On the spin-up of a stably stratified,electrically conducting fluid. Part 1: Spin-up controlled by the hartmann layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady Hartmann boundary layer control the fluid interior. It is shown how to obtain the known spin-up times for a homogeneous, nonconducting fluid (τ = E ^-½), a stably stratified, nonconducting fluid (τ = (σS/E, E ^?1) and a homogeneous conducting fluid (τ = α^?1 E ^-½) from the present formulation where τ = v/ωt, E = v/ωL ², σS = vN²/κω² and 2α² = σB²/pω. The problem is solved in the parameter range E?α²?1, α²/E?σS using the Laplace transform and two new spin-up times are obtained. Combined into one expression, they are τ = (1 + δ)α^?1E^-½ where δ = σμv. The spin-up mechanism is investigated and it is found that, in contrast to the homogeneous, conducting case, torsional Alfvén waves may be instrumental in the spin-up of a stratified conducting fluid. The effects of viscous and ohmic diffusion on the torsional Alfvén wave fronts are studied and the following regimes are identified: 0 < δ ?E/α², spin-up by meridional circulation of electric current with no Alfvén waves; E^-½/α ? δ ? 1, spin-up by meridional circulation of electric current with transient Alfvén waves; α/E^½ ? δ ? α²/E, spin-up by meridional circulation of current with weak Alfvén waves; 1 ? δ ? α/E^½, spin-up by strong Alfvén waves; α^½/E ? δ ? α²/E, spin-up by viscous diffusion with transient Alfvén waves; α/E ? δ < ∞, spin-up by viscous diffusion with no Alfvén waves.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Impact of Ca2+ and Mg2+ on the Removal of F− by Magnesium Potassium Phosphate

This study investigates the influence of Ca²⁺ and Mg²⁺ on the removal of F^? by magnesium potassium phosphate (MPP) from water. The kinetic experiments reveal that the F^? concentration decreased from 3.5 to 3.31 mg L^?1 in a single (F^?) system and to 1.45 mg L^?1 in a ternary system (F^?, Ca²⁺, and Mg²⁺) after 1 min, respectively. Thus, the F^? removal efficiencies are found to increase by about 53% with the co‐active effect of Ca²⁺ and Mg²⁺ in the solution. Moreover, Ca²⁺ and Mg²⁺ are almost completely removed in the F^?, Ca²⁺, and Mg²⁺ system. According to the pseudo‐first‐order modeling, the rate constants k for F^?, Ca²⁺, and Mg²⁺ are 0.00348, 0.0106, and 0.0159 min^?1 respectively; thus, Mg²⁺ > Ca²⁺ > F^?. In the ternary system, the removal efficiencies are 53.29–66.03% for F^?, 99.99–100% for Ca²⁺, and 87.21–95.19% for Mg²⁺ with initial pH 5–10. The removal efficiencies of F^? increases with increases in initial concentrations of F^?, Ca²⁺, and Mg²⁺. The removal of F^? is governed by two routes: 1) adsorption by electrostatic interactions and outer sphere surface complexation; 2) co‐precipitation with Ca₃(PO₄)₂, CaHPO₄, Mg₃(PO₄)₂, and Mg(OH)₂.     

Energy flux partitioning and evapotranspiration in a sub‐alpine spruce forest ecosystem

In this study, we examined the year 2011 characteristics of energy flux partitioning and evapotranspiration of a sub‐alpine spruce forest underlain by permafrost on the Qinghai–Tibet Plateau (QPT). Energy balance closure on a half‐hourly basis was H + λE = 0.81 × (R_n ? G ? S) + 3.48 (W m^?2) (r² = 0.83, n = 14938), where H, λE, R_n, G and S are the sensible heat, latent heat, net radiation, soil heat and air‐column heat storage fluxes, respectively. Maximum H was higher than maximum λE, and H dominated the energy budget at midday during the whole year, even in summer time. However, the rainfall events significantly affected energy flux partitioning and evapotranspiration. The mean value of evaporative fraction (Λ = λE/(λE + H)) during the growth period on zero precipitation days and non‐zero precipitation days was 0.40 and 0.61, respectively. The mean daily evapotranspiration of this sub‐alpine forest during summer time was 2.56 mm day^?1. The annual evapotranspiration and sublimation was 417 ± 8 mm year^?1, which was very similar to the annual precipitation of 428 mm. Sublimation accounted for 7.1% (30 ± 2 mm year^?1) of annual evapotranspiration and sublimation, indicating that the sublimation is not negligible in the annual water balance in sub‐alpine forests on the QPT. The low values of the Priestley–Taylor coefficient (α) and the very low value of the decoupling coefficient (Ω) during most of the growing season suggested low soil water content and conservative water loss in this sub‐alpine forest. Copyright © 2013 John Wiley & Sons, Ltd.     

On the spin-up of a stably stratified,electrically conducting fluid. Part 2: Spin-up controlled by the mac layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady MAC layer control the fluid interior, The MAC layer is a new boundary layer first studied by Loper (1976a) which controls the fluid in the parameter range E/α² ? σS ? α²/E, α² ? 1 Where E = vωL², 2α² = σB²/pω and σS = vN²/κω;². The problem is solved using the Laplace transform and four new spin-up times are obtained. Combined into one expression they are t = ω;^?1E-½[1+(σSE/α⁶)^½ + δα^-2] [1+(σSE/α^{6 1/4}]^?1 where δ = σμv. The internal spin-up mechanisms for this problem are shown to be very similar to those discussed in part 1 (Loper, 1976b). The ten known spin-up times are summarized and their inter-relationships are investigated. It is shown how to obtain the seven hydromagnetic spin-up times from a simple torsional Alfvén wave model involving a single parameter which measures the strength of the boundary layer dissipation. Finally, the present theory is applied to the solar spin-down problem and it is found that if the magnetic field in the solar interior is at least as strong as the interplanetary field of 10^-5 gauss, then the hydromagnetic spin-down time is much shorter than the Eddington-Sweet time and is comparable to the age of the sun.     

A scattering model for seismic attenuation and its global applications

The attenuation characteristics of Indian lithosphere and its comparison with different tectonic settings in the world are determined from the observations of the Q for L_g(Q_Lg)-, and S(Q_S)-waves in the 1-30 Hz frequency range. The scattering is approximated with a Gaussian distribution of spherical scatterers. To approximate single scattering, we use Dainty's [Geophy. Res. Lett. 8 (11) (1981) 1126] model that attenuation is given by 1/Q(ω) = 1/Q_i + g(ω)v/ω, where Q_i is intrinsic Q due to anelastic attenuation, v is shear wave velocity, ω is angular frequency, g = ∫n(a)σ da is the total scattering coefficient for S-to-S scattering, n(a) da is the number of scattering spheres of radius a per unit volume, and σ is the scattering cross-section for the sphere. We find that if n(a) is described by a simple two parameter (a₀ and c) Gaussian of amplitude c and standard deviation and mean a₀, the attenuation data for different regions of the world are well approximated over the frequency band of seismic observations. Our major findings are: (1) the maximum effect of scattering on attenuation occurs at 0.84 Hz or a wavelength of 4.16 km; (2) the values of g are frequency dependent. Values of g are of the order of 10⁻³ km⁻¹ at 1-30 Hz, varying from 0.0031 to 0.01 and 0.001 to 0.0083 km⁻¹ for tectonically active and stable regions, respectively; (3) regions of active tectonics and seismicity generally have lower Q_i values (1000) than that in stable regions (2000); and (4) regions of high Q_i value exhibit low intensity of scattering.     

Evolution of non-linear α 2-dynamos and taylor's constraint

A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear?α?²-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5× 10^?3 to 5.0× 10^?5, for?α?=α ₀cos?θ?sin?π?(r?r_i ) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of?α?₀. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.     

Non-axisymmetric α2Ω-dynamo waves in thin stellar shells

Linear α²Ω-dynamo waves are investigated in a thin turbulent, differentially rotating convective stellar shell. A simplified one-dimensional model is considered and an asymptotic solution constructed based on the small aspect ratio of the shell. In a previous paper Griffiths et al. (Griffiths, G.L., Bassom, A.P., Soward, A.M. and Kuzanyan, K.M., Nonlinear α²Ω-dynamo waves in stellar shells, Geophys. Astrophys. Fluid Dynam., 2001, 94, 85–133) considered the modulation of dynamo waves, linked to a latitudinal-dependent local α-effect and radial gradient of the zonal shear flow. These effects are measured at latitude θ by the magnetic Reynolds numbers R _α f(θ) and R _Ω g(θ). The modulated Parker wave, which propagates towards the equator, is localised at some mid-latitude θ_p under a Gaussian envelope. In this article, we include the influence of a latitudinal-dependent zonal flow possessing angular velocity Ω_*(θ) and consider the possibility of non-axisymmetric dynamo waves with azimuthal wave number m. We find that the critical dynamo number D _c?=?R _α R _Ω is minimised by axisymmetric modes in the αΩ-limit (Rα→0). On the other hand, when Rα?≠?0 there may exist a band of wave numbers 0?m?m ^? for which the non-axisymmetric modes have a smaller D _c than in the axisymmetric case. Here m ^? is regarded as a continuous function of R _α with the property m?→0 as R _α→0 and the band is only non-empty when m??>1, which happens for sufficiently large R _α. The preference for non-axisymmetric modes is possible because the wind-up of the non-axisymmetric structures can be compensated by phase mixing inherent to the α²Ω-dynamo. For parameter values resembling solar conditions, the Parker wave of maximum dynamo activity at latitude θ_p not only propagates equatorwards but also westwards relative to the local angular velocity Ω_*(θ _p ). Since the critical dynamo number D _c?=?R _α R _Ω is O (1) for small R _α, the condition m ^??>?1 for non-axisymmetric mode preference imposes an upper limit on the size of |dΩ_*/dθ|.     

Pan evaporation modelling and changing attribution analysis on the Tibetan Plateau (1970–2012)

Pan evaporation (E_p) is an important indicator of water and energy and the decline of E_p has been reported in many regions over the last decades. The climate and E_p are dependent on each other. In this study, the temporal trends of E_p and main E_p drivers, namely mean air temperature (T_a), wind speed (u), global solar radiation (R_s), net long‐wave radiation(R_nl) and vapour pressure deficit (D) from 1970 to 2012, were calculated on the basis of 26 meteorological stations on the Tibetan Plateau. The arithmetic average of E_p from 26 stations decreased with the rate of ?11.91 mm a^?2; the trends of R_s, R_nl, T_a, u and D were ?1.434 w m^?2 decade^?1, 0.2511 w m^?2 decade^?1, 0.3590°C decade^?1, ?0.2376 m s^?1 decade^?1 and 9.523 Pa decade^?1, respectively. The diffuse irradiance is an essential parameter to model E_p and quantify the contribution of climatic factors to changing E_p. 60 724 observations of R_s and diffuse solar irradiance (R_d) from seven of the 26 stations were used to develop the correlation between the diffuse fraction (R_d/R_s), and the clearness index (R_s/R_o). On the basis of the estimation of the diffuse component of R_s and climatic data, we modified the PenPan model to estimate Chinese micro‐pan evaporation (E_p) and assess the attribution of E_p dynamics using partial derivatives. The results showed that there was a good agreement between the observed and calculated daily E_p values. The observed decrease in E_p was mostly due to declining wind speed (?13.7 mm a^?2) with some contributions from decreasing solar irradiance (?3.1 mm a^?2); and the increase of temperature had a large positive effect (4.55 mm a^?2) in total whilst the increase of R_nl had insignificant effect (0.35 mm a^?2) on E_p rates. The change of E_p is the net result of all the climatic variables. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparison of Magnetic Properties and Shadow Area of Leading and Trailing Spots with Different Asymmetries

The magnetic properties of the shadow of magnetic-related leading and trailing spots (those connected by forces lines of magnetic field, which are calculated from a field in potential approximation) are studied in this work. The correlations are established between individual characteristics of the field in the spot shadow and these characteristics from the shadow area S for spot pairs, for which the minimum angle between the measured vector of magnetic induction B in the shadow of the leading (L) spot and positive normal to the solar surface is lower than in the trailing (F) spot (α_min-L < α_min-F) and, vice versa, when α_min-L > α_min-F. It is shown that the α_min-L(S_L), α_min-F(S_F), B_max-L(S_L) and B_max-F(S_F) correlations are similar behaviorally and quantitatively for two groups of spots with different asymmetries of a magnetically connected field (B_{max-L, F} is the maximum of magnetic induction in the shadow of leading and trailing spots). The correlation between the average angles within the spot shadow 〈α_{L, F}〉 and the area of the spot shadow S_{L, F} and between the average value of magnetic induction in the spot shadow 〈B_{L, F}〉 differ in two cases. In most studied spot pairs, the leading spot is closer to the dividing line of polarity between the spots rather than the trailing one.     

α2-Dynamos and taylor's constraint

Abstract

An idealised α²ω-dynamo is considered in which the α-effect is prescribed. The additional ω-effect results from a geostrophic motion whose magnitude is determined indirectly by the Lorentz forces and Ekman suction at the boundary. As the strength of the α-effect is increased, a critical value α? _c is reached at which dynamo activity sets in; α? _c is determined by the solution of the kinematic α²-dynamo problem. In the neighbourhood of the critical value of α? the magnetic field is weak of order E ^1/4(μηρω)^½ due to the control of Ekman suction; E(?1) is the Ekman number. At certain values of α?, viscosity independent solutions are found satisfying Taylor's constraint. They are identified by the bifurcation of a nonlinear eigenvalue problem. Dimensional arguments indicate that following this second bifurcation the magnetic field is strong of order (μηρω)^½. The nature of the transition between the kinematic linear theory and the Taylor state is investigated for various distributions of the α-effect. The character of the transition is found to be strongly model dependent.     

The effect of the number of charges carried by the argon ion on the darkening of ilford Q2 emulsion as ion detectors in mass-spectrometer

Summary The darkening (S) of Illford Q₂ photographic plates as ion detectors in mass spectrometer has been investigated. The dependence of the darkening (S) on the ion density (n=ions/mm²) i.e.S=S(n)E for constant energy (E)=z U ranging from 4U20 Kv of the impinging⁴⁰A⁺¹-,⁴⁰A⁺²- and⁴⁰A⁺³-ions whenS does not exceed the value 0.15 and the second relationn=n(z U) _S for darkening 0.05S0.15 constructed from the above relationS=S(n) _E has been determined. The darkening was found to increase with increasing ion-density which inturn decreases with the ionenergy. For⁴⁰A⁺¹-,⁴⁰A⁺²-, and⁴⁰A⁺³-ion of equal energy and ion-density the darkening effect was independent of the number of the charges carried by the argon ion.     

Energy partitioning over a semi‐arid shrubland in northern China

During the last decade, the widely distributed shrublands in northern China have shown significant signs of recovery from desertification, the result of widespread conservation practices. However, to support the current efforts in conservation, more knowledge is needed on surface energy partitioning and its biophysical controls. Using eddy‐covariance measurements made over a semi‐arid shrubland in northwest China in 2012, we examined how surface energy‐balance components vary on diurnal and seasonal scales, and how biophysical factors control bulk surface parameters and energy exchange. Sensible heat flux (H) exceeded latent heat flux (λE) during most of the year, resulting in an annual Bowen ratio (β, i.e. H/λE) of 2.0. λE exceeded H only in mid‐summer when frequent rainfall co‐occurred with the seasonal peak in leaf area index (LAI). Evapotranspiration reached a daily maximum of 3.3 mm day^?1, and summed to 283 mm yr^?1. The evaporative fraction (EF, i.e. λE/R_n), Priestley–Taylor coefficient (α), surface conductance (g_s) and decoupling coefficient (Ω) were all positively correlated with soil water content (SWC) and LAI. The direct enhancement of λE by high vapour pressure deficit (VPD) was buffered by a concurrent suppression of g_s. The g_s played a direct role in controlling EF and α by mediating the effects of LAI, SWC and VPD. Our results highlight the importance of adaptive plant responses to water scarcity in regulating ecosystem energy partitioning, and suggest an important role for revegetation in the reversal of desertification in semi‐arid areas. Copyright © 2015 John Wiley & Sons, Ltd.     

Drought analysis of monthly hydrological sequences: a case study of Canadian rivers

Abstract

Two parameters of importance in hydrological droughts viz. the longest duration, L_T and the largest severity, S_T (in standardized form) over a desired return period, T years, have been analysed for monthly flow sequences of Canadian rivers. An important point in the analysis is that monthly sequences are non-stationary (periodic-stochastic) as against annual flows, which fulfil the conditions of stochastic stationarity. The parameters mean, μ, standard deviation, σ (or coefficient of variation), lag1 serial correlation, ρ, and skewness, γ (which is helpful in identifying the probability distribution function) of annual flow sequences, when used in the analytical relationships, are able to predict expected values of the longest duration, E(L_T ) in years and the largest standardized severity, E(S_T ). For monthly flow sequences, there are 12 sets of these parameters and thus the issue is how to involve these parameters to derive the estimates of E(L_T ) and E(S_T ). Moreover, the truncation level (i.e. the monthly mean value) varies from month to month. The analysis in this paper demonstrates that the drought analysis on an annual basis can be extended to monthly droughts simply by standardizing the flows for each month. Thus, the variable truncation levels corresponding to the mean monthly flows were transformed into one unified truncation level equal to zero. The runs of deficits in the standardized sequences are treated as drought episodes and thus the theory of runs forms an essential tool for analysis. Estimates of the above parameters (denoted as μ_av, σ_av, ρ_av, and γ_av) for use in the analytical relationships were obtained by averaging 12 monthly values for each parameter. The product- and L-moment ratio analyses indicated that the monthly flows in the Canadian rivers fit the gamma probability distribution reasonably well, which resulted in the satisfactory prediction of E(L_T ). However, the prediction of E(S_T ) tended to be more satisfactory with the assumption of a Markovian normal model and the relationship E(S_T ) ≈ E(L_T ) was observed to perform better.     

A laboratory study of baroclinic instability

Abstract

Experimental and theoretical results are presented for a simple system which exhibits baroclinic instability. We consider the motion of two immiscible fluids with densities ρ ₁ and ρ ₂ contained in a cylinder rotating with angular frequency ω. The motion is driven by a contact lid rotating with frequency ω + ω. In this paper ω, ω, 2(ρ ₂ – ρ ₁)/(ρ ₂ + ρ ₁), and the geometry are such that the interface does not intersect the “ground” (e.g. an almost horizontal boundary). The motions are described by two-layer quasi-geostrophic equations which are identical, except perhaps for the presence of interfacial friction and tension, with those used in meteorology and oceanography. For small enough internal Froude number F = 4ω² L ²/(g(Δρ/ρ)H) or small enough Rossby number ? = ω/2ω the flow is steady and axisymmetric, the velocity field in each layer being determined primarily by frictional effects in top, bottom, and interfacial Ekman layers. For certain (F, ?) the flow becomes non-axisymmetric. The transition points for the case where the basic potential vorticity gradient is due to interface slope alone have been carefully measured and are in very good agreement with a linear instability theory which neglects sidewall effects. Some preliminary observations of supercritical motion, which include repeatable amplitude and wavenumber vacillation, are reported.     

Studies on Primary Productivity and some Hydrochemical Aspects of a Polluted Water-body of the Himalayan Jhelum Valley

The lake without any outlet (11 ha, 55000 m³, z_max 2,25 m) has a weak thermal stratification with maximum surface temperatures of 32.5 °C. The annual variation of temperature and depth of visibility is unimodal, with the maxima or minima in August. Phytoplankton consists mainly of Cyanophyceae. The primary production determined by the light-dark bottle technique (oxygen method) varies in the annual variation between 0.3… 0.5 g m^?2 d^?1 C (winter) and 3.4… 4.6 g m^?2 d^?1 C (summer); as the annual means of 1975 and 1976 there were found 1.9 and 2.4 g m^?2 d^?1 C, resp., gross production at a utilization of 0.42… 2.85% of the radiation energy. The chemism is a well-buffered hydrogen-carbonate water (pH 8.1… 9.0) with 74… 90 mg/1 Na and 20.5… 31.5 mg/1 K and with a good nutrient supply (20… 40 μg/1 PO₄—P and 100… 240 μg/1 NO₃—N) at the same time.     

Analysis of the nonlinear storage–discharge relation for hillslopes through 2D numerical modelling

Storage–discharge curves are widely used in several hydrological applications concerning flow and solute transport in small catchments. This article analyzes the relation Q(S) (where Q is the discharge and S is the saturated storage in the hillslope), as a function of some simple structural parameters. The relation Q(S) is evaluated through two‐dimensional numerical simulations and makes use of dimensionless quantities. The method lies in between simple analytical approaches, like those based on the Boussinesq formulation, and more complex distributed models. After the numerical solution of the dimensionless Richards equation, simple analytical relations for Q(S) are determined in dimensionless form, as a function of a few relevant physical parameters. It was found that the storage–discharge curve can be well approximated by a power law function Q/(LK_s) = a(S/(L²(? ? θ_r)))^b, where L is the length of the hillslope, K_s the saturated conductivity, ? ? θ_r the effective porosity, and a, b two coefficients which mainly depend on the slope. The results confirm the validity of the widely used power law assumption for Q(S). Similar relations can be obtained by performing a standard recession curve analysis. Although simplified, the results obtained in the present work may serve as a preliminary tool for assessing the storage–discharge relation in hillslopes. Copyright © 2012 John Wiley & Sons, Ltd.     

Heat transfer and thermal boundary layers in high amplitude annulus waves

Abstract

The heat transfer by a rotating, differentially-heated annulus of fluid is measured throughout the high amplitude wave regime. Only Δr_w T was varied (although v(T₁₅ ).K(T₁₅ ) varied by 46%), and it is found that Nu = C₁(λ)Ra^? away from the symmetry and low amplitude to wave transition curves and this is independent of ω. (λ is the wavelength.) On the wave side of these transition curves a region exists in which Nu (symmetry) λ Nu λ C₁(λ)Ra^?. The local heat transfer rate also varies strongly with wave phase.

Using a selection of measured internal thermal fields in the steady, high amplitude wave regime, the side-wall thermal boundary layer structure is examined. It is found that Nu, = C₂·Gr₂ ^A2; both C ₂ and A ₂ are independent of ω and λ to first order. For the time mean profiles, A ₂ ≈ 0.25; in the high heat transfer portion of the wave A ₂ < ¼ and in the low heat transfer portion of the wave A ₂ > ?. These relations hold over most of the vertical extent of the side walls. The deviations of the boundary layers from the above behavior which occur on the remainder of the walls is illustrated. The average thicknesses of the wall boundary layers ∞ Ra^?¼ except in that phase of the wave in which the wall to mid-gap temperature difference is the largest.     

Biologischer Abbau von 2,4-Dinitrotoluol in einer kontinuierlich betriebenen Versuchsanlage und kinetische Untersuchungen

Biological Degradation of 2,4-Dinitrotoluene in a Continuous Bioreactor and Kinetic Studies Experimental results on the aerobic biological degradation with complete mineralization of 2,4-dinitrotoluene (2,4-DNT) are presented. A culture of Pseudomonas sp. DNT from Spain and Nishino was used. The degradation was examined with batch cultures for the determination of kinetic and stoichiometric coefficients. Further experiments were carried out with a continuous culture in a fixed-bed reactor with recirculation in order to obtain high degradation rates. The reactor was packed with ceramic Raschig rings (55 mL) and had a liquid reaction volume of 160 mL. The minimal salt media from Spanggord et al. with and without (NH₄)₂S)₄ as nitrogen source was used as substrate. 2,4-DNT was the sole source of carbon and energy. From batch experiments a yield coefficient Y_B/S = (0.30 ± 0.05) g g^?1 was calculated from a mass balance of the elements. This result was confirmed by calculations using literature data. Fitting the experimental data to the Monod equation, μ_max = 0.1 h^?1 and K_S = 0.01…0.03 mmol L^?1 were obtained. It was demonstrated by batch experiments that 2,4-DNT is not only used as the source of carbon and energy but also as the nitrogen source. In the fixed-bed reactor, a degradation of 92…97% was reached with a maximal 2,4-DNT load of 95 mg L^?1 h^?1. The rate of continuous degradation could be described by a pseudo-first-order reaction (k = 9.73 h^?1). The complete mineralization of 2,4-DNT was verified by the measurement of DOC and the formed nitrite and nitrate. The formed nitrite was nitrified simultaneously. It was demonstrated by these experiments that large scale biological treatment of industrial effluent containing 2,4-DNT may be successful.