Magnetic reynolds number and model-z geodynamo

Abstract

The magnetic Reynolds number (MRN) is used in estimating the quantities appearing in the current theory of the nearly symmetric dynamo. In kinematic theory, all expansions can be developed in terms of the MRN, but this seems to be less advantageous in the case of hydromagnetic theory and in particular the model-Z. An attempt has been made to replace the role of the MRN in the nearly symmetric expansion by the amplitudes of the individual quantities, where the amplitudes of the non-axisymmetric quantities are considered to be small compared with those of the azimuthal quantities. The amplitude of the axially asymmetric velocities and the amplitude of Archimedean buoyancey play essential roles here.

The expansions of the theory are valid only when certain assumptions are made about the field amplitude, and the velocity and buoyancy forces, even though the amplitude of the resulting a-effect is unaffected. The a-effect can be altered only by rapid changes in the non-symmetric velocities in the generation region.     

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) A. I. H. S. / A) A. I. H. S.

Abstract

A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.

Editor D. Koutsoyiannis

Citation Ilich, N., 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series. Hydrological Sciences Journal, 59 (1), 85–98.     

Radial expansion of the magnetohydrodynamic equations for axially symmetric configurations

Abstract

We introduce a general expansion approach to obtain a fully consistent closed set of magnetohydrodynamic equations in two independent variables, which is particularly useful to describe axially symmetric, time-dependent problems with weak variation of all quantities in the radial direction. This is done by considering the hierarchy of expanded magnetofluid equations in cylindrical coordinates and equating terms with equal powers in the radial coordinate r. From geometrical considerations it is shown that the radial expansions of the pertaining physical quantities are either even series or odd series in r; this introduces a significant reduction in the number of variables and equations. The closure of the system is provided by appropriate boundary conditions. Among other possible applications, the method is relevant for the analysis of structure and dynamics of magnetic field concentrations in stellar atmospheres.     

Characteristics of the response of isothermal atmospheres with nonlinear waves

Abstract

We have studied the behavior of nonlinear waves in isothermal atmospheres using an improved beam scheme method. It is shown that although the magnitude of the mass leakage due to side beams is significant, nevertheless in a motion close to hydrostatic equilibrium it can be suppressed, if special density distributions and/or suitable mesh intervals are selected. We adopt as the parameters for our model of the atmospheres M=1 M[odot], R=50 R[odot] and T=4864 K. The time variation of the physical quantities in each cell is found for several oscillation periods. The critical frequency for the model atmosphere in the case of waves with a weak nonlinearity seems to be consistent with that in the linear theory.     

Linear theory of rotating fluids using spherical harmonics part I: Steady flows

Abstract

It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids.

These solutions are regular throughout the whole domain of the fluid and are not much affected by the equatorial singularity of steady boundary layers in spherical geometries.

A comparison between this method and the one based on boundary layer theory is carried out in the case of the steady spin-up of a fluid inside a sphere.     

A NATIONAL SYSTEM FOR EXCHANGE OF WATER DATA

ABSTRACT

This paper describes a system proposed by a Federal Interagency Work Group for providing access to large quantities of hydrological data. The National Water Data Exchange (NAWDEX) will be a confederation of data-acquisition organizations that are willing to make their data available to other data users. NAWDEX will take full advantage of on-going data handling activities and will provide the means to present data in a standard format. An ultimate goal of the system will be standardization and quality control of all of the data. Management of NAWDEX will be lodged in a Systems Central, which will assure that data are made available according to the time frame and the format required by the user. Access to the data will be through an index maintained by Systems Central. Full implementation of NAWDEX will require 4 to 5 years. A technical advisory group, consisting of members representing the Federal and non-Federal sectors, and topical work groups, established in response to specific needs, will provide input during the development of NAWDEX.     

Analyses of suspended sediment loads in Slovenian rivers

ABSTRACT

Suspended solids are present in every river, but high quantities can worsen the ecological conditions of streams; therefore, effective monitoring and analysis of this hydrological variable are necessary. Frequency, seasonality, inter-correlation, extreme events, trends and lag analyses were carried out for peaks of suspended sediment concentration (SSC) and discharge (Q) data from Slovenian streams using officially monitored data from 1955 to 2006 that were made available by the Slovenian Environment Agency. In total more than 500 station-years of daily Q and SSC data were used. No uniform (positive or negative) trend was found in the SSC series; however, all the statistically significant trends were decreasing. No generalization is possible for the best fit distribution function. A seasonality analysis showed that most of the SSC peaks occurred in the summer (short-term intense convective precipitation produced by thunderstorms) and in the autumn (prolonged frontal precipitation). Correlations between Q and SSC values were generally relatively small (Pearson correlation coefficient values from 0.05 to 0.59), which means that the often applied Q–SSC curves should be used with caution when estimating annual suspended sediment loads. On average, flood peak Q occurred after the corresponding SSC peak (clockwise-positive hysteresis loops), but the average lag time was rather small (less than 1 day).

Editor M.C. Acreman; Associate editor Y. Gyasi-Agyei     

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.     

Reynolds stresses and differential rotation. I. On recent calculations of zonal fluxes in slowly rotating stars

Abstract

In order to derive general zonal flux expressions this paper deals with the influence of slow (Ωτ<1) rotation on highly anisotropic stochastic motions. The radial and latitudinal fluxes of angular momentum are derived and depend on two spectral functions. The results are applied to the often used example of spatially periodic correlations, i.e., to one-mode spectra. The zonal fluxes in this case can be expressed as combinations of the intensities of the three velocity components and the wave number vector. Specializing these quantities to the cases discussed in the literature. we are able to reproduce previously published results. Moreover, after a replacement of the ensemble averages by those over the longitudinal coordinate, fluxes result which hare been derived for non-axisymmetric modes with l=m. Thus, a fairly complete account is given of results published in this field up to the present.     

B) Une série d'études indépendantes du colloque

Abstract

The study of relation between the flow and the surface area for river basins of different size and under different climatic conditions aids us to consider it as a possible basis for hydrological analysis of the streams, and permits us to deduce a method which is very valuable in regions having few or insufficient number of hydrological stations. The fundamental relation connecting the flow of a stream Q, with the surface area A, Q = hA^g , this formular being extended to all frequences of the flow is the essential tool of this method. Wether or not the basin posesses hydrometric stations, using the relation is possible: on one hand we have shown that there was a relation between the parametres h and g in a given physico-geographic circunstance that on the other hand a basin could be identified to another one on condition that their morphometric characteristics are equivalent. In all cases the unknown quantities h and g can be determined, the relation Q = hA^g being defined then; so from the measure of A we can estimate the values of the flow Q for the frequences of it which are interesting on any part of this basin.     

Spatio-temporal drought analysis in the Trakya region,Turkey

Abstract

Since droughts are natural phenomena, their occurrence cannot be predicted with certainty and thus it must be treated as a random variable. Once drought duration and magnitude have been found objectively, it is possible to plan for the transport of water in known quantities to drought-stricken areas either from alternative water resources or from water stored during wet periods. The summation of deficits over a particular period is referred to as the drought magnitude. Drought intensity is the ratio of drought magnitude to its duration. These drought properties at different truncation levels provide significant hydrological and hydrometeorological design quantities. In this study, the run analysis and z-score are used for determining drought properties of given hydrological series. In addition, kriging is used as a spatial drought analysis for mapping. This study is applied to precipitation records for Istanbul, Edirne, Tekirdag and Kirklareli in the Trakya region, Turkey and then the drought period, magnitude and standardized precipitation index (SPI) values are presented to depict the relationships between drought duration and magnitude.     

A study on hydrological series of the Niger River

Abstract

The Hubert segmentation procedure has been applied to historical series of annual average discharges of the Niger River at Koulikoro (Mali), Niamey (Niger) and Lokoja (Nigeria) stations. The breaks, especially those identified at Koulikoro and Niamey, match well with those identified in the Senegal River series at Bakel using the same procedure. Lokoja departs from this regional pattern, as it shows in the late 1980s a return to wetter conditions much earlier than the other three stations. The magnitudes of the variation of the inter-annual means between the alternating wet and dry periods are significant and similar. These results seem to suggest that phenomena causing non-stationarity in hydrological series can have a sub-continental impact or, in contrast, may be more limited in their spatial coverage.

Editor Z.W. Kundzewicz; Associate editor H. Aksoy

Citation Abrate, T., Hubert, P., and Sighomnou, D., 2013. A study on hydrological series of the Niger River. Hydrological Sciences Journal, 58 (2), 271–279.     

A STOCHASTIC MODEL FOR DRAINAGE PATTERNS INTO AN INTRAMONTANE TREINCH

Abstract

The typical drainage patterns observed on the sides of intramontane trenches can be explained by a random walk medel of fluvial erosion.     

High-resolution simulation of the spatial pattern of water use in continental China

ABSTRACT

High-resolution data on the spatial pattern of water use are a prerequisite for appropriate and sustainable water management. Based on one well-validated hydrological model, the Distributed Time Variant Gains Model (DTVGM), this paper obtains reliable high-resolution spatial patterns of irrigation, industrial and domestic water use in continental China. During the validation periods, ranges of correlation coefficient (R) and Nash-Sutcliffe efficiency (NSE) coefficient are 0.67–0.96 and 0.51–0.84, respectively, between the observed and simulated streamflow of six hydrological stations, indicating model applicability to simulate the distribution of water use. The simulated water use quantities have relative errors (RE) less than 5% compared with the observed. In addition, the changes in streamflow discharge were also correctly simulated by our model, such as the Zhangjiafen station in the Hai River basin with a dramatic decrease in streamflow, and the Makou station in the Pearl River basin with no significant changes. These changes are combined results of basin available water resources and water use. The obtained high-resolution spatial pattern of water use could decrease uncertainty of hydrological simulation and guide water management efficiently.

Editor M.C. Acreman; Associate editor X. Fang     

Monitoring the erosion of an expressway during its construction: problems and lessons

Abstract

The large quantities of sediment eroded from the Sydney F3 Expressway extension and the lack of defined channels within the catchment presented several problems of discharge and sediment load sampling. The monitoring equipment at the catchment outlet, namely pump samplers and capacitance-based water level sensors, was computer controlled, but for partial area monitoring manual methods were used together with Gerlach traps and erosion pins. The monitoring at the catchment outlet was cost-effective because of the use of electronic equipment. The sampling strategies are described and recommendations for future sampling programs are presented. Coarse sand and silt-clay concentrations in many samples were more than 10 g 1^?1 at the outlet. In some samples the silt-clay concentrations exceeded 30 g 1^?1 and the coarse sand concentrations 100 g 1^?1.     

Analytic scaling laws in planetary dynamo models

ABSTRACT

Numerical models of planetary MHD dynamos have led to many advances in the last twenty years. However, the accessible parameter space of these models is somewhat limited due to computational constraints. A number of numerically based scaling laws have been proposed, but it has been difficult to reliably confirm them from the simulation data alone. Since these scaling laws have to be used to extend the numerical models into the planetary parameter regime, getting correct scalings is an important issue. Here some possible balances between the relevant terms in the dynamo equations are considered, and a number of different known and new scaling laws are proposed and justified from analytical point of view. Some of these laws are compatible with the widely known Christensen and Aubert (Geophys. J. Int. 2006, 166) scaling for the magnetic field strength. Plausible estimates of the typical values of the important quantities in the Earth's core and other Terrestrial planets are made, and the extent to which the various scaling laws are consistent with these estimates is discussed.     

A comparative study on a simple two-parameter monthly water balance model and the Kajiyama formula for monthly runoff estimation

ABSTRACT

A two-parameter monthly water balance model to simulate runoff can be used for a water resources planning programme and climate impact studies. However, the model estimates two parameters of transformation of time scale (c) and of the field capacity (SC) by a trial-and-error method. This study suggests a modified methodology to estimate the parameters c and SC using the meteorological and geological conditions. The modified model is compared with the Kajiyama formula to simulate the runoff in the Han River and International Hydrological Programme representative basins in South Korea. We show that the estimated c and SC can be used as the initial or optimal values for the monthly runoff simulation study in the model.

EDITOR M.C. Acreman; ASSOCIATE EDITOR S. Kanae     

A continuous simulation model for design-hydrograph estimation in small and ungauged watersheds

Abstract

A detailed investigation of the behaviour of various hydraulic parameters, using data from rivers in Greece, was conducted in order to explore the universality of features that many natural streams are believed to have in common. Analysis of vertical profiles of temporal mean of horizontal velocities (u) in the longitudinal (river flow) direction and of transverse profiles of depth-mean longitudinal velocities (U) estimated from these vertical profiles, measured at 232 cross-sections of several rivers in Greece, provided valuable information: on the distribution of local roughness coefficients (n_i ) along the wetted perimeter of the cross-sections examined; on the shape of u profiles; on the ratio of maximum to mean cross-sectional velocity, V_max/V_m , and its relation to a dimensionless entropy parameter, M; on the shape of U profiles; and on the normalized intensity, r, of the spatial departure of u velocities from V_m . The similarities among the quantities (u, U, n, V_max/V_m , M, r) analysed in this study and in pertinent literature reveal that the rivers examined exhibit many of the basic features, of rather universal character, shown by other rivers (all over the world) having different geometric and/or other characteristics (aspect ratios, bottom roughness, flow kinematics, etc.). Corresponding differences are also described and explained.     

A multivariate design framework for river confluences

ABSTRACT

Throughout the last decade copula functions were widely used to assess a wide range of hydrological problems, often focusing on two distinct variables. In many of these studies it was ignored whether the two variables of interest actually occurred simultaneously (e.g. two annual maximum time series were analysed in a multivariate statistical framework). Here we introduce a novel approach to derive bivariate design events using copula functions allowing both simultaneous and non-simultaneous occurrence of the variables to be modelled. The methodology is exemplarily applied to assess the combined flood occurrence at the confluence of the rivers Rhine and Sieg (Germany). The results underline the validity of the methodology. Employing a hydrodynamic numerical model furthermore shows that commonly used statistical approaches to select a single design event out of a vast number of possible combinations can be critical for practical design purposes.

Editor Z.W. Kundzewicz; Associate editor S. Grimaldi