Persistent weak thermal stratification inhibits mixing in the epilimnion of north-temperate Lake Opeongo,Canada

Persistent weak temperature stratification characterizes the epilimnion of Lake Opeongo, Ontario, Canada, and reduces the magnitude of turbulent mixing. Throughout July and August 2009, the epilimnion was isothermal for only 34 % of the record, while for 28 % of the record there was at least a 2 °C temperature difference across the 5 m deep epilimnion. During these stratified periods, there were increases in gradient Richardson numbers (Ri _g ), and decreases in rates of dissipation of turbulent kinetic energy ( $\varepsilon$ ), the turbulence activity parameter (I = ε/νN ²), an indicator of active mixing, and vertical eddy diffusivity (K _z ) inferred from temperature microstructure profiles. During periods of shear induced mixing, values of ε approached 10^?6 m² s^?3 and decreased during periods of increasing Ri _g . For 0 < Ri _g  < 1, average values of I were ~1,000 and values of K _z were slightly higher than 10^?4 m² s^?1. For Ri _g >1, average values of I were ~300 and K _z was reduced by one to three orders of magnitude. Mixing during cold fronts occurred over time scales of minutes to hours, which worked to erode diurnal thermoclines. However, during periods of persistent secondary thermoclines, mixing was suppressed throughout the epilimnion.     

Oxysulfates of copper, sodium, and potassium in the lava flows of the 2012–2013 Tolbachik Fissure Eruption

Samples from the surface of lava flows discharged by the 2012–2013 Tolbachik Fissure Eruption were found to contain oxysulfates of copper, sodium, and potassium: K₂Cu₃O(SO₄)₂ (fedotovite), NaKCu₂O(SO₄)₂, and Na₃K₅Cu₈O₄(SO₄)₈. The last two phases have no naturally occurring or synthetic analogues that we are aware of. They form flattened crystals of prismatic to long-prismatic habits. The crystals of Na₃K₅Cu₈O₄(SO₄)₈ have a chemical composition corresponding to the empirical formula Na_2.22K_5.47Cu_8.02S_8.05O₃₆. An X-ray analysis of this compound showed that it has a monoclinic symmetry, P2/c, a = 13.909(4), b = 4.977(1), c = 23.525(6) Å, β = 90.021(5)°, V = 1628.3(7) ų. The crystal structure was determined by direct techniques and refined to yield R ₁ for 3955 reflexes//web// with F ² > 4σF. The compound NaKCu₂O(SO₄)₂ also belongs to the monoclinic system, P2/c, a = 14.111(4), b = 4.946(1), c = 23.673(6) Å, β = 92.052(6)°, V = 1651.1(8) ų. The structure was determined by direct techniques to yield a tentative structural model that has been refined up to R ₁ = 0.135 for 4088 reflexes with F ² > 4σF. The crystal structure of Na₃K₅Cu₈O₄(SO₄)₈ is based on chains of [O₂Cu₄]⁴⁺ consisting of rib-coupled oxy-centered tetrahedrons of (OCu₄)⁶⁺. The chains are surrounded by sulfate radicals, resulting in columns of {[O₂Cu₄](SO₄)₄}^4? aligned along the b axis. The interchain space contains completely ordered positions of Na⁺ and K⁺ cations. The principle underlying the connection of NaKCu₂O(SO₄)₂ columns in the crystal structure of {[O₂Cu₄](SO₄)₄}^4? is different, in view of the relation Na:K = 1 as contrasted with 3:5 for the compound Na₃K₅Cu₈O₄(SO₄)₈. The presence of oxy-centered tetrahedrons in the structure of these new compounds furnishes an indirect hint at the importance of polynuclear copper-oxygen radicals with centering oxygen atoms as forms of transport of copper by volcanic gases.     

Strontium and neodymium isotopes in hot springs on the East Pacific Rise and Guaymas Basin

We have determined the concentrations and isotopic compositions of Sr and Nd in hydrothermal fluids from 21°N, East Pacific Rise and Guaymas Basin, Gulf of California. The purest solutions analyzed from 21°N exhibit a small range in Sr concentration between individual vents from 5.8 to 8.7 ppm, close to normal seawater Sr concentrations. They exhibit a small range in⁸⁷Sr⁸⁶Sr fromε_Sr(0) = −13.4 to −17.7, corresponding toε_Sr(0) ≈ −18 ± 2 in the pure hydrothermal end-member. These results indicate extensive but not complete isotopic exchange with Sr in the depleted oceanic crust (ε_Sr(0) = −31.8) and suggest that Sr concentrations in these solutions are buffered. In contrast, the concentration and isotopic composition of Nd in solutions show large variations between vents. The concentration of Nd ranges from 20 to 336 pg/g (6–100 times seawater Nd concentrations). The isotopic composition ranges fromε_Nd(0) = −3.6 (similar to Pacific seawater) to +7.9. Many samples show substantial contributions from MORB, but all haveε_Nd(0) well below MORB at this locality (ε_Nd(0) = +9.7) in spite of very large enrichments in Nd concentrations. While complete isotopic exchange withwater/rock≈ 2 or exchange with anomalous oceanic crust can explain the Sr data, the Nd data require exchange with a reservoir havingε_Nd(0) < Pacific seawater. Low-temperature reactions with metalliferous sediments on the ridge flanks may provide such a source. Both Sr and Nd in the Guaymas Basin solution are very different from21°N. ε_Sr(0) = +11.0 andε_Nd(0) = −11.4 and are consistent with the fluid exchanging Sr and Nd with heated sediments having a substantial component of old continental detritus. Some irregularities in the Nd isotopic data reported here indicate that there must be a problem of contamination for some ultra-low-level trace elements during sample collection and processing which requires further attention.Using a simple box model, the estimates for hydrothermal Nd fluxes are compared with fluxes which would be required to maintain the relatively radiogenic value ofε_Nd(0) ≈ −3 in the Pacific against the influx of more negative Antarctic waters (ε_Nd(0) ≈ −9). It is shown that the hydrothermal flux of Nd from mid-ocean ridges falls far short of that necessary to maintain the isotopic balance. This indicates that weathered material from volcanic terranes (ε_Nd(0) ≈ +7) is the most reasonable major source of radiogenic Nd in the Pacific.     

Meridional distribution of226Ra in the eastern Pacific along GEOSECS cruise tracks

We present the distribution of²²⁶Ra in eight vertical profiles from the eastern Pacific. The profiles are located along a meridional trend near 125°W, from 43°S to 29°N. Surface²²⁶Ra concentrations are about 7 dpm/100 kg, except for the two stations south of 30°S where the higher values are due to the Antarctic influence. Deep waters show a distinctive south-to-north increase in the²²⁶Ra content, from about 26 to 41 dpm/100 kg near the bottom. Unlike in the Atlantic and Antarctic Oceans, the effect of²²⁶Ra injection from bottom sediments is clearly discernible in the area. The presence of this primary²²⁶Ra can be traced up to at least 1–1.5 km above the ocean floor, making this part of the sea bed among the strongest source regions for the oceanic²²⁶Ra. Numerical solutions of a two-dimensional vertical advection-diffusion model applied to the deep (1.2–4 km)²²⁶Ra data give the following set of best fits: upwelling velocity(V_z) = 3.5m/yr, vertical eddy diffusivity(K_z) = 0.6cm²/s, horizontal (north-south) eddy diffusivity(K_y) = 1 × 10⁷cm²/s, and water-column regeneration flux of²²⁶Ra(J) = 3.3 × 10^?5dpmkg^?1yr^?1 as an upper limit. These parametric values are in general agreement with one-dimensional (vertical) model fits for the Ra-Ba system. However, consideration of²²⁶Ra balance leads us to suspect the appropriateness of describing the vertical exchange processes in the eastern Pacific with constantV_z and K_z. If future modeling is attempted, it may be preferable to treat the area as a diffusion-dominant mixing regime with depth-dependent diffusivities.     

An advanced process for evaluating a linear dielectric constant–bulk electrical conductivity model using a capacitance sensor in field conditions

Abstract

The Hilhorst model was used to convert bulk electrical conductivity (σ_b) to pore water electrical conductivity (σ_p) under laboratory conditions by using the linear relationship between the soil dielectric constant (ε_b) and σ_b. In the present study, applying the linear relationship ε_b–σ_b to data obtained from field capacitance sensors resulted in strong positive autocorrelations between the residuals of that regression. We were able to derive an accurate offset of the relationship ε_b–σ_b and to estimate the evolution of σ_p over time by including a stochastic component to the linear model, rearranging it to a time-varying dynamic linear model (DLM), and using Kalman filtering and smoothing. The offset proved to vary for each depth in the same soil profile. A reason for this might be the changes in soil temperature along the soil profile.

Editor D. Koutsoyiannis; Associate editor M.D. Fidelibus     

The relationship between vertical eddy diffusion and buoyancy gradient in the deep sea

Vertical eddy diffusivities (K_v's) have been estimated at fourteen widely separated locations from fourteen²²²Rn profiles and two²²⁸Ra profiles measured near the ocean floor as part of the Atlantic and Pacific GEOSECS programs. They show an inverse proportionality to the local buoyancy gradient [(g/?)(??_pot/?z)] calculated from hydrographic measurements. The negative of the constant of proportionality is the buoyancy flux [?K_v(g/?)(??_pot/?z)] which has a mean of ?4 × 10^?6 cm²/sec³. Our results suggest that the buoyancy flux varies very little near the ocean floor. K_v's for the interior of the deep Pacific calculated from the relationship K_v = (4 × 10^?6cm²/sec³)/[(g/?)(??_pot/?z)] agree well with published estimates. K_v's calculated for the pycnocline are one to two orders of magnitude smaller than upper limits estimated from tritium and⁷Be distributions.Heat fluxes calculated with the model K_v's obtained from the²²²Rn profiles average 31 μcal cm^?2 sec^?1 in the Atlantic Ocean and 8 μcal cm^?2 sec^?1 in the Pacific Ocean.     

Flow directions in ash-flow tuffs: a comparison of geological and magnetic susceptibility measurements,Tshirege member (upper Bandelier Tuff), Valles caldera,New Mexico,USA

This study concludes that the elongation axis (K ₁) of the ellipsoid of anisotropic magnetic susceptibility (AMS) is a suitable proxy for flow axis in ashflow tuffs. 153 oriented samples (176 specimens) were studied from 18 sites in the 1.1 Ma Tshirege member of the Bandelier Tuff. These sites are distributed around the Valles caldera at distances of 5–25 km outside of the rim.K ₁ axes correlate well with postulated radial flow axes at 13 sites.K ₁ also agrees with measured geological flow indicators, mainly imbricated larger clasts, at 7 sites. At 2 of the 5 sites where significant disagreement is seen between theoretical radial flow directions and measuredK ₁ axes, theK ₁ axes correspond well with geological flow indicators, indicating that the divergence of flow from the predicted radial flow pattern is real. Two major topographic buttresses are suggested as the cause of flow divergence for the Tshirege ash flows: the San Pedro buttress northwest of the caldera, and the San Miguel buttress in the southeast. In situK ₁ axes plunge about 7° toward the source at two-thirds of the sites; therefore the plunge ofK ₁ is a plausible in situ indicator for thedirection of flow. Multiple flow zones in sections of several meters thickness indicate changes of flow direction that are both rapid and large during ash-flow emplacement. These observations raisre the question of how best to represent ‘mean’ flow directions in ash-flow sheets: by eigenvector methods, by vector-sum methods, or by modes. A method for measuring imbrication of larger clasts using apparent dips in vertical joints is outlined. Imbrication, determined in this way at one-third of the sites, dips toward the source, i.e., up-flow. The minimum (K ₃) axis of the AMS ellipsoid correlates with the flow foliation rather than with the larger clast imbrication. The flow axes of ash flows correspond with theK ₁ axes, not with the declination ofK ₃ axes as suggested by some authors. Initial dip of the sampled ash flows is not large and does not affect the paleomagnetic remanence direction, which is reversed with a mean ofD=173.5°,I=-38.4°, α₉₅=3.4°N=18. This mean is not different at the 95% confidence level from that of earlier workers. The mean pole, at 098.0°E, 74.8°N,A ₉₅=3.3°,N=18, is about 15° far-sided relative to the expected time-averaged geomagnetic pole, suggesting a history of emplacement too short to adequately average secular variation.     

Variability of the ionosphere

Hourly foF2 data from over 100 ionosonde stations during 1967–89 are examined to quantify F-region ionospheric variability, and to assess to what degree the observed variability may be attributed to various sources, i.e., solar ionizing flux, meteorological influences, and changing solar wind conditions. Our findings are as follows. Under quiet geomagnetic conditions (K_p<1), the 1-σ (σ is the standard deviation) variability of N_max about the mean is approx. ±25–35% at ‘high frequencies’ (periods of a few hours to 1–2 days) and approx. ±15–20% at ‘low frequencies’ (periods approx. 2–30 days), at all latitudes. These values provide a reasonable average estimate of ionospheric variability mainly due to “meteorological influences” at these frequencies. Changes in N_max due to variations in solar photon flux, are, on the average, small in comparison at these frequencies. Under quiet conditions for high-frequency oscillations, N_max is most variable at anomaly peak latitudes. This may reflect the sensitivity of anomaly peak densities to day-to-day variations in F-region winds and electric fields driven by the E-region wind dynamo. Ionospheric variability increases with magnetic activity at all latitudes and for both low and high frequency ranges, and the slopes of all curves increase with latitude. Thus, the responsiveness of the ionosphere to increased magnetic activity increases as one progresses from lower to higher latitudes. For the 25% most disturbed conditions (K_p>4), the average 1-σ variability of N_max about the mean ranges from approx. ±35% (equator) to approx. ±45% (anomaly peak) to approx. ±55% (high-latitudes) for high frequencies, and from approx. ±25% (equator) to approx. ±45% (high-latitudes) at low frequencies. Some estimates are also provided on N_max variability connected with annual, semiannual and 11-year solar cycle variations.     

High-precision 40Ar/39Ar age of the Jänisjärvi impact structure (Russia)

The ～ 14 km diameter Jänisjärvi impact structure is located in Svecofennian Proterozoic terrain in the southeastern part of the Baltic shield, Karelia, Russia. Previous radioisotopic dating attempts gave K/Ar and ⁴⁰Ar/³⁹Ar ages of 700 ± 5 Ma and 698 ± 22 Ma, respectively, with both results being difficult to interpret. Recent paleomagnetic results have challenged these ages and proposed instead ages of either 500 Ma or 850–900 Ma. In order to better constrain the age of the Jänisjärvi impact structure, we present new ⁴⁰Ar/³⁹Ar data for the Jänisjärvi impact melt rock. We obtained five concordant isochron ages that yield a combined isochron age of 682 ± 4 Ma (2σ) with a MSWD of 1.2, P = 0.14, and ⁴⁰Ar/³⁶Ar intercept of 475 ± 3. We suggest that this date indicates the age of the impact and therefore can be used in conjunction with existing paleomagnetic results to define the position of the Baltica paleocontinent at that time. Argon isotopic results imply that melt homogenization was achieved at the hundred-micrometer scale certainly, because of the low-silica content of the molten target rock that allows fast ⁴⁰Ar^? diffusion in the melt. However, the large range of F(⁴⁰Ar^?_inherited) (4.1% to 11.0%) observed for seven grains shows that complete isotopic homogenization was not reached at the centimeter and perhaps the millimeter scale. The F(⁴⁰Ar^?_inherited) results are also in good agreement with previous Rb and Sr isotopic data.     

The role of vibrationally excited oxygen and nitrogen in the D and E regions of the ionosphere

In this paper we present the results of a study of the effect of vibrationally excited oxygen, O^* ₂, and nitrogen, N^* ₂, on the electron density, N _e, and the electron temperature, T _e, in the D and E regions. The sources of O^* ₂ are O-atom recombination, the photodissociation of O₃, and the reaction of O₃ with O at D region altitudes. The first calculations of O^* ₂(j) number densities, N _j , are obtained by solving continuity equations for the models of harmonic and anharmonic oscillator energy levels, j=1-22. It is found that day time values of N _j are less than nighttime values. We also show that the photoionization of O^* ₂ (j\geq11) by L_<alpha>-radiation has no influence on the D region N _e . In the nighttime D region the photoionization O^* ₂ (j\geq11) by scattered L _<alpha>-radiation can be a new source of O⁺ ₂. We show that the N^* ₂ and O^* ₂ de-excitation effect on the electron temperature is small in the E region of the ionosphere and cannot explain experimentally observed higher electron temperatures.     

Comparison of models and data at Millstone Hillduring the 5–11 June 1991 storm

We compare measurements of the ionospheric F region at Millstone Hillduring the severe geomagnetic disturbances of 5–11 June 1991 with results from the IZMIRANand FLIP time-dependent mathematical models of the Earths ionosphere and plasmasphere. Somecomparisons are also made with the Millstone Hill semi-empirical model which was previouslyused to model this storm. New rate coefficients from recent laboratory measurements of the O⁺+N₂ and O⁺+O₂ loss rates are included in theIZMIRAN and Millstone Hill models. The laboratory measurements show that vibrationallyexcited N₂ and O₂ (N₂(v) and O₂(v)) are both important at high temperatures such as found in the thermosphere during disturbedconditions at summer solar maximum. Increases in the O⁺+N₂ loss ratedue to N₂(v) result in a factor ∼2 reduction in the daytime F₂ peak electron density. On some days inclusion of N₂(v) improves theagreement between the models and the data, and on other days it worsens it. In the present workwe show for the first time the significant effect that the increase in the O⁺recombination rate due to O₂(v) may have on the calculated NmF₂. There are considerable uncertainties in the model calculations during the unusual,extremely disturbed conditions found during the daytime on 6 June. The results illustratedifficulties involved and the current state of the art in modelling severe disturbances, and thusprovide a benchmark against which future progress can be gauged.     

Effects of multiple scattering on coda waves in three-dimensional medium

The contribution of multiple scattering to the coda waves for three-dimensional elastic medium is investigated by extending the computational procedures developed earlier for the two-dimensional medium. It is shown that the effects of multiple scattering start to become important at a shorter lapse time,t _c = 0.65(n ₀σu)^?1, than in the two-dimensional case (t _c = 0.8(n ₀σu)^?1).     

Some Atmospheric Surface Layer Characteristics over Varanasi from MONTBLEX-90

—An attempt has been made to study the atmospheric surface layer characteristics such as Richardson number (Ri). Monin-Obukhov length scale (L), friction velocity (U _* ?), friction temperature (θ _*?), roughness length (Z ₀?), turbulent kinetic energy (TKE), ratio of eddy conductivity to eddy diffusivity (K _m ?/K _h ?) over a semi-moist convective regime. Data which were collected at Varanasi (25°18′N, 83°E) as part of the experiment known as MONTBLEX-90 (Monsoon Trough Boundary Layer Experiment) during the summer monsoon season was used in the present study. The variation of the above parameters with stability has been discussed. The differences within the surface layer are also pointed out. Some broad features are found to coincide with that of Businger et al. (1971). The heterogeneity and the anisotropic turbulence typical of monsoon tropical atmosphere are shown to be responsible for the deviations noticed within the surface layer.     

Petrogenesis of basalts from the project FAMOUS area: experimental study from 0 to 15 kbars

Tholeiitic basalt glasses from the FAMOUS area of the Mid-Atlantic Ridge are among the most primitive basaltic liquids reported from the ocean basins. One of the more primitive of these[Mg/(Mg+Fe²⁺) = 0.68;Ni= 232ppm;TiO₂ = 0.61] glasses (572-1-1) was selected for an experimental investigation. This study found olivine to be the liquidus phase from 1 atm to 10.5 kbar where it is replaced by clinopyroxene. The sequence of appearance of phases at 1 atm pressure is olivine (1268°C), plagioclase (1235°C) and clinopyroxene (1135°C). The sample is multiply saturated at 10.5 kbar with olivine (Fo₈₈), clinopyroxene (Wo₃₂En₆₀Fs₉), and orthopyroxene (Wo₅En₈₃Fs₁₂). From the 1-atm data we have measured (FeO/MgO) olivine/(FeO*/MgO) liquid (K′_D) for olivine-melt pairs equilibrated at 12 temperatures in the range 1268–1205°C.K′_D varies from 0.30 at 1205°C to 0.27 at 1268°C. Analysis of high-pressure olivine melt pairs indicates a systematic increase inK′_D with pressure.Evaluation of the 1-atm experiments reveals that fractionation of olivine followed by olivine + plagioclase can generate much of the variation in major element chemistry observed in the FAMOUS basalt glasses. However, it cannot account for the entire spectrum of glass compositions — particularly with respect to TiO₂ and Na₂O. The variations in these components are such as to require different primary liquids.Comparison of clinopyroxene microphenocrysts/xenocrysts found in oceanic tholeiites with experimental clinopyroxenes reveal that the majority of those in the tholeiites may have crystallized from the magma at pressures greater than ～ 10 kbar and are not accidental xenocrysts. Clinopyroxene fractionation at high pressures may be a viable mechanism for fractionating basaltic magmas.The major and minor element mineral/meltK′_d's from our experiments have been used to model the source region residual mineralogy for given percentages of partial melting. These data suggest that ～20% partial melting of a lherzolite source containing 0–10% clinopyroxene can generate the major and minor element concentrations in the parental magmas of the Project FAMOUS basalt glasses.     

Water and nutrient fluxes in a cool temperate rainforest at the Cordillera de la Costa in southern Chile

Water and nutrient fluxes were studied during a 12-month period in an alerce (Fitzroya cupressoides) forest, located in a remote site at the Cordillera de la Costa (40°05′S) in southern Chile. Measurements of precipitation, throughfall, stemflow, effective precipitation, soil infiltration and stream flow were carried out in an experimental, small watershed. Simultaneously, monthly water samples were collected to determine the concentrations and transport of organic-N, NO₃-N, total-P, K⁺, Ca²⁺, Na⁺ and Mg²⁺ in all levels of forest. Concentration of organic-N, NO₃-N, total-P and K⁺ showed a clear pattern of enrichment in the throughfall, stemflow, effective precipitation and soil infiltration. For Ca²⁺ and Mg²⁺, enrichment was observed in the effective precipitation, soil infiltration and stream flow. Annual transport of K⁺, Na⁺, Ca²⁺ and Mg²⁺ showed that the amounts exported from the forest via stream flow (K⁺=0·95, Na⁺=32·44, Ca²⁺=8·76 and Mg²⁺=7·16 kg ha⁻¹ yr⁻¹) are less than the inputs via precipitation (K⁺=6·39, Na⁺=40·99, Ca²⁺=15·13 and Mg²⁺=7·61 kg ha⁻¹ yr⁻¹). The amounts of organic-N and NO₃-N exported via stream flow (organic-N=1·04 and No₃-N=3·06 kg ha⁻¹ yr⁻¹) were relatively small; however, they represented greater amounts than the inputs via precipitation (organic-N=0·74 and NO₃-N=0·97 kg ha⁻¹ yr⁻¹), because of the great contribution of this element in the superficial soil horizon, where the processes of decomposition of organic material, mineralization and immobilization of the nutrients occurs. © 1998 John Wiley & Sons, Ltd.     

Thermal equation of state of magnesiowüstite (Mg0.6Fe0.4)O

Volume measurements for magnesiowüstite (Mg_0.6Fe_0.4)O, were carried out up to pressures of 10.1 GPa in the temperature range 300–1273 K, using energy-dispersive synchrotron X-ray diffraction. These data allow reliable determination of the temperature dependence of the bulk modulus and good constraint on the thermal expansitivity at ambient pressure which was previously not known for magnesiowüstite. From these data, thermal and elastic parameters were derived from various approaches based on the Birch–Murnaghan equation of state (EOS) and on the relevant thermodynamic relations. The results from three different equations of state are remarkably consistent. With (∂K_T/∂P)_T fixed at 4, we obtained K₀=158(2) GPa, (∂K_T/∂T)_P=−0.029(3) GPa K⁻¹, (∂K_T/∂T)_V=−3.9(±2.3)×10⁻³ GPa K⁻¹, and α_T=3.45(18)×10⁻⁵+1.14(28)×10⁻⁸T. The K₀, (∂K_T/∂T)_P, and (∂K_T/∂T)_V values are in agreement with those of Fei et al. (1992) and are similar to previously determined values for MgO. The zero pressure thermal expansitivity of (Mg_0.6Fe_0.4)O is found to be similar to that for MgO (Suzuki, 1975). These results indicate that, for the compositional range x=0–0.4 in (Mg_1−xFe_x)O, the thermal and elastic properties of magnesiowüstite exhibit a dependence on the iron content that is negligibly small, within uncertainties of the experiments. They are consequently insensitive to the Fe–Mg partitioning between (Mg, Fe)SiO₃ perovskite and magnesiowüstite when applied to compositional models of the lower mantle. With the assumption that (Mg_0.6Fe_0.4)O is a Debye-like solid, a modified equation of heat capacity at constant pressure is proposed and thermodynamic properties of geophysically importance are calculated and tabulated at high temperatures.     

The electric field produced in the mantle by the dynamo in the core

A rigorous singular perturbation theory is developed to estimate the electric field E produced in the mantle M by the core dynamo when the electrical conductivity σ in M depends only on radius r, and when |r?_rln σ| ? 1 in most of M. It is assumed that σ has only one local minimum in M, either (a) at the Earth's surface ?V, or (b) at a radius b inside the mantle, or (c) at the core-mantle boundary ?K. In all three cases, the region where σ is no more than e times its minimum value constitutes a thin critical layer; in case (a), the radial electric field E_r ≈ 0 there, while in cases (b) and (c), E_r is very large there. Outside the critical layer, E_r ≈ 0 in all three cases. In no case is the tangential electric field E_S small, nearly toroidal, or nearly calculable from the magnetic vector potential A as ??_tA_S. The defects in Muth's (1979) argument which led him to contrary conclusions are identified. Benton (1979) cited Muth's work to argue that the core-fluid velocity u just below ?K can be estimated from measurements on ?V of the magnetic field B and its time derivative $\text{?}{}_{\mathrm{t}}\text{B}$. A simple model for westward drift is discussed which shows that Benton's conclusion is also wrong.In case (a), it is shown that knowledge of σ in M is unnecessary for estimating E_S on ?K with a relative error |r?_r 1nσ|^?1from measurements of E_S on ?V and knowledge of ?_tB in M (calculable from ?_tB on ?V if σ is small). Then, in case (a), u just below ?K can be estimated as $\text{?}\text{r}\text{×}\text{E}{}_{\mathrm{S}}\text{/B}{}_{\mathrm{r}}$. The method is impractical unless the contribution to E_S on ?V from ocean currents can be removed.The perturbation theory appropriate when σ in M is small is considered briefly; smallness of σ and of |r?_r ln σ|^?1 a independent questions. It is found that as σ → 0, B approaches the vacuum field in M but E does not; the explanation lies in the hydromagnetic approximation, which is certainly valid in M but fails as σ → 0. It is also found that the singular perturbation theory for |r?_r ln σ|^?1 is a useful tool in the perturbation calculations for σ when both σ and |r?_r ln σ|^?1 are small.     

Vertical mixing in Überlinger See,western part of Lake Constance

Depth variable vertical eddy diffusion coefficients for heat (K _z) were calculated from continuously measured temperature profiles in Überlinger See (western part of Lake Constance). The temperatures were averaged over vertical intervals of 10 m yielding 14 discrete values (maximum depth of Überlinger See: 147 m). A linear fit from 10 June to 29 September 1987 was used to smooth the significant temperature fluctuations caused by internal seiches of Lake Constance.Assuming horizontal homogeneity for the smoothed data the Gradient-Flux-Method was applied to compute vertical diffusion coefficientsK _z at different depths using the depth variable volumes and surfaces of the 14 layers. The resulting mean diffusion coefficients for the period from June to September are 0.04 cm²/s near the thermocline and up to 0.8 cm²/s in deeper strata (accuracy: ± 50%). It is shown that horizontal mixing between Überlinger See and Obersee (main lake) alters the computation ofK _z by less than 50%.A relationship betweenK _z and stability (Brunt-Väisälä) frequencyN is found which corresponds well to the theory of internal wave induced turbulence.Combining the diffusion coefficients with measured phosphorus profiles, a phosphorus flux from the hypolimnion to the epilimnion of (0.7 ± 0.4) mg P m^–2 d^–1 was calculated, corresponding to about 20% of the average external loading per area of Lake Constance in 1986.     

Analytical solutions to steady state unsaturated flow in layered,randomly heterogeneous soils via Kirchhoff transformation

In this study, we derive analytical solutions of the first two moments (mean and variance) of pressure head for one-dimensional steady state unsaturated flow in a randomly heterogeneous layered soil column under random boundary conditions. We first linearize the steady state unsaturated flow equations by Kirchhoff transformation and solve the moments of the transformed variable up to second order in terms of σ_Y and σ_β, the standard deviations of log hydraulic conductivity Y=ln(K_s) and of the log pore size distribution parameter β=ln(α). In addition, we also give solutions for the mean and variance of the unsaturated hydraulic conductivity. The analytical solutions of moment equations are validated via Monte Carlo simulations.     

Excess222Rn and the benthic boundary layer in the western and southern Indian Ocean

We present 9 bottom²²²Rn profiles measured from the western and southern Indian Ocean during the 1977–1978 GEOSECS expedition. These profiles can be grouped into three cypes: one-layer, two-layer, and irregular types. The one-layer profiles with quasi-exponential distributions allow one to estimate the apparent vertical eddy diffusivity,K_v, with a simple model. The two-layer profiles show that there is a benthic boundary layer of the order of 50–100 m in which the excess²²²Rn distribution shows a vertical gradient much smaller than that of the layer immediately above. Within the boundary layer, the STD potential temperature (θ) and density(σ₄) profiles are practically constant, and theK_v values are of the order of 1000 cm²/s. The STD profiles for the water column above the boundary layer show gradients of increasing stability, and theK_v values are of the order of 100 cm²/s. Modeling of the Rn data in the water column above the boundary layer indicates that there is a transition layer which effectively reduces the penetration of excess Rn from the benthic boundary layer into the upper layer.Sarmiento et al. [10] have shown that the buoyancy gradient or stability is inversely correlated with the apparent vertical eddy diffusivity, and the resulting buoyancy flux is fairly uniform, ranging from 1 to 14 × 10^?6 cm²/s³ in the Atlantic and Pacific Oceans. However, Sarmiento et al. [11] show that a much higher buoyancy flux is associated with an intensified flow of the bottom water through a passage. In the Indian Ocean basins, we have found that the buoyancy flux has a comparable range (3–14 × 10^?6 cm²/s³), except for a couple of stations where both stability and apparent vertical diffusivity are higher, resulting in a much higher buoyancy flux, probably indicative of rapid bottom water flow.