chart forS ₁ ist also presented; the presence of this component is attributed not to the tidal forces but to some irregularity in the shape of the Earth or in the distribution of its mass. Third order effects of a magnitude of 1 to 9 mm are evident in the semidiurnal band; they actually exceed the second order input at some stations. The presence of compound harmonics of nonlinear origin, such as2MK ₂ ,MOK ₂ andNK ₃ is also detectable.

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Über einige sehr kleine harmonische Konstanten, die in den Gezeiten des Pazifiks vorkommen

Zusammenfassung Über 85% der harmonischen Komponenten entlang der Westküste von Mexiko haben Amplituden kleiner als 2 cm. Dennoch sind sie vollständig aus dem Hintergrundrauschen herauszufiltern, so daß für kleinere Komponenten wieQ ₁ undT ₂ Karten der Linien gleicher Amplitude und Phase gezeichnet werden können. FürS ₁ wird ebenfalls eine solche Karte dargestellt. Das Vorhandensein dieser Komponente ist nicht auf die Gezeitenkräfte zurückzuführen, sondern auf Unregelmäßigkeiten in der Gestalt der Erde oder in der Verteilung ihrer Masse. Effekte dritter Ordnung in einer Größe von 1 bis 9 mm sind offensichtlich in halbtägigen Gezeiten enthalten. Sie übersteigen sogar die der zweiten Ordnung an einigen Stationen. Das Vorhandensein von Verbundtiden nichtlinearen Ursprungs wie2MK ₂ ,MOK ₂ undNK ₃ ist ebenfalls erkennbar.

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Propos sur les très petites constantes harmoniques perceptibles dans les marées du Pacifique

Résumé Plus de 85% des composantes de la marée, le long de la côte occidentale du Mexique, ont une amplitude qui n'excède pas 2 cm. Néanmoins, elles émergent clairement du bruit de fond, ce qui permet même d'en tracer des cartes cotidales, soient celles deQ ₁ ouT ₂ par exemple. Nous présentons aussi une telle carte pourS ₁ : nous attribuons son existence non à la force de marée, mais plutôt à quelque déformité dans la géoide ou dans la distribution de sa masse. Des effets de troisième ordre, de 1 à 9 mm d'envergure, sont manifestes dans la bande semidiurne; en fait ils dépassent la contribution du deuxième ordre en certains endroits. Des composantes d'origine non linéaire, comme2MK ₂ ,MOK ₂ etNK ₃ , se descernent aussi.

     

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small but finite inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,?v,?t), x and v being the particle position and velocity, respectively. For arbitrary inertia, position and velocity variables are coupled, with the result that p(x,?v,?t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small (but nevertheless finite) inertia, (x,?v)-variables decouple and the determination of p(x,?v,?t) is reduced to solve a system of two standard forced advection–diffusion equations in the space variables x. The latter equations are derived here from first principles, i.e., from the well-known Lagrangian evolution equations for position and particle velocity.     

Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves are complex-valued, p = P + iA, where P is the propagation vector, and A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0), homogeneous plane waves (A ≠ 0, P and A parallel), and inhomogeneous plane waves (A ≠ 0, P and A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace. The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail. vcerveny@seis.karlov.mff.cuni.cz     

Inhomogeneous Harmonic Plane Waves in Viscoelastic Anisotropic Media

In viscoelastic media, the slowness vector p of plane waves is complex-valued, p = P + iA. The real-valued vectors P and A are usually called the propagation and the attenuation vector, repectively. For P and A nonparallel, the plane wave is called inhomogeneousThree basic approaches to the determination of the slowness vector of an inhomogeneous plane wave propagating in a homogeneous viscoelastic anisotropic medium are discussed. They differ in the specification of the mathematical form of the slowness vector p. We speak of directional specification, componental specification and mixed specification of the slowness vector. Individual specifications lead to the eigenvalue problems for 3 × 3 or 6 × 6 complex-valued matrices.In the directional specification of the slowness vector, the real-valued unit vectors N and M in the direction of P and A are assumed to be known. This has been the most common specification of the slowness vector used in the seismological literature. In the componental specification, the real-valued unit vectors N and M are not known in advance. Instead, the complex-valued vactorial component p of slowness vector p into an arbitrary plane with unit normal n is assumed to be known. Finally, the mixed specification is a special case of the componental specification with p purely imaginary. In the mixed specification, plane represents the plane of constant phase, so that N = ±n. Consequently, unit vector N is known, similarly as in the directional specification. Instead of unit vector M, however, the vectorial component d of the attenuation vector in the plane of constant phase is known.The simplest, most straightforward and transparent algorithms to determine the phase velocities and slowness vectors of inhomogeneous plane waves propagating in viscoelastic anisotropic media are obtained, if the mixed specification of the slowness vector is used. These algorithms are based on the solution of a conventional eigenvalue problem for 6 × 6 complex-valued matrices. The derived equations are quite general and universal. They can be used both for homogeneous and inhomogeneous plane waves, propagating in elastic or viscoelastic, isotropic or anisotropic media. Contrary to the mixed specififcation, the directional specification can hardly be used to determine the slowness vector of inhomogeneous plane waves propagating in viscoelastic anisotropic media. Although the procedure is based on 3 × 3 complex-valued matrices, it yields a cumbersome system of two coupled equations.     

Scenario of the January 1997 West Bohemia Earthquake Swarm

In order to learn more about the nature of the dynamic processes taking place in the West Bohemia/Vogtland earthquake swarm region, we investigated the temporal and spatial variations of the source mechanisms of the January 1997 swarm beneath Nový Kostel (NKC). Visual analyses of WEBNET seismograms of over 800 events revealed that a specific feature of this swarm was the occurrence of eight classes of multiplet events. The result of single-source, absolute moment tensor inversion of the P and SH peak amplitudes of a subset of 70 events representing all multiplet classes indicated that eight statistically significant types of mechanisms occurred during the swarm. Two of them, types A and B in our denotation, comprised all M _L 1.3 events and predominated in the swarm. Type A were pure strike-slip mechanisms or strike-slip mechanisms containing a small normal component, with a nearly pure double-couple source. For class B events, oblique-thrust faulting and non-double-couple components significant at a fairly high confidence level were typical. Type A events predominated in the southern subcluster of the swarm, whereas most of type B events occurred in the subcluster northwards from NKC. This indicates that two major seismogenic planes were active during the swarm. The swarm essentially developed in four phases: in the first, type A events prevailed and the southern plane was active; during the second, characterised by the occurrence of both type A and B events (the former in the southern, the latter predominantly in the northern subcluster), the activity of the swarm culminated; in the third and fourth, the occurrence of type B events in the northern plane predominated, and only weak single events occurred southwards from NKC. Mechanisms of types AB , C , D , E , F and G , which were typical for M _L 1.2 events, occurred randomly throughout the swarm. Type AB events were identified in both the southern and northern clusters, type C , E , F and G mechanisms only southwards from NKC. Type D events exhibited a large scatter of hypocentres which fell in neither the southern nor the northern cluster. Focal mechanisms like those reported in this study and with analogous temporal and spatial variations were observed by other authors already fifteen years ago in the 1985/86 earthquake swarm and may, therefore, be typical for the region under study.     

Fluidization of sediments in a conical basin by subterranean springs: relevance to Lake Banyoles

: An experimental study was carried out to investigate the resuspension of particles by a momentum jet discharging from below into a conical basin. The work was motivated by its relevance to Lake Banyoles, where sediments are suspended in different conical basins by bottom jets fed by a groundwater karstic system. Two different flow regimes were identified: a "Jet Flow" regime (JF) and a "Lutocline Flow" regime (LF). In the LF regime, the particles were resuspended, forming a well-established interface along the entire cross-sectional ara of the cone. This regime occurs when the particle Reynolds number Re_p = (u-w_s)d_p/ n {\bf Re_p = (u-w_s)d_p/ \nu} where u is the mean velocity of the flow at the jet entry, ws is the settling velocity of particles, dp is the diameter of that particles and n {\bf \nu} is the kinematic viscosity of water) is below a critical number Rec that depends on the slope of the basin. The maximum height to which particles rise in the LF regime was also determined as a function of four non-dimensional variables: D1 = ho/(Mo^1/2/ws), D2 = ho/dp, Rep and tan  b {\bf tan \, \beta} (where ho is the height of the particle bed, Mo is the kinematic momentum flux of the jet and tan  b {\bf tan \, \beta} is the slope of the basin). Application of the results to the basins of Lake Banyoles showed a good agreement provided that the aggregate properties of the suspensions are used. It is also shown that, in the LF regime, inflows to the basins can be estimated by a simple technique based on a balance between the sedimentation flux and the upward advection of sediments by the mean flow.     

Ranking of river basin alternatives using ELECTRE

Abstract

Ranking of river basin planning and development alternatives under a multi-criterion environment, including both qualitative and quantitative aspects, is examined. The purpose is to find the most suitable planning for reservoirs with their associated purposes aimed at the development of the major peninsular river (Krishna) basin in India. A total of seven reservoirs and a diversion network are considered for the formulation of 24 alternative systems with 18 criteria, of which nine are qualitative and the remainder are quantitative in nature. A set of best alternatives with their ordering is obtained using ELECTRE (ELimination Et (and) Choice Translating REality).     

Superhelicity,helicity and potential vorticity

Abstract

‘‘Helicity'’ density H ≡ u · ω and other pseudo-scalar fields such as P ≡ ω · Vlnρ (which is related to Ertel potential vorticity) are useful quantities in theoretical fluid dynamics and magneto-fluid dynamics. Here u denotes the Eulerian flow velocity relative to the chosen frame of reference, ω ≡ V × u is the corresponding relative vorticity and ρ the mass density of the fluid. A general expression is readily obtained for ?H/?t (where t denotes time) in terms of P and the ‘‘superhelicity'’ density S ≡ ω · V × ω which, in fluids of low viscosity, has its highest values in boundary layers. One need for such a relationship became evident during an attempt to interpret the findings of laboratory experiments on thermal convection in rotating fluids in containers of various geometrical shapes and topological characteristics.

In electrodynamics an analogous expression can be found relating the time rate of change of ‘‘magnetic helicity'’ A · B to ‘‘magnetic superhelicity'’ B · ? × B (where B · ? × A is the magnetic field) and a scalar quantity analogous to P which involves non-Ohmic contributions to the relationship between the electric current density and the electric field.     

A dual-porosity model for nitrogen leaching from a watershed/Un modèle à double porosité pour le lessivage de l’azote d’un bassin versant

Abstract

Abstract The MASONW (MACRO + SOILN + Watershed) model describing nitrogen leaching in watersheds was developed and tested. The model is based on the MACRO and SOILN models. The dual-porosity model MACRO simulates water flow on the field scale. The SOILN model describes turnover and leaching of nitrogen. Two main features of a watershed have been added into these two models: (a) the existence of a river system, and (b) variable thickness of the aeration zone within a watershed. Good agreement between the output of the MASONW model and observed data for water discharge and nitrate concentrations were achieved in the Odense watershed (496 km²) in Denmark.     

Cross helicity and related dynamo

The turbulent cross helicity is directly related to the coupling coefficients for the mean vorticity in the electromotive force and for the mean magnetic-field strain in the Reynolds stress tensor. This suggests that the cross-helicity effects are important in the cases where global inhomogeneous flow and magnetic-field structures are present. Since such large-scale structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity effect is expected to play an important role in geo/astrophysical flows. In the presence of turbulent cross helicity, the mean vortical motion contributes to the turbulent electromotive force. Magnetic-field generation due to this effect is called the cross-helicity dynamo. Several features of the cross-helicity dynamo are introduced. Alignment of the mean electric-current density J with the mean vorticity Ω , as well as the alignment between the mean magnetic field B and velocity U , is supposed to be one of the characteristic features of the dynamo. Unlike the case in the helicity or α effect, where J is aligned with B in the turbulent electromotive force, we in general have a finite mean-field Lorentz force J ?×? B in the cross-helicity dynamo. This gives a distinguished feature of the cross-helicity effect. By considering the effects of cross helicity in the momentum equation, we see several interesting consequences of the effect. Turbulent cross helicity coupled with the mean magnetic shear reduces the effect of turbulent or eddy viscosity. Flow induction is an important consequence of this effect. One key issue in the cross-helicity dynamo is to examine how and how much cross helicity can be present in turbulence. On the basis of the cross-helicity transport equation, its production mechanisms are discussed. Some recent developments in numerical validation of the basic notion of the cross-helicity dynamo are also presented.     

Discussion of “Neuro-fuzzy models employing wavelet analysis for suspended sediment concentration prediction in rivers”

Citation Abrahart, R.J. & Mount, N.J. (2011) Discussion of “Neuro-fuzzy models employing wavelet analysis for suspended sediment concentration prediction in rivers by S.A. Mirgagheri et al. (2010, Hydrol. Sci. J. 55(7), 1175–1189).” Hydrol. Sci. J. 56(7), 1325–1329.     

Note on the scalar dynamo model

Abstract

Bayly (1993) introduced and investigated the equation (? _t + v·▽-η ▽²)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.     

A steady state of the disc dynamo

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.     

Discussion of “Effects of temporal resolution on hydrological model parameters and its impact on prediction of river discharge”

Citation Littlewood, I. G., Croke, B. F. W. & Young, P. C. (2011) Discussion of “Effects of temporal resolution on hydrological model parameters and its impact on prediction of river discharge” by Y. Wang, B. He & K. Takase (2009, Hydrol. Sci. J. 54(5), 886–898). Hydrol. Sci. J. 56(3), 521–524.     

A shell model for anisotropic magnetohydrodynamic turbulence

Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B ₀, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 10⁵ have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B ₀ with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.     

On the probability of exceeding a given river flow threshold

ABSTRACT

To obtain estimates of the probability that a river flow will exceed a given threshold at time t + 1, given the flow value at time t, two stochastic models are considered: a filtered Poisson process and a diffusion process with jumps. Estimates derived from linear regression are also considered. The model parameters are assumed to depend on the flow value. An application to the Delaware River is presented.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Historical water resources in South Asia: the hydrological background

Abstract

The development of historical water resources in the South Asian subcontinent has been largely dependent on the hydrological background. The runoff patterns are derived from climate statistics and the historical developments in different areas are related to these patterns.

Citation Sutcliffe, J., Shaw, J. & Brown, E. (2011) Historical water resources in South Asia: the hydrological background. Hydrol. Sci. J. 56(5), 775–788.     

Response of the high-latitude polar ionosphere to changes in the orientation of the Poynting vector near the Earth orbit relative to the geomagnetic moment orientation

The effect of the mutual orientation of the Poynting vector P of the electromagnetic energy density in the solar wind and the vector M of the Earth’s magnetic moment (taking into account its orbital and diurnal motions) on the geomagnetic activity has been examined for the first time using the measurements of the solar wind parameters on the Earth orbit in 1963–2005. The component P _m of the vector P along the vector M is shown to have a pronounced annual variation with the extrema in November and May and a diurnal variation with the extrema at ∼6 and 18 UT. The phases of the variations are shown to be determined only by the geometric parameters and are independent of the sign of the sector structure of the interplanetary magnetic field. The experimental data on the planetary and high-latitude geomagnetic activity, which is a response to changes in the orientation of P relative to M, are presented. The power of the sources of the electromagnetic energy of the solar wind during strong geomagnetic disturbances is also estimated.     

Randomness: a property of the mathematical and physical systems

ABSTRACT

This article is a concept paper, which discusses the definition of randomness, and the sources of randomness in the mathematical system as well as in the physical system (the Universe). We document that randomness is an inherited property of mathematics and of the physical world, shaping all observed forms and structures, and we discuss its role.

Editor D. Koutsoyiannis; Guest editor E. Volpi     

Investigations du caractère multifractal des débits maximaux annuels de crue / Investigation of multifractality of maximum annual flood discharges

Abstract

Abstract The multifractal analysis of maximum annual flood discharges at 55 stations of the Tunisian gauging network allows one to associate the various statistical moments of surface discharges of the basins through a scale-invariant law. On this basis, a random cascades model is identified. The scale-invariant law obtained for extreme values represents a theoretical foundation for empirical models proposed since the 1960s which link extreme values, and their associated hazards, with surfaces of drainage areas.