Topographically generated steady currents in barotropic turbulence

Abstract

Steady currents develop in oceanic turbulence above topography even in the absence of steady forcing. Mesoscale steady currents are correlated with mesoscale topography with anticyclonic eddies above topographic bumps, and large scale westward flows develop when β is non-zero. The relationship between those two kinds of steady currents, as well as their dependence on various parameters, is studied using a barotropic quasi-geostrophic channel model. The percentage of steady energy is found to depend on the forcing, friction and topography in a non-monotonic fashion. For example, the percentage of steady currents grows with the energy level in the linear regime (low energies) and decreases when the energy level increases in the nonlinear regime (high energies). Mesoscale steady currents are the energy source for the steady westward flow U, and therefore U is the maximum when large scale and mesoscale currents are of the same order of magnitude. This happens when the ratio S of the large scale slope βH/f ₀ and the mesoscale rms topographic slope α is of order one. U decreases for both small and large values of S.     

13C/12C- und 18O16O-Signaturen von Calcit-Abscheidungen in Drainagesystemen

¹³C/¹²C- and ¹⁸O/16O-signatures of Calcite Precipitations in Drainage Systems Measurements of drainage waters show two distinct processes of calcite precipitation: 1. reprecipitation of calcium carbonate previously dissolved in groundwaters and 2. absorption of atmospheric CO₂ by alkaline solutions. Both processes may be distinguished by the stable isotopes of oxygen and carbon. Calcite precipitated from carbonate groundwater yields δ¹³C ≈ ?13%₀ (PDB) and δ¹⁸O ≈ 24%₀ (SMOW), whereas calcite produced by CO₂-absorption shows δ¹³C ≈ ?25%₀ (PDB) and δ¹⁸O ≈ 10%₀ (SMOW).     

An antidynamo theorem for partly symmetric flows

Abstract

It is shown that magnetic fields generated by flows v _r,(r,t)e_r+v_T where v_T is an arbitrary toroidal component (e_r˙v_T≡V≡v_T≡0), cannot be maintained indefinitely against ohmic dissipation. The poloidal field variable max |r ² B _r| is shown to decay strictly monotonically with an undetermined decay rate. A bound on the growth of the toroidal field norm ∥T∥₁ is established solely dependent on the rate of conversion of poloidal to toroidal field, so that when the poloidal field is negligible then ∥T∥₁ decays strictly monotonically. The main application of these results is to models of stellar evolution based on axisymmetric differential rotation and spherically symmetric contraction. This symmetric velocity theorem overlaps with two already known theorems, namely the toroidal velocity theorem where v _r≡0 and the radial velocity theorem where v_T≡0. The new theorem does not entirely include the already established ones, principal differences being in the rates of decay and the field variables for which the decay is proven (see Table 1).     

Transmission electron microscope observation of α, β and γ (Mg,Fe)2SiO4 in shocked meteorites: planar defects and polymorphic transitions

High pressure polymorphs of olivine (Mg, Fe)₂SiO₄ have been observed by transmission electron microscopy in the shocked Tenham and Catherwood meteorites. Planar defects are characterized in β and γ polymorphs and their possible role in polymorphic transitions is assessed and discussed in relation with the published literature. The stacking fault $\text{1}\text{2}\text{[}\text{1}\text{?}\text{01](010)}$ observed in the β-phase can produce a shear transformation to the γ-phase if it occurs on every other (010) plane. Conversely, the stacking fault $\text{1}\text{2}\text{[1}\text{1}\text{?}\text{2](110)}$ observed in the γ-phase can be transformed to the β-phase if it is repeated on every other (110) plane and to an intermediate, yet unobserved, ε1-phase if it is repeated on every (110) plane. Shear transformation between olivine and γ-spinel could involve the ε1-phase as an intermediate stage.     

High-pressure X-ray diffraction studies on β- and γ-Mg2SiO4

Pressure effects on the lattice parameters of β- and γ-Mg₂SiO₄ have been measured at room temperature and at pressures up to 100 kbar using a multi-anvil high-pressure X-ray diffraction apparatus. The volume changes (ΔV/V₀) at 90 kbar are 5.4 · 10^?2 and 4.2 · 10^?2 for β- and γ-Mg₂SiO₄, respectively. Isothermal bulk moduli at zero pressure have been calculated from least-square fits of the data to straight lines. They turn out to be 1.66 ± 0.4 and 2.13 ± 0.1 Mbar for β- and γ-Mg₂SiO₄, respectively. The α → γ transition obeys Wang's linear V_φ?ρ relation but the α → β transition does not.     

Bounds on the infimum decay rate for axisymmetric incompressible dynamos

Abstract

The variational lower bound v > 0.39π² determined by Ivers (1984) for the infimum decay rate v of axisymmetric poloidal magnetic fields is corroborated numerically and an upper bound v < 0.66°² established. This is achieved by correcting and extending results for certain flows considered by Chandrasekhar (1956).     

Geochemical evidence for mixing of magmatic fluids with seawater,Nisyros hydrothermal system,Greece

The chemical and isotopic compositions (δD_H2O, δ¹⁸O_H2O, δ¹⁸O_CO2, δ¹³C_CO2, δ³⁴S, and He/N₂ and He/Ar ratios) of fumarolic gases from Nisyros, Greece, indicate that both arc-type magmatic water and local seawater feed the hydrothermal system. Isotopic composition of the deep fluid is estimated to be +4.9±0.5‰ for δ¹⁸O and ?11±5‰ for δD corresponding to a magmatic water fraction of 0.7. Interpretation of the stable water isotopes was based on liquid–vapor separation conditions obtained through gas geothermometry. The H₂–Ar, H₂–N₂, and H₂–H₂O geothermometers suggest reservoir temperatures of 345±15 °C, in agreement with temperatures measured in deep geothermal wells, whereas a vapor/liquid separation temperature of 260±30 °C is indicated by gas equilibria in the H₂O–H₂–CO₂–CO–CH₄ system. The largest magmatic inputs seem to occur below the Stephanos–Polybotes Micros crater, whereas the marginal fumarolic areas of Phlegeton–Polybotes Megalos craters receive a smaller contribution of magmatic gases.     

Hydromagnetic waves in rapidly rotating spherical shells generated by poloidal decay modes

Abstract

This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor number T_m ? 10⁵. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.     

Rotating flow over long shallow ridges

Abstract

The flow of a rotating homogeneous, incompressible fluid past a long ridge is investigated. An analysis is presented for flows in which E ? 1, Ro ～ E^½, H/D ～ E⁰, h/D ～ E^½ and cosα ～ E⁰ where E is the Ekman number, Ro the Rossby number, H/D the fluid depth to ridge width ratio, h/D the ridge height to ridge width ratio and α the angle between the free stream flow and a line perpendicular to the ridge axis. The analysis includes effects of the nonlinear inertial terms. Particular examples of a ridge of triangular cross section and a sinusoidal topography are investigated in some detail. Experiments are presented for a triangular ridge which are in good agreement with the theory.     

Empirical relationship between leaf wax n-alkane δD and altitude in the Wuyi,Shennongjia and Tianshan Mountains,China: Implications for paleoaltimetry

Estimating past elevation not only provides evidence for vertical movements of the Earth's lithosphere, but also increases our understanding of interactions between tectonics, relief and climate in geological history. Development of biomarker hydrogen isotope-based paleoaltimetry techniques that can be applied to a wide range of sample types is therefore of continuing importance. Here we present leaf wax-derived n-alkane δD (δD_wax) values along three soil altitudinal transects, at different latitudes, in the Wuyi, Shennongjia and Tianshan Mountains in China, to investigate δD_wax gradients and the apparent fractionation between leaf wax and precipitation (ε_wax-p).We find that soil δD_wax track altitudinal variations of precipitation δD along the three transects that span variable environment conditions and vertical vegetation spectra. An empirical δD_wax-altitude relation is therefore established in which the average δD_wax lapse rate of ? 2.27 ± 0.38‰/100 m is suitable for predicting relative paleoelevation change (relative uplift). The application of this empirical gradient is restricted to phases in the mountain uplift stage when the atmospheric circulation had not distinctly changed and to when the climate was not arid. An empirical δD_wax–latitude–altitude formula is also calculated: δD_wax = 3.483LAT ? 0.0227ALT ? 261.5, which gives the preliminary spatial distribution pattern of δD_wax in modern China.Mean value of ε_wax-p in the extreme humid Wuyi Mountains is quite negative (? 154‰), compared to the humid Shennongjia (? 129‰) and the arid (but with abundant summer precipitation) Tianshan Mountains (? 130‰), which suggests aridity or water availability in the growing season is the primary factor controlling soil/sediment ε_wax-p. Along the Tianshan transects, values of ε_wax-p are speculated to be constant with altitude; while along the Wuyi and Shennongjia transects, ε_wax-p are also constant at the low-mid altitudes, but become slightly more negative at high altitudes which could be attributed to overestimates of precipitation δD or the vegetation shift to grass/conifer.Additionally, a reversal of altitude effect in the vertical variation of δD_wax was found in the alpine zone of the Tianshan Mountains, which might be caused by atmospheric circulation change with altitude. This implies that the paleo-circulation pattern and its changes should also be evaluated when stable isotope-based paleoaltimetry is applied.     

Quasi-geostrophic shallow-water vortex–patch equilibria and their stability

We examine the equilibrium form, properties, stability and nonlinear evolution of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L _D called the “Rossby deformation length” relating the strength of the stratification to that of the background rotation. Here, we generate steadily-rotating vortex equilibria for a wide range of γ?=?L/L _D , where L is the typical horizontal length scale of the vortex. We vary both γ (over the range 0.02?≤?γ?≤?10) and the vortex aspect ratio λ (over the range 0?<?λ?<?1). We find two modes of instability arising at sufficiently small aspect ratio λ?<?λ _c (γ): an asymmetric (dominantly wave 3) mode at small γ (or large L _D ) and a symmetric (dominantly wave 4) mode at large γ (or small L _D ). At marginal stability, the asymmetric mode dominates for γ???3, while the symmetric mode dominates for γ???3. The nonlinear evolution of weakly-perturbed unstable equilibria results in major structural changes, in most cases producing two dominant vortex patches and thin, quasi-passive filaments. Overall, the nonlinear evolution can be classified into three principal types: (1) vacillations for a limited range of aspect ratios λ when 5?≤?γ?≤?6, (2) filamentation and a single-dominant vortex for γ???1, and (3) vortex splitting – asymmetric for 1???γ???4 and symmetric for γ???4.     

Instability of flows near the onset of convection in a rotating layer with stress-free horizontal boundaries

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 ε^8/5, 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 ε^4/3. In the case of Eckhaus instability the growth rate is of the order of α².     

Inflow and outflow in a rotating circular container—A laboratory model for the Loop Current of the Gulf of Mexico

The Loop Current of the Gulf of Mexico is simulated in the laboratory. A circular tank is filled with water and is placed off-center on a rotating table and the flow field is generated by injecting and withdrawing water at two openings on the wall. The free surface becomes parabolic due to balance of gravitational and centrifugal forces, simulating the latitudinal change of the Coriolis parameter (-effect) in the ocean. The flow characteristics depend on the influx and the rate of rotation and can be classified according to non-dimensional parameters (Rossby, Ekman and Froude numbers denoted byR ₀,E andF, respectively). When the influx is small and the rotation rate is large (smallR ₀,E andF) the flow will be almost linear, and the fluid flows along the side-wall boundary layer under constraint of the -effect. For a very large influx (largeR ₀ andE) inertial forces become very large compared to the Coriolis force and the flow behaves like a potential flow. The flow studied had characteristics between these two extreme cases and hasR ₀ andF similar to the Gulf circulation, though similarity inE is ambiguous. Photographs of the flow indicate that the inflow penetrates further into the interior when the rotation rate is increased while the influx is kept constant. The numerical analysis of the non-linear vorticity equation confirms this for the parameters corresponding to the experiment. In addition, the photographs reveal eddies embedded on both sides of the main stream, particularly near the inflow region. These eddies are intensified and become uniform in size as the influx increases. It is pointed out that such eddies were actually observed near the Loop Current north of the Yucatan Straits.     

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.     

Theoretical investigation of the time variation of drainage density

A theoretical equation was developed to express the time variation of drainage density in a basin or geomorphic surface: D_i(t, T) is the drainage density at time T on the i-th basin or geomorphic surface, which was formed at time t; β(τ) is a factor related to the erosional force causing the development of the rivers of the basin or surface at time τ; δ_i is the maximum drainage density; and D_i is the initial drainage density on the i-th geomorphic surface or basin. The equation is based on the assumption that the drainage density increases with time until it reaches a specific upper limit δ_i(t)), the maximum drainage density, which is related to certain physical properties of the basin. The equations for various dated basins or geomorphic surfaces can be combined into one modified equation if the same relative erosional forces have acted on those basins or surfaces (β(t) = β(t) and if the basins or surfaces have the same physical properties δ_i(t) = δ_i(t), (D_i = D₀). The application of this equation to coastal terraces and glacial tills shows that the model is compatible with observed drainage densities on various dated basins or surfaces.     

Mechanisms for magnetic field generation in precessing cubes

ABSTRACT

It is shown that flows in precessing cubes develop at certain parameters large axisymmetric components in the velocity field which are large enough to either generate magnetic fields by themselves, or to contribute to the dynamo effect if inertial modes are already excited and acting as a dynamo. This effect disappears at small Ekman numbers. The critical magnetic Reynolds number also increases at low Ekman numbers because of turbulence and small-scale structures.     

Standing Alfvén waves with m ≫ 1 in an axisymmetric magnetosphere excited by a stochastic source

In the framework of an axisymmetric magnetospheric model, we have constructed a theory for broad-band standing Alfvén waves with large azimuthal wave number m 1 excited by a stochastic source. External currents in the ionosphere are taken as the oscillation source. The source with statistical properties of –white noise is considered at length. It is shown that such a source drives oscillations which also have the –white noise properties. The spectrum of such oscillations for each harmonic of standing Alfvén waves has two maxima: near the poloidal and toroidal eigenfre-quencies of the magnetic shell of the observation. In the case of a small attenuation in the ionosphere the maximum near the toroidal frequency is dominated, and the oscillations are nearly toroidally polarized. With a large attenuation, a maximum is dominant near the poloidal frequency, and the oscillations are nearly poloidally polarized.     

Global electromagnetic induction in the Moon and planets

A summary of experiments and analyses concerning electromagnetic induction in the Moon and other extraterrestrial bodies is presented. Magnetic step-transient measurements made on the lunar dark side show the eddy current response to be the dominant induction mode of the Moon. Analysis of the poloidal field decay of the eddy currents has yielded a range of monotonic conductivity profiles for the lunar interior: the conductivity rises from 3·10^?4 mho/m at a depth of 170 km to 10^?2 mho/m at 1000 km depth. The static magnetization field induction has been measured and the whole-Moon relative magnetic permeability has been calculated to be $\text{μ}\text{μ}{}_0\text{= 1.01 ± 0.06}$. The remanent magnetic fields, measured at Apollo landing sites, range from 3 to 327 γ. Simultaneous magnetometer and solar wind spectrometer measurements show that the 38-γ remanent field at the Apollo 12 site is compressed to 54 γ by a solar wind pressure increase of 7·10^?8 dyn/cm². The solar wind confines the induced lunar poloidal field; the field is compressed to the surface on the lunar subsolar side and extends out into a cylindrical cavity on the lunar antisolar side. This solar wind confinement is modeled in the laboratory by a magnetic dipole enclosed in a superconducting lead cylinder; results show that the induced poloidal field geometry is modified in a manner similar to that measured on the Moon. Induction concepts developed for the Moon are extended to estimate the electromagnetic response of other bodies in the solar system.     

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.