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1.
In the framework of the eddy dynamic model developed in two previous papers (Dubovikov, M.S., Dynamical model of mesoscale eddies, Geophys. Astophys. Fluid Dyn., 2003, 97, 311–358; Canuto, V.M. and Dubovikov, M.S., Modeling mesoscale eddies, Ocean Modelling, 2004, 8, 1–30 referred as I–II), we compute the contribution of unresolved mesoscale eddies to the large-scale dynamic equations of the ocean. In isopycnal coordinates, in addition to the bolus velocity discussed in I–II, the mesoscale contribution to the large scale momentum equation is derived. Its form is quite different from the traditional down-gradient parameterization. The model solutions in isopycnal coordinates are transformed to level coordinates to parameterize the eddy contributions to the corresponding large scale density and momentum equations. In the former, the contributions due to the eddy induced velocity and to the residual density flux across mean isopycnals (so called Σ-term) are derived, both contributions being shown to be of the same order. As for the large scale momentum equation, as well as in isopycnal coordinates, the eddy contribution has a form which is quite different from the down-gradient expression.  相似文献   

2.
Dubovikov and Canuto (Dubovikov, M.S. and Canuto, V.M., Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. Astrophys. Fluid Dyn., 2006, 100, 197–214), after averaging the tracer conservation equation in density coordinates and transforming to height coordinates, concluded that present ocean models are missing important terms in their mean tracer equations. Here we point out some errors made by Dubovikov and Canuto (2006 Dubovikov, MS and Canuto, VM. 2006. Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. & Astrophys. Fluid Dynam., 100: 197–214. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in their isopycnal averaging procedure. We draw on the temporal-residual-mean (TRM) theory and show that when the isopycnal averaging and coordinate transformation are performed correctly, the tracer equations of present ocean circulation models are recovered. We therefore conclude that present ocean circulation models are not neglecting the leading order terms identified by Dubovikov and Canuto (2006 Dubovikov, MS and Canuto, VM. 2006. Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. & Astrophys. Fluid Dynam., 100: 197–214. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).  相似文献   

3.
Abstract

Edited by Charlotte W. Gordon, V. Canuto and W. Ian Axford, Gordon and Breach Science Publishers, 412 pp., $63.00 ($35.00). (ISBN O 677 16100 X.) 1978.  相似文献   

4.
Abstract

In discrete water quality surveys, riverine fluxes are associated with unknown uncertainties (biases and imprecisions). Annual flux errors have been determined from the generation of discrete surveys by Monte Carlo sorting for monthly sampling, from 10 years of daily records (120 records). Eight calculation methods were tested for suspended particulate matter, dissolved solids and dissolved and total nutrients in medium to large basins (103 to 106 km2) covering a wide range of hydrological conditions and riverine biogeochemistry. The performance of each method was analysed first by type of riverine material, which appeared to be much less pertinent than the flux variability matrix. The latter combines the river flow duration in two percent of time (W2%) and the truncated exponent (b50sup) defining the relationship of concentration vs discharge (C–Q) at higher flows (C = aQb50sup). As flux variability increases (high W2% and/or high b50sup), averaging and rating curve methods become less efficient compared to hydrograph separation methods. Flux biases and imprecisions were plotted in the [W2%, b50sup] matrix for discrete monthly surveys.

Editor Z. W. Kundzewicz

Citation Raymond, S., Moatar, F., Meybeck, M., and Bustillo, V., 2013. Choosing methods for estimating dissolved and particulate riverine fluxes from monthly sampling. Hydrological Sciences Journal, 58 (6), 1326–1339.  相似文献   

5.
Abstract

Suspended sediment and bedload discharges in sand-bed rivers shape semi-arid landscapes and impact sediment delivery from these landscapes, but are still incompletely understood. Suspended sediment and bedload fluxes of the intermittent Exu River, Brazil, were sampled by direct measurements. The highest suspended sediment concentration observed was 4847.4 mg L-1 and this value was possibly associated with the entrainment of sediment that was deposited in the preceding year. The bedload flux was well related to the stream power and the river efficiently transported all available bedload with a mean rate of 0.0047 kg m-1 s-1, and the percentage of bedload to suspended sediment varied between 4 and 12.72. The bed sediment of Exu River was prone to entrainment and showed a proclivity for transport. Thus, sand-bed and gravel-bed rivers of arid environments seem to exhibit the same mobility in the absence of armour layer.

Editor D. Koutsoyiannis; Associate editor B. Touaibia

Citation Cantalice, J.R.B., Cunha Filho, M., Stosic, B.D., Piscoya, V.C., Guerra, S.M.S., and Singh, V.P., 2013. Relationship between bedload and suspended sediment in the sand-bed Exu River, in the semi-arid region of Brazil. Hydrological Sciences Journal, 58 (8), 1789–1802.  相似文献   

6.
Abstract

This study presents an analysis of three hydrological years (2007/08, 2008/09 and 2009/10) of precipitation, runoff and sediment yield collected from a small (669.7 ha) semi-arid watershed in southeastern Spain (Lanjarón). At the watershed outlet the runoff, suspended sediment concentration, total solute concentrations and dissolved nutrients (N-NO3, N-NH4, H2PO4 and K) in streamflow were continuously monitored. The runoff was highly variable, ranging between 53.4 and 154.7 mm year?1, with an average of 97.6 mm year?1. In contrast, sediment yields were more regular, averaging 1.8 Mg ha?1 year?1. The hydrological response of the watershed depended mainly on rainfall intensity. Formerly, 32% of the watershed was forested and runoff was more regular, despite the typical Mediterranean rainfall cycle; however, due to forest area reduction to 17% and the increase in abandoned farmland area (18%) in recent decades, the runoff variability has increased. Greater amounts of solutes (32.7 Mg ha?1 year?1) were exported, so that this water is considered as poor for irrigation use. The temporal nutrient export was related to seasonal discharge fluctuations as well as daily concentrations. In addition, the nutrient concentrations of the water discharged were lower than threshold limits cited in water-quality standards for agricultural use and for potable water, with the exception of K (65.9 mg L?1), which may degrade surface waters as well as irrigated soils. Thus, hydrological and erosive processes depended on the watershed features, but also on prior conditions in combination with the characteristics of rainfall episodes.

Citation Durán, Z.V.H., Francia, M.J.R., Garcia, T.I., Rodríguez, P.C.R., Martínez, R.A., and Cuadros, T.S., 2012. Runoff and sediment yield from a small watershed in southeastern Spain (Lanjarón): implications for water quality. Hydrological Sciences Journal, 57 (8), 1610–1625.  相似文献   

7.
Abstract

The objective of this study is to analyse three rainfall–runoff hydrological models applied in two small catchments in the Amazon region to simulate flow duration curves (FDCs). The simple linear model (SLM) considers the rainfall–runoff process as an input–output time-invariant system. However, the rainfall–runoff process is nonlinear; thus, a modification is applied to the SLM based on the residual relationship between the simulated and observed discharges, generating the modified linear model (MLM). In the third model (SVM), the nonlinearity due to infiltration and evapotranspiration is incorporated into the system through the sigmoid variable gain factor. The performance criteria adopted were a distance metric (δ) and the Nash-Sutcliffe coefficient (R2) determined between simulated and observed flows. The good results of the models, mainly the MLM and SVM, showed that they could be applied to simulate FDCs in small catchments in the Amazon region.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Blanco, C.J.C., Santos, S.S.M., Quintas, M.C., Vinagre, M.V.A., and Mesquita, A.L.A., 2013. Contribution to hydrological modelling of small Amazonian catchments: application of rainfall–runoff models to simulate flow duration curves. Hydrological Sciences Journal, 58 (7), 1–11.  相似文献   

8.
Abstract

Rivers have been channelized, deepened and constrained by embankments for centuries to increase agricultural productivity and improve flood defences. This has decreased the hydrological connectivity between rivers and their floodplains. We quantified the hydrological regime of a wet grassland meadow prior to and after the removal of river embankments. River and groundwater chemistry were also monitored to examine hydrological controls on floodplain nutrient status. Prior to restoration, the highest river flows (～2 m3 s?1) were retained by the embankments. Under these flow conditions the usual hydraulic gradient from the floodplain to the river was reversed so that subsurface flows were directed towards the floodplain. Groundwater was depleted in dissolved oxygen (mean: 0.6 mg O2 L?1) and nitrate (mean: 0.5 mg NO3 ?-N L?1) relative to river water (mean: 10.8 mg O2 L?1 and 6.2 mg NO3 ?-N L?1, respectively). Removal of the embankments has reduced the channel capacity by an average of 60%. This has facilitated over-bank flow which is likely to favour conditions for improved flood storage and removal of river nutrients by floodplain sediments.

Editor Z.W. Kundzewicz; Associate editor K. Heal

Citation Clilverd, H.M., Thompson, J.R., Heppell, C.M., Sayer, C.D., and Axmacher, J.C., 2013. River–floodplain hydrology of an embanked lowland Chalk river and initial response to embankment removal. Hydrological Sciences Journal, 58 (3), 627–650.  相似文献   

9.
Abstract

This paper analyses the temporal dynamics of soil water balance components in a representative recharge area of the Sierra de Gádor (Almeria, southeastern Spain) in two hydrological years. Two approaches are used to estimate daily potential recharge (PR): Approach 1 based on deriving PR from the water balance as the difference between measurements of rainfall (P) and actual evapotranspiration (E) obtained by eddy covariance; and Approach 2 with PR obtained from the dynamic pattern of the soil moisture (θ) recorded at two depths in the site's thin soil (average 0.35 m thickess). For the hydrological year 2003/04, which was slightly drier than the 30-year average, E accounted for 64% of rainfall and occurred mainly in late spring and early summer. The PR estimated by Approach 1 was 181 ± 18 mm year-1 (36% of rainfall), suggesting an effective groundwater recharge in the study area. In the unusually dry hydrological year 2004/05, E was about 215 mm year-1, close to the annual rainfall input, and allowing very little (8 ± 12 mm year-1) PR according to Approach 1. Estimation of PR based on Approach 2 resulted in PR rates lower than those found by Approach 1, because Approach 2 does not take into account the recharge that occurs through preferential flow pathways (cracks, joints and fissures) which were not monitored with the θ probes. Moreover, using Approach 2, the PR estimates differed widely depending on the time scale considered: with daily mean θ data, PR estimation was lower, especially in late spring, while θ data at 30 min resolution yielded a more reliable prediction of the fraction of total PR resulting from the downward movement of soil water by gravity.

Citation Cantón, Y., Villagarcía, L., Moro, M. J., Serrano-Ortíz, P., Were, A., Alcalá, F. J., Kowalski, A. S., Solé-Benet, A., Lázaro, R. & Domingo, F. (2010) Temporal dynamics of soil water balance components in a karst range in southeastern Spain: estimation of potential recharge. Hydrol. Sci. J. 55(5), 737–753.  相似文献   

10.
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   

11.
A review of the important constraints on gravity wave induced diffusion of chemical tracers, heat, and momentum is given. Ground-based microwave spectroscopy measurements of H2O and CO and rocket-based mass spectrometer measurements of Ar constrain the eddy diffusion coefficient for constituent transport (K zz ) to be (1–3)×105 cm2s–1 in the upper mesosphere. Atomic oxygen data also limitsK zz to a comparable value at the mesopause. From the energy balance of the upper mesosphere the eddy diffusion coefficient for heat transport (D H ) is, at most 6×105 cm2s–1 at the mesopause and decreasing substantially with decreasing altitude. The available evidence for mean wind deceleration and the corresponding eddy diffusion coefficient for momentum stresses (D M ) suggests that it is at least 1×106 cm2s–1, in the upper mesosphere. Consequently the eddy Prandtl number for macroscopic scale lengths is >3.  相似文献   

12.
A decade of Predictions in Ungauged Basins (PUB)—a review   总被引：2，自引：0，他引：2  
Abstract

The Prediction in Ungauged Basins (PUB) initiative of the International Association of Hydrological Sciences (IAHS), launched in 2003 and concluded by the PUB Symposium 2012 held in Delft (23–25 October 2012), set out to shift the scientific culture of hydrology towards improved scientific understanding of hydrological processes, as well as associated uncertainties and the development of models with increasing realism and predictive power. This paper reviews the work that has been done under the six science themes of the PUB Decade and outlines the challenges ahead for the hydrological sciences community.

Editor D. Koutsoyiannis

Citation Hrachowitz, M., Savenije, H.H.G., Blöschl, G., McDonnell, J.J., Sivapalan, M., Pomeroy, J.W., Arheimer, B., Blume, T., Clark, M.P., Ehret, U., Fenicia, F., Freer, J.E., Gelfan, A., Gupta, H.V., Hughes, D.A., Hut, R.W., Montanari, A., Pande, S., Tetzlaff, D., Troch, P.A., Uhlenbrook, S., Wagener, T., Winsemius, H.C., Woods, R.A., Zehe, E., and Cudennec, C., 2013. A decade of Predictions in Ungauged Basins (PUB)—a review. Hydrological Sciences Journal, 58 (6), 1198–1255.  相似文献   

13.
Abstract

Water discharge and suspended and dissolved sediment data from three rivers (Napo, Pastaza and Santiago) in the Ecuadorian Amazon basin and a river in the Pacific basin (Esmeraldas) over a 9-year period, are presented. This data set allows us to present: (a) the chemical weathering rates; (b) the erosion rates, calculated from the suspended sediment from the Andean basin; (c) the spatio-temporal variability of the two regions; and (d) the relationship between this variability and the precipitation, topography, lithology and seismic activity of the area. The dissolved solids load from the Esmeraldas basin was 2 × 106 t year-1, whereas for the Napo, Pastaza and Santiago basins, it was 4, 2 and 3 × 106 t year-1, respectively. For stations in the Andean piedmont of Ecuador, the relationship between surface sediment and the total sediment concentration was found to be close to one. This is due to minimal stratification of the suspended sediment in the vertical profile, which is attributed to turbulence and high vertical water speeds. However, during the dry season, when the water speed decreases, sediment stratification appears, but this effect can be neglected in the sediment flux calculations due to low concentration rates. The suspended sediment load in the Pacific basin was 6 × 106 t year-1, and the total for the three Amazon basins was 47 × 106 t year-1. The difference between these contributions of the suspended sediment load is likely due to the tectonic uplift and the seismic and volcanic dynamics that occur on the Amazon side.

Editor Z.W. Kundzewicz

Citation Armijos, E., Laraque, A., Barba, S., Bourrel, L., Ceron, C., Lagane, C., Magat, P., Moquet, J.-S., Pombosa, R., Sondag, F., Vauchel, P., Vera, A., and Guyot, J.L., 2013. Yields of suspended sediment and dissolved solids from the Andean basins of Ecuador. Hydrological Sciences Journal, 58 (7), 1478–1494.  相似文献   

14.
Abstract

The exact numerical and approximate analytical solutions of the simplest nonlinear integral equation with second order nonlinearity for the averaged Green function are presented. It is assumed that the turbulence is stationary, homogeneous, isotropic and incompressible. Numerous examples of turbulent spectra are considered (peak-like spectrum, spectra of Kolmogorov's type with different forms of “pumping” regions, stepwise spectra etc.). Special emphasis is given to investigating the case of so called “frozen” turbulence when the parameter ξ =u 0τ/R→∞ where uτ0,R 0 are characteristic velocity, lifetime and space scale of turbulent pulsations, respectively. It is shown that these solutions allow us to calculate the turbulent diffusivities accurately for arbitrary spectra with any values of the parameter ξ. The results take into account the possible helicity of turbulence concerned only with scalar passive fields (number density and temperature).  相似文献   

15.
Abstract

Floods from the middle part of the River Morava (eastern Czech Republic) are considered over the course of the past three centuries, the study being based on data derived from documentary evidence (1691–1880), measured peak water stages, Hk (1881–1920) and peak discharges, Qk (1916–2009), evaluated with respect to their N-year return period (HN and QN ). Changes in land use and water management (water reservoirs, channel modifications) are discussed, as are factors influencing runoff conditions in the Morava catchment. Decadal synthesis of flood series identifies the highest flood activity in the decades of 1911–1920 and 1961–1970 (11 floods each), 1831–1840, 1891–1900, 1901–1910 and 1931–1940 (10 floods each). Uncertainty in this series is related to some incompleteness of documentary data in the pre-1881 period. Very low flood frequency occurred in the 1990s–2000s, although the most disastrous floods were recorded in this particular period (July 1997 at Q 100 and March/April 2006 at Q 20–Q 50). Changes in flood frequency correspond partly to long-term changes in temperature and precipitation patterns.

Citation Brázdil, R., ?ezní?ková, L., Valá?ek, H., Havlí?ek, M., Dobrovolný, P., Soukalová, E., ?ehánek, T. & Skokanová, H. (2011) Fluctuations of floods of the River Morava (Czech Republic) in the 1691–2009 period: interactions of natural and anthropogenic factors. Hydrol. Sci. J. 56(3), 468–485.  相似文献   

16.
Abstract

This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S2c 2 kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (R M2) and it was assumed that the magnetic Reynolds number of the core (R M1) and of the shell (R M3) were prescribed parameters. Hence R M2 was studied as a function of R M1 and R M3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. For R M1 =R M3= 103, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values of R M2 are found to be three orders of magnitude lower than R M1, R M3 so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, for R M2 (or R M3) lying in the range 102 to 105, the self-excitation condition is found to be of the form R M2˙R ½ M1=constant (or R M2˙R½ M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limit R M2˙R?½; M1=constant.

An analysis of known three-dimensional dynamo models indicates the importance of the absence of mirror symmetry planes for the efficient generation of magnetic fields.  相似文献   

17.
Formulated as an inverse problem, the diffusion parameters associated with length-scale dependent eddy diffusivities can be viewed as the unknowns in the mass conservation equation for coastal zone transport problems. The values of the diffusion parameters can be optimized according to an error function incorporated with observed concentration data. Examples are given for the Fickian, shear diffusion and inertial subrange diffusion models. Based on a new set of dyeplume data collected in the coastal zone off Bronte, Lake Ontario, it is shown that the predictions of turbulence closure models can be evaluated for different flow conditions. The choice of computational schemes for this diagnostic approach is based on tests with analytic solutions and observed data. It is found that the optimized shear diffusion model produced a better agreement with observations for both high and low advective flows than, e.g., the unoptimized semi-empirical model, Ky=0.075 σy1.2, described by Murthy and Kenney.  相似文献   

18.
Abstract

Stable isotopes are powerful research tools in environmental sciences and their use in ecosystem research is increasing. Stable isotope measurements allow the study of evapotranspiration fluxes, soil evaporation and leaf transpiration phenomena. Soil water and leaf water are the sources of the evapotranspiration that transfers large quantities of water from land to the atmosphere; as a result the isotopic composition of water left in the leaves is modified towards enrichment. Evaporation also changes the isotopic composition of water bodies creating a natural isotopic signal. The isotopic identity of soil water affects the oxygen isotopic signature of leaf and stem water. In this paper we present the isotopic data of bulk leaf water, showing the enrichment in isotopic value of oxygen due to evapotranspiration from leaves in conjunction with the isotopic signal of rainwater and other environmental factors such as humidity and temperature. Results suggest that the variation in the values of δ18O of Eucalyptus citriodora, Dalbergia sissoo, Melia azedarach and Pinus roxburghii is due to the seasonal changes in the δ18O of the source water for plants, i. e. rain. It is further observed that leaf water δ18O values are depleted during the months of July, August and September. This occurs due to the following reasons: (a) the sampling areas receive about 50% of the average annual rain during these months, and (b) rainfalls during these months are isotopically depleted compared with winter rains.

Citation Butt, S., Ali, M., Fazil, M. & Latif, Z. (2010) Seasonal variations in the isotopic composition of leaf and stem water from an arid region of Southeast Asia. Hydrol. Sci. J. 55(5), 844–848.  相似文献   

19.
Abstract

Electromagnetic induction measurements (EM) were taken in a saline gypsiferous soil of the Saharan-climate Fatnassa oasis (Tunisia) to predict the electrical conductivity of saturated soil extract (ECe) and shallow groundwater properties (depth, Dgw, and electrical conductivity, ECgw) using various models. The soil profile was sampled at 0.2 m depth intervals to 1.2 m for physical and chemical analysis. The best input to predict the log-transformed soil salinity (lnECe) in surface (0–0.2 m) soil was the EMh/EMv ratio. For the 0–0.6 m soil depth interval, the performance of multiple linear regression (MLR) models to predict lnECe was weaker using data collected over various seasons and years (R a 2 = 0.66 and MSE = 0.083 dS m-1) as compared to those collected during the same period (R a 2 = 0.97, MSE = 0.007 dS m-1). For similar seasonal conditions, for the Dgw–EMv relationship, R 2 was 0.88 and the MSE was 0.02 m for Dgw prediction. For a validation subset, the R 2 was 0.85 and the MSE was 0.03 m. Soil salinity was predicted more accurately when groundwater properties were used instead of soil moisture with EM variables as input in the MLR.

Editor D. Koutsoyiannis; Associate editor K. Heal

Citation Bouksila, F., Persson, M., Bahri, A., and Berndtsson, R., 2012. Electromagnetic induction predictions of soil salinity and groundwater properties in a Tunisian Saharan oasis. Hydrological Sciences Journal, 57 (7), 1473–1486.  相似文献   

20.
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.  相似文献   

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