Inversion of gravity anomalies over spreading oceanic ridges

Models of spreading ocean ridges are derived by Bayesian gravity inversion with geophysical and geodynamic a priori information. The aim is to investigate the influence of spreading rate, plate dynamics and tectonic framework on crust and upper mantle structure by comparing the Mid Atlantic Ridge (MAR), the Indian Ocean Ridge (IND) and the East Pacific Rise (PAC). They differ in mean spreading rate, dynamic settings, as attached slabs, and plume interaction. Topography or bathymetry, gravity, isostasy, seismology and geology, etc. are averaged along the ridges and guide the construction of initial 2D models, including features as mean plumes, i.e. averaged along the ridge. This is a gross simplification, and the results are considered preliminary.Three model types are tested: (a) the temperature anomaly; (b) asthenospheric rise into thickening lithosphere; (c) a crustal root as had been anticipated before seafloor spreading was discovered. Additional model components are a mean plume, a non-compensated ridge uplift, an under-compensated asthenospheric rise, e.g. of partially molten material, and seismic velocity models for P and S waves. Model type (c), tends to permute to model type (b) from thick crust to thin axial lithosphere. Model type (a) renders ‘realistic’ values of the thermal expansivity, but is insufficient to fit the gravity data; partial melt may disturb the simple temperature effect. A combination of (a) and (b) is most adequate. Exclusive seismic velocity models of S or P waves do not lead to acceptable densities nor to adequate gravity fitting. The different ridges exhibit significant differences in the best models: ATL and IND show an axial mass excess fostering enhanced ridge push, and ATL, in addition, suggests a mean plume input, while PAC shows an axial mass deficit reducing ridge push, most probably due to dominance of slab pull in the force balance.Goodness of the gravity fit alone is no justifiable criterion for goodness of model, indeed minor modifications to each model within the uncertainties of the assumptions can make the fit arbitrarily good. Goodness of model is quantified exclusively by a priori information.     

A model for grain-size sorting over tidal sand ridges

A model was developed and analyzed to quantify the effect of graded sediment on the formation of tidal sand ridges. Field data reveal coarse (fine) sediment at the crests (in the troughs), but often phase shifts between the mean grain-size distribution and the bottom topography occur. Following earlier work, this study is based on a linear stability analysis of a basic state with respect to small bottom perturbations. The basic state describes an alongshore tidal current on a coastal shelf. Sediment is transported as bed load and dynamic hiding effects are accounted for. A one-layer model for the bed evolution is used and two grain size classes (fine and coarse sand) are considered. Results indicate an increase in growth and migration rates of tidal sand ridges for a bimodal mixture, whilst the wavelength of the ridges remains unchanged. A symmetrical externally forced tidal current results in a grain-size distribution which is in phase with the ridges. Incorporation of an additional external M₄ tidal constituent or a steady current results in a phase shift between the grain-size distribution and ridge topography. These results show a general agreement with observations. The physical mechanism responsible for the observed grain-size distribution over the ridges is also discussed.Responsible Editor: Jens Kappenberg     

A gradational density model for gravity anomalies over oceanic ridges

The long-wavelength gravity anomalies observed over oceanic ridges have been interpreted in terms of horizontal slabs with lateral variation of density. The location of such a slab in the earth's interior is estimated to be between the depths of 350 and 430 km, which defines the boundaries of the upper phase-transition zone of the mantle. A total density contrast, between the end planes of the horizontal slab, of 0.3 g/cm³ appears to be satisfactory for the interpretation. This remarkable coincidence in depth and density contrast associated with the pyroxene-garnet transformation process is considered to suggest that this process may possibly be: (1) taking place laterally; and (2) generating the gradational density contact which is reflected in the gravity anomalies. In turn, the mechanism for this lateral phase transformation may ultimately be attributable to the convection currents in the asthenosphere.     

Nocturnal low-level jet over a shallow slope

A simple theory is presented for a nocturnal low-level jet (LLJ) over a planar slope. The theory extends the classical inviscid inertial-oscillation model of LLJs to include up- and downslope motion in the boundary layer within a stably stratified environment. The particular scenario considered is typical of LLJs over the Great Plains of the United States: southerly geostrophic wind over terrain that gently slopes down toward the east. First, an initial value problem for the coupled equations of motion and thermodynamic energy is solved for air parcels suddenly freed of a frictional constraint near sunset. The solution is an oscillation that takes, on the hodograph plane, the form of an ellipse having an eastward-oriented major axis and an eccentricity that increases with increasing stratification and slope angle. Next, the notion of a tilted residual layer (TRL) is introduced and used to relate initial (sunset) air parcel buoyancy to free-atmosphere stratification and thermal structure of the boundary layer. Application of the TRL-estimated initial buoyancy in the solution of the initial value problem leads to expressions for peak jet strength and the slope angle that maximizes the jet strength. Analytical results are in reasonable qualitative agreement with observational data.     

Rotating channel flow: Control and upstream currents

Abstract

Theory and experiments are presented for critically controlled flow of a layer of inviscid rotating fluid. Flow is controlled by a level passage. For a wide upstream channel of fixed depth (i.e. constant potential vorticity) the volume flux on the right-hand wall is unaffected by passage flow. This suggests that specifying Bernoulli potential on the right-hand passage wall produces a physically well-posed condition. The specification results in one less dimensionless number than was required by previous formulations to specify flow in the controlled passage. The upstream flow needs the same number as before, so that a range of upstream conditions produce exactly the same passage flow. A laboratory study is conducted using a thin layer of water under air. This is pumped in steadily at various locations in a deep rotating upstream basin, with fluid leaving through a level passage. All currents in the upstream basin cross to the left-hand wall as the current approaches the passage over a sloping bottom. The current crosses back to the right-hand wall within the passage. Velocity profiles of currents agree reasonably well with constant potential vorticity theory. To the right of the detached upstream current is a closed gyre that connects the upstream flows (that have different patterns depending on source location) with the unique passage flows. The results suggest that gyres upstream of critically controlling passages in the ocean might serve as adjustment regions between the relatively unconstrained upstream flows and the tightly controlled passage flows.     

Velocities of shallow overland flow on semiarid hillslopes

A series of 188 rainfall plot simulations was conducted on grass, shrub, oak savanna, and juniper sites in Arizona and Nevada. A total of 897 flow velocity measurements were obtained on 3.6% to 39.6% slopes with values ranging from 0.007 m s^‐1 to 0.115 m s^‐1. The experimental data showed that shallow flow velocity on rangelands was related to discharge and ground litter cover and was largely independent of slope gradient or soil characteristics. A power model was proposed to express this relationship. These findings support the slope–velocity equilibrium hypothesis. Namely, eroding soil surfaces evolve such that steeper areas develop greater hydraulic roughness. As a result overland flow velocity becomes independent of the slope gradient over time. Our findings have implications for soil erosion modeling suggesting that hydraulic friction is a dynamic, slope and discharge dependent property. Copyright © 2018 John Wiley & Sons, Ltd.     

Jet flow over foredunes

Jet flows, which are localized flows exhibiting a high speed maxima, are relatively common in nature, and in many devices. They have only been occasionally observed on dunes, and their dynamics are poorly known. This paper examines computational fluid dynamic (CFD) two‐dimensional (2D) modelling of jet flow over a foredune topography. Flow was simulated in 10° increments from onshore (0°) to highly oblique alongshore (70°) incident wind approach angles. CFD modelling reveals that the formation of a jet is not dependent on a critical wind speed, and an increase in incident wind velocity does not affect the magnitude of jet flow. A jet is first formed at ~1.0 m seawards of the foredune crest on the Prince Edward Island foredune morphology example examined here. A jet is not developed when the incident wind is from an oblique approach angle greater than ~50° because there is significantly less flow acceleration across a much lower slope at this incident angle. The presence of a scarp does influence the structure of the crest jet, in that the jet is more pronounced where a scarp is present. Surface roughness affects the magnitude of jet expansion and jets are better developed on bare surfaces compared to vegetated ones. Copyright © 2016 John Wiley & Sons, Ltd.     

Constraints on melt production rate beneath the mid-ocean ridges based on passive flow models

Pure and Applied Geophysics - We present a model for computing the total melt production rate from the decompression partial melting region beneath a mid-ocean ridge, and the maximum oceanic...     

Weakly-reflective boundary conditions for two-dimensional shallow water flow problems

In this paper weakly-reflective boundary conditions are derived for the two-dimensional shallow water equations, including bottom friction and Coriolis force. The essential aspects of the derivation are given. Zeroth and first order approximations are applied to the test problem of an initially Gaussian-shaped free surface elevation. For the numerical solution a finite element program is used and various aspects of the numerical implementation are discussed. For small scale practical problems a rather simple (one parameter) formulation might be sufficient. The influence of this parameter is discussed on the weakly-reflectiveness of the boundary condition.     

Lithospheric model with thick oceanic crust at the continental boundary: A mechanism for shallow spreading ridges in young oceans

In a general lithospheric model of a simple divergent ocean and continental margin that satisfies the constraints of isostasy and gravity anomalies, the free-air gravity anomaly at the margin is modelled by an oceanic crust that thickens exponentially toward the margin from its common value of 6.4 km about 600 km from the margin to 17.7 km at the margin; this postulated thickening is supported empirically by seismic refraction measurements made near continental margins. The thickness of the oceanic crust matches that of the continental lithosphere at breakup, as observed today in Afar and East Africa, and is interpreted as the initial oceanic surface layer chilled against the continental lithosphere. With continued plate accretion, the chilled oceanic crust thins exponentially to a steadystate thickness, which is achieved about 40 m.y. after breakup. These findings contrast with the generally held view that the oceanic crust has a uniform thickness.During the first 40 m.y. of spreading, the thicker oceanic crust, of density 2.86 g/cm³, displaces the denser (3.32 g/cm³) subjacent material; by isostasy, the spreading ridge and the rest of the seafloor thus stand higher in younger( <40m.y.) oceans than they do in older(>40m.y.) oceans. This is postulated to be the cause of the empirical relationship between the crestal depth of spreading ridges and the age (or half-width) of ocean basins.     

Oxygen isotope evidence for short-lived high-temperature fluid flow in the lower oceanic crust at fast-spreading ridges

Millimeter-scale amphibole veins in the lower oceanic crust record fracture-controlled fluid flow at high-temperatures but the importance of this fluid flow for the thermal and chemical evolution of the lower oceanic crust is unclear. In the section of lower oceanic crust recovered at Hess Deep from ODP Hole 894G, which formed at the fast-spreading East Pacific Rise, these veins are randomly distributed with an average spacing of  1 m. We unravel the history of fluid flow through one of these veins by combining in situ O-isotope analyses of wall-rock plagioclase with major element analyses, geothermometry and diffusion modeling. Thermometry indicates vein sealing by amphibole at  720 °C over a narrow temperature interval (± 20 °C). In situ O-isotope analyses by ion microprobe, with a precision of < 0.5‰, reveal zoning of O-isotopes in plagioclase adjacent to the vein. The zoning profiles can be reproduced using a diffusion model if the duration of O-isotope exchange was ≤ 100 yr. A similar interval of fluid–rock exchange is suggested by modeling potassium depletion in plagioclase adjacent to the vein. If representative of fracture controlled fluid flow in the lower oceanic crust the limited duration of fluid flow, and its occurrence over a narrow temperature interval, suggest that high-temperature fluid flow in this porosity network does not transport significant heat.     

Vertical mixing of gravel over a long flood series

Vertical sediment exchange is a fundamental component of bedload transport in gravel‐bed channels. This paper describes the characteristic depth of exchange achieved over a long flood series. Analysis is based on 11 recoveries of magnetically tagged gravels deployed in Carnation Creek, Canada, completed between 1990 and 2008. Vertical grain exchange mixes gravels throughout the streambed relatively rapidly. Within one to eight floods the mean burial depth approaches two times the surface layer thickness, quantified by the 90th percentile of the size distribution. Finer gravels are mixed more rapidly into the bed than coarser gravels. Both active and passive grain exchanges throughout most of the bed produce the overall vertical distribution of marked grains. Gravel exchanges exhibit fairly consistent patterns once tracers are well mixed by large floods. Results highlight the role of flood sequence in determining exchange depths, support the notion of an upper limit to exchange, and underscore the importance of passive grain exchange. Copyright © 2011 John Wiley & Sons, Ltd.     

Rotating flow past a short,sliced cylinder at finite Rossby number

Abstract

Flow past a short obstacle in a rotating reference frame generates a wake that is crucial to the overall flow structure if the Rossby number is of the order of the quarter power of the Ekman number. We present here a theory for such flows for the case when the obstacle's top is an oblique, planar surface. The results arise from a combination of asymptotic analysis and numerical computation, and show that even weak asymmetry generates significant global effect on the entire flow-field. Comparisons with the experiments reported by Foster and Davies (1996) are generally good when the high edge is at 90° to the oncoming flow.     

Strong tidal currents over two shallow banks in the western subarctic Pacific

The south-flowing waters of the Kamchatka and Oyashio currents are key components of the western subarctic Pacific gyre. The dissipation of tidal energy in shallow and coastal regions of these currents and the attendant mixing are the important processes that affect the upper layer temperature and salinity. Examples of the impact of tidal currents on water temperature and salinity are the persistent tide-driven mixing around the Kashevarov and Kruzenshtern banks. The Kruzenshtern Bank is a shallow submarine bank stretching along the eastern continental slope of the Kuril Islands with the minimum depth of 86 m. Surface drifters observations are used to determine the characteristics of tidal currents and the circulation over these banks. New software that allows more versatility in the harmonic analysis is used for drifter’s data. The two banks have similar features. The variations in current velocities are dominated by the diurnal signals. The K₁ and O₁ tidal ellipses over the banks are the largest and clockwise. The enhanced tidal currents suggest that the formation of cold and saline water in summer is due to mixing of water column over the banks with intermediate waters. Variations of tidal ellipses over the bank may explain the formation of polynya at the western end of the Kashevarov Bank. We found that the 18.6-year lunar nodal cycle is a significant characteristic of salinity variation at the temperature minimum in the eddies eastward of the Boussole Strait over the period 1990–2015.     

Evolution of rifted ocean ridges

A major question in seafloor tectonics has been, how does the 2-km-deep rift valley characteristic of slow-spreading ridges evolve into the relatively horizontal undulating relief of the rift mountains? Deep-tow studies of the Mid-Atlantic Ridge suggest that the primary mechanism for transformation of the rift valley topography is normal faulting along fault planes which dip away from the valley axis. The faulting occurs in a narrow zone just beyond the outer walls of the rift valley. This model allows for a steady-state evolution of the rift valley into the rift mountains in which the state of stress in the oceanic lithosphere continues to be in horizontal deviatoric tension throughout the entire process. Alternate mechanisms involving reverse faulting or regional tilt may be active but are found to be of less importance. Implications for various dynamic models of the rift valley are discussed.     

Sensitivity analysis of 2D steady-state shallow water flow. Application to free surface flow model calibration

This paper presents the analytical properties of the solutions of the sensitivity equations for steady-state, two-dimensional shallow water flow. These analytical properties are used to provide guidelines for model calibration and validation. The sensitivity of the water depth/level and that of the longitudinal unit discharge are shown to contain redundant information. Under subcritical conditions, the sensitivities of the flow variables are shown to obey an anisotropic elliptic equation. The main directions of the contour lines for water depth and the longitudinal unit discharge sensitivity are parallel and perpendicular to the flow, while they are diagonal to the flow for the transverse unit discharge sensitivity. Moreover, the sensitivity for all three variables extends farther in the transverse direction than in the longitudinal direction, the anisotropy ratio being a function of the sole Froude number. For supercritical flow, the sensitivity obeys an anisotropic hyperbolic equation. These findings are confirmed by application examples on idealized and real-world simulations. The sensitivities to the geometry, friction coefficient or model boundary conditions are shown to behave in different ways, thus providing different types of information for model calibration and validation.     

Spatially-averaged oscillatory flow over a rough bed

A rigorous framework involving flow decomposition and averaging is presented, within which the mechanics of rough-(e.g., rippled-) bed oscillatory flows can be better interpreted and understood. Spatiallyaveraged equations for conservation of fluid mass and momentum are developed for analyses of rapidly-changing bed conditions, e.g., for growing ripples. Where repeated observations of the changing bed conditions are available, the ensemble and spatially-averaged versions of these equations can be used for more detailed analyses of the flow dynamics. The double-averaged (in space and phase or time) equations of mass and momentum conservation are shown to be appropriate for analyses of flows over fixed rough beds and equilibrium ripples. The value of the present framework is highlighted herein by its application to PIV-measured oscillatory-flow velocities, stresses and vorticities over growing and equilibrium wave-induced intermediate-depth orbital-vortex ripples. In particular, discussions are provided regarding the mechanisms by which gravity-induced and pressure-gradient-induced momentum is transferred to the bed, with the analysis framework naturally and explicitly including the combination of the full range of fluid stresses and boundary form and skin friction drag that is important in defining the flow mechanics.