Finite amplitude convection and magnetic field generation in a rotating spherical shell

Abstract

Finite amplitude solutions for convection in a rotating spherical fluid shell with a radius ratio of η=0.4 are obtained numerically by the Galerkin method. The case of the azimuthal wavenumber m=2 is emphasized, but solutions with m=4 are also considered. The pronounced distinction between different modes at low Prandtl numbers found in a preceding linear analysis (Zhang and Busse, 1987) is also found with respect to nonlinear properties. Only the positive-ω-mode exhibits subcritical finite amplitude convection. The stability of the stationary drifting solutions with respect to hydrodynamic disturbances is analyzed and regions of stability are presented. A major part of the paper is concerned with the growth of magnetic disturbances. The critical magnetic Prandtl number for the onset of dynamo action has been determined as function of the Rayleigh and Taylor numbers for the Prandtl numbers P=0.1 and P=1.0. Stationary and oscillatory dynamos with both, dipolar and quadrupolar, symmetries are close competitors in the parameter space of the problem.     

Riparian alder fens — source or sink for nutrients and dissolved organic carbon? — 2. Major sources and sinks

Natural riparian forest wetlands are known to be effective in their ability to remove nitrate by denitrification and sediments with attached phosphorus via sedimentation. On the other hand, litter input and decomposition is a process of crucial importance in cycling of nitrogen and phosphorus in a forest ecosystem.In this study we investigated the amount of nitrogen and phosphorus entering the alder fen ecosystem through leaf litter and its decomposition and the removal capacity of nitrogen and phosphorus by measuring denitrification and sedimentation in the alder fen.We found an average input of leaf litter during fall 1998 of 226 g m⁻² yr⁻¹ DW with nutrient concentration of 0.17% P and 1.6% N. This means a yearly input of 0.4 g m⁻² yr⁻¹ P and 3.6 g m⁻² yr⁻¹ N. The decomposition of leaf litter using litter bags with small and large mesh size resulted in bags with macroinvertebrates (large mesh size) and without macroinvertebrates (small mesh size). After 57 days the litter bags with macroinvertebrates had a decomposition rate of 79%.Denitrification was measured in May and June of 1997 using the acetylene inhibition technique on intact soil cores and slurry-experiments. The average annual denitrification rate was 0.2 g m⁻² yr⁻¹ N using data from the core experiments. The denitrification rate was higher after addition of nitrate, indicating that denitrification in the riparian alder fen is mainly controlled by nitrate supply.The sedimentation rate in the investigated alder fen ranged from 0.47 kg m⁻² yr⁻¹ DW to 4.46 kg m⁻² yr⁻¹ DW in 1998 depending on the study site and method we used. Sedimentation rates were lower in newly designed plate traps than in cylinder traps. The alder fen also showed lower rates than the adjacent creek Briese. Average phosphorus removal rate was 0.33 g m⁻² yr⁻¹ P.Input sources for the surface water of the alder fen are sediment mineralization and decomposition of leaf litter; output sources are sedimentation and denitrification. This study showed that a nutrient input of 24.58 kg ha⁻¹ yr⁻¹ N, 8.8 kg ha⁻¹ yr⁻¹ P and 419 kg ha⁻¹ yr⁻¹ DOC into the surface water of the alder fen is possible. Alder fens cannot improve water quality of an adjacent river system. This is only true for a nearly pristine alder fen with the hydrology of 10 months flooded conditions and 2 months non-flooding conditions a year.     

On the onset of convection in rotating spherical shells

Abstract

The linear problem of the onset of convection in rotating spherical shells is analysed numerically in dependence on the Prandtl number. The radius ratio η=r _i/r _o of the inner and outer radii is generally assumed to be 0.4. But other values of η are also considered. The goal of the analysis has been the clarification of the transition between modes drifting in the retrograde azimuthal direction in the low Taylor number regime and modes traveling in the prograde direction at high Taylor numbers. It is shown that for a given value m of the azimuthal wavenumber a single mode describes the onset of convection of fluids of moderate or high Prandtl number. At low Prandtl numbers, however, three different modes for a given m may describe the onset of convection in dependence on the Taylor number. The characteristic properties of the modes are described and the singularities leading to the separation with decreasing Prandtl number are elucidated. Related results for the problem of finite amplitude convection are also reported.     

Spherical dynamos with anisotropic α-effect

Abstract

The mean field induction equation of Steenbeck, Krause and Rädler (1966) is solved for anisotropic α _ik -tensors of varying anisotropy. The attention is restricted to α²-dynamos in spheres with steady axisymmetric magnetic fields. The ratio of the electrical conductivity outside and inside the sphere is varied, but in all cases it is found that a steady dynamo does not exist when the anisotropy of the α _ik -tensor exceeds a critical value. Such a critical value does not exist in the exceptional case of the Fermi boundary condition. The results emphasize the important effect of boundaries on the existence of solutions of the dynamo problem.     

Shear flow instabilities in a rotating system

Abstract

The stability of a plane parallel shear flow with the profile U(z) = tanh z is considered in a rotating system with the axis of rotation in the z-direction. The establishment of the basic flow requires a baroclinic state, but baroclinic effects are suppressed in the stability analysis by assuming a limit of high thermal conductivity. It is shown that the strongest growing disturbance changes from a purely transverse form in the limit of vanishing rotation rate to a nearly longitudinal form as the angular velocity of rotation increases. An analytical solution of the stability equation is obtained for vanishing growth rates of the transverse form of the instability. But, in general, the solution of the problem requires numerical integrations which demonstrate that the preferred direction of the wave vector of the instability is towards the left of the direction of the mean flow.     

Generation of planetary magnetism by convection

Reliable measurements of the magnetic fields of Jupiter and Mercury have been obtained recently. Convection appears to be the most probable origin of Jovian and Hermaean magnetism as well as of geomagnetism. The similarity of the dynamo mechanism in the electrically conducting core of these planets offers opportunities for comparing different hypotheses and testing theoretical models. It is proposed in this paper that the realized magnetic field reaches a maximum amplitude in accordance with the dynamical constraints of nearly geostrophic motion and the condition for dynamo action.     

AOX‐Bildung bei der sonolytischen Oxidation von Salicylsäure in Gegenwart von Chlorid

AOX‐formation by the Sonochemical Treatment of Salicylic Acid in Presence of Chloride Ultrasound shows great potential for improving water, wastewater and sludge treatment processes. However, a number of questions exist: for example the influence of suspended solids or salts. In this paper the influence of chloride in view of AOX‐formation should be investigated. As organic model compound salicylic acid (0.05…1 mmol/L) was used. Formation of AOX (adsorbable organically bound halogens) was measured in dependence upon chloride concentrations (1.4…141 mmol/L) and pH 2 and 9. Ultrasound irradiation was performed in glass reactor (500 mL) at 206 kHz and 353 kHz by continuous bubbling argon:oxgen (4:1) at a flow rate of 1 L/min into the solutions. The elimination of salicylic acid and the formation of hydrogen peroxide were not influenced by the presence of chloride (up to 56 mmol/L). The rate of salicylic acid elimination and the formation rate of hydrogen peroxide are at concentrations of mmol/(L min) levels but those of AOX formation of μmol/(L min) levels. The reactions leading to chlorinated by‐products can be seen as minor reaction paths. The yield of AOX depending on frequency, pH and chloride concentration lies between 10 μg/L and 900 μg/L. In acidic medium they were twice as high as in basic medium. Below the ratio chloride : salicylic acid of 2 mol/mol, AOX could not be identified.     

A distribution-free ordinal classification of floods based on moments

ABSTRACT

Classification of floods is often based on return periods of their peaks estimated from probability distributions and hence depends on assumptions. The choice of an appropriate distribution function and parameter estimation are often connected with high uncertainties. In addition, limited length of data series and the stochastic characteristic of the occurrence of extreme events add further uncertainty. Here, a distribution-free classification approach is proposed based on statistical moments. By using robust estimators the sampling effects are reduced and time series of different lengths can be analysed together. With a developed optimization procedure, locally and regionally consistent flood categories can be defined. In application, it is shown that the resulting flood categories can be used to assess the spatial extent of extreme floods and their coincidences. Moreover, groups of gauges, where simultaneous events belong to the same classes, are indicators for homogeneous groups of gauges in regionalization.     

Thermal convection in differentially rotating systems

Abstract

The onset of convection in a cylindrical fluid annulus is analyzed in the case when the cylindrical walls are rotating differentially, a temperature gradient in the radial direction is applied, and the centrifugal force dominates over gravity. The small gap approximation is used and no-slip conditions on the cylindrical walls are assumed. It is found that over a considerable range of the parameter space either convection rolls aligned with the axis of rotation or rolls in the perpendicular (azimuthal) direction are preferred. It is shown that by a suitable redefinition of parameters, results for finite amplitude Taylor vortices and for convection rolls in the presence of shear can be applied to the present problem. Weakly nonlinear results for transverse rolls in a Couette flow indicate the possibility of subcritical bifurcation for Prandtl numbers P less than 0.82. Heat and momentum transports are derived as functions of P and the problem of interaction between transverse and longitudinal rolls is considered. The relevance of the analysis for problems of convection in planetary and stellar atmospheres is briefly discussed.