Numerical computation of the tidally induced Lagrangian residual current in a model bay

With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.     

Flow in natural shear zones—the consequences of spinning flow regimes

The ancient flow regime in natural shear zones is often considered to have followed a deformation path comparable to that in theoretical shear zones, i.e. progressive simple shear between rigid wall rocks with a persistent flow plane orientation parallel to the edges of the zone. This is often based on the presence of monoclinic fabric elements in the zones which indicate a dominantly non-coaxial flow regime, though not necessarily persistent simple shear. The deformation fabric of a shear zone from the Pyrenees illustrates that, even at a kinematic vorticity number ofW′ = 1 (simple shear) along the entire deformation path, obliqueness of the flow planes with the edges of the zone is possible for some time if incremental stretching axes were rotating with respect to zone edges. This implies that ductile deformation must have taken place in the wall rock of the zone. Such a flow regime may be difficult to recognize with the fabric criteria used at present but leads to an unusual kinematic significance of the shear zone involved; in extreme cases the zone may have acted as a passive marker in a ductilely deforming medium. It also means that not onlyW′ must be known to reconstruct the ancient flow regime in natural shear zones, but at least also the time dependence of the orientation of the incremental stretching axes.     

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.     

Internal hydraulic control in rotating fluids—applications to oceans

Abstract

Laboratory experiments and analysis of shallow water equations in a rotating fluid show that channel flow is governed by the ratio of the width of the channel to the Rossby radius of deformation R= √[g&Delta;ρH/ρf ²]. Flows through narrow ocean openings exhibit blocking and clear evidence of hydraulic control. These imply that formulae can be derived for width, volume flux, and velocity scales of the currents. A new version of the constant potential vorticity problem is solved, and it is shown to predict volume flux within 22% of the zero potential vorticity results. Next a systematic method of predicting volume flux through ocean passages is described. Some examples are given from the Denmark Straits overflow and the flow of Antarctic Bottom Water into the western Atlantic Ocean. Two-layer flows and counter-flows with rotation in a narrow passage, the so-called lock exchange flow problem, duplicate flows at a number of important straits and openings to bays. A potential vorticity formulation is reviewed. The flows in the mouths of various bays such as Funka Bay in Hokkaido, Japan, Spencer Gulf in South Australia, and Chesapeake Bay in the United States has R < width of the mouth, and the two currents are separated by a front. The width of the front and the density difference can be predicted with good results.     

On reduced-gravity flow through sills

Abstract

The hydraulic flow of a reduced-gravity fluid of non-negative potential vorticity through a sill is considered. It is shown that for any flow with a reversal of current, another, physically realisable, flow exists which is unidirectional and/or resting, and carries more flux than the original flow. Thus only non-negative flows need be considered when examining maximal hydraulic fluxes. Then, for a simple sill (one which slopes downward on the left and upward on the right, looking downstream), it is shown that zero potential vorticity flow, possibly modified by having a region of motionless fluid at its right, carries the maximum flux possible for that sill shape. This makes the calculation of maximal fluxes for a given sill considerably simpler, and examples of parabolic and V-shaped sills are computed.     

Observations of submesoscale eddies using high-frequency radar-derived kinematic and dynamic quantities

The spatio-temporal variability of submesoscale eddies off southern San Diego is investigated with two-year observations of subinertial surface currents [O(1) m depth] derived from shore-based high-frequency radars. The kinematic and dynamic quantities — velocity potential, stream function, divergence, vorticity, and deformation rates — are directly estimated from radial velocity maps using optimal interpolation. For eddy detection, the winding-angle approach based on flow geometry is applied to the calculated stream function. A cluster of nearly enclosed streamlines with persistent vorticity in time is identified as an eddy. About 700 eddies were detected for each rotation (clockwise and counter-clockwise). The two rotations show similar statistics with diameters in the range of 5–25 km and Rossby number of 0.2–2. They persist for 1–7 days with weak seasonality and migrate with a translation speed of 4–15 cm s⁻¹ advected by background currents. The horizontal structure of eddies exhibits nearly symmetric tangential velocity with a maximum at the defined radius of the eddy, non-zero radial velocity due to background flows, and Gaussian vorticity with the highest value at the center. In contrast divergence has no consistent spatial shape. Two episodic events are presented with other in situ data (subsurface current and temperature profiles, and local winds) as an example of frontal-scale secondary circulation associated with drifting submesoscale eddies.     

Capillary Crack Imbibition: A Theoretical and Experimental Study Using a Hele-Shaw Cell

—?We study the filling of horizontal cracks with constant aperture driven by capillary forces. The physical model of the crack consists of a narrow gap between two flat glass plates (Hele-Shaw cell). The liquid enters the gap through a hole in the bottom plate. The flow is driven purely by the force acting on the contact lines between solid, liquid, and gas. We developed a theoretical model for this type of flow on the basis of Darcy's law; it allows for the consideration of different surface conditions.¶We run the experiment for two surface conditions: Surfaces boiled in hydrogen peroxide to remove initial contamination, and surfaces contaminated with 2-propanol after boiling in hydrogen peroxide. The flow rate depends on the gap aperture and on the interaction of the liquid with the air and the solid surfaces: The smaller the aperture, the lower the flow rate due to viscous resistance of the liquid. The flow rate is also reduced when the glass surfaces are contaminated with 2-propanol. The contact line force per unit length is approximately 60% higher on clean glass surfaces than it is on glass surfaces with the 2-propanol contamination. These experimental results are in agreement with our theoretical model and are confirmed by independent measurements of the liquid-solid interaction in capillary rise experiments under static conditions with the same Hele-Shaw cell.¶Another aspect of this study is the distribution of the liquid for the different surface conditions. The overall shape is a circular disk, as assumed in the theoretical model. However, a pronounced contact line roughness develops in case of the surfaces contaminated with 2-propanol, and air bubbles are trapped behind the contact line. A further analysis of the flow regime using the capillary number and the ratio of the viscosities of the involved fluids (water and air) reveals that the experiments take place in the transition zone between stable displacement and capillary fingering, i.e., neither viscous nor capillary fingers develop under the conditions of the experiment. The contact line roughness and the trapped air bubbles in the contaminated cell reflect local inhomogeneities of the surface wettability.     

Fluid flow through rough fractures in rocks. II: A new matching model for rough rock fractures

An understanding of fluid flow through natural fractures in rocks is important in many areas, such as in the hydrocarbon and water industries, and in the safe design of disposal sites for domestic, industrial and nuclear waste. It is often impractical to obtain this information by field or laboratory scale measurements, so numerical modelling of fluid flow must be carried out using synthetic fractures with rough fracture surfaces that are representative of the natural rock fractures. Clearly there are two practical requirements; (i) the development of a method for analysing natural rock fractures to obtain their characteristic parameters, and (ii) the development of techniques for creating high quality synthetic fractures using these parameters. We have implemented these practical requirements in two new software packages. The first, ParaFrac allows the analysis and parameterisation of fracture surfaces and apertures. The second, SynFrac, enables the numerical synthesis of fracture surfaces and apertures with basic prescribed parameters. Synthetic fractures are created using, (i) a new model, which takes full account of the complex matching properties of fracture surfaces using two new parameters, a minimum matching fraction and a transition length and (ii) an improved method of partially correlated random number generation. This model more closely captures the often complex matching properties of real rock fractures than previous more simplified models.     

Kinematics and dynamics of the Mesozoic orogeny and late-orogenic extensional collapse in the Sino-Mongolian border areas

Extensional tectonic models with the major features of metamorphic core complexes were established in the Cordilleran region of western North America dur- ing the late 1970s to early 1980s of last century[1—4].Since there were previous thrust events, some re- searchers attributed the extension to crust-thickening of Mesozoic orogen[5—8], i.e. the crust thickening dur- ing orogeny led to the fact that the materials at depthswere heated and partially melted, and the heated and low-density mat…     

Surface semi-geostrophic dynamics in the ocean

The surface quasi-geostrophic approximation is re-written in an oceanic context using the two-dimensional semi-geostrophic approximation. The new formulation allows to take into account the presence of out-of-balance flow features at scales comparable to or smaller than the Rossby radius of deformation and for small bulk Richardson numbers. Analytical solutions show that, while the surface quasi-geostrophic approximation tends to underestimate the buoyancy anomaly, the inclusion of finite Rossby number allows for larger values of the buoyancy anomaly at depth. The projection of the surface semi-geostrophic solution on the first baroclinic modes is calculated. The result of the projection is a functional form that decreases with the values of the Rossby number and toward smaller scales. Solutions for constant and exponential profile for the background potential vorticity are compared. Results of the comparison show that, in agreement with the results found for balanced flows, even for large Rossby number the exponential profile for the background potential vorticity retains smaller values for the buoyancy anomaly at depth than the solution found using a constant potential vorticity profile.     

A note on the use of zero potential vorticity models

Abstract

The acceptability of zero potential vorticity models as approximations for natural systems of small, but finite, potential vorticity is studied for bounded frontal flows of arbitrary profile. It is demonstrated that all (infinitely) long-wave solutions of the zero potential vorticity front are asymptotic limits for some (not necessarily long-wave) solutions of the small potential vorticity front. In contrast, for downstream-varying solutions there is no simple way of demonstrating this property. These findings suggest that the use of zero potential vorticity models should be carefully examined in other, non-frontal, problems as well. Finally we show that the longwave solutions of the zero potential vorticity flow are at most neutral (quasi-stable).     

Propagation of barotropic modons over topography

Abstract

This is a broad survey of the interaction of modons with topography in a one-layer, quasigeostrophic model. Numerical simulations of modons interacting with ridges, hills, random topography and other obstacles are presented. The behavior of the modon is compared to numerical simulations of a two-point-vortex model, which proves a useful guide to the basic trajectory deflection mechanism. Under sufficiently strong but quasigeostrophically valid topographic perturbations, the modon is shown to fission into two essentially independent, oppositely-signed vortices. In the breakup of a modon near a hill it is found that the positive vortex migrates to the top of the hill. The resulting correlation between the positive vorticity trapped over the hill and the topography is in sharp contrast with the theories of turbulent flow over topography and generation of flow over topography by large scale forcing, both of which describe the development of vorticity anticorrelated with topography. A heuristic explanation of this new behavior is provided in terms of the dynamics of β bT-plane vortices. Further, it is found that a modon travelling over rough topography homogenizes the field of potential vorticity in its vicinity. This behavior is explained in terms of the induced eddy activity near the modon.     

Subantarctic mode water: distribution and circulation

The subduction and export of subantarctic mode water (SAMW) as part of the overturning circulation play an important role in global heat, freshwater, carbon and nutrient budgets. Here, the spatial distribution and export of SAMW is investigated using Argo profiles and a climatology. SAMW is identified by a dynamical tracer: a minimum in potential vorticity. We have found that SAMW consists of several modes with distinct properties in each oceanic basin. This conflicts with the previous view of SAMW as a continuous water mass that gradually cools and freshens to the east. The circulation paths of SAMW were determined using (modified) Montgomery streamlines on the density surfaces corresponding with potential vorticity minima. The distribution of the potential vorticity minima revealed “hotspots” where the different SAMW modes subduct north of the Subantarctic Front. The subducted SAMWs follow narrow export pathways into the subtropical gyres influenced by topography. The export of warmer, saltier modes in these “hotspots” contributes to the circumpolar evolution of mode water properties toward cooler, fresher and denser modes in the east.     

Emergent Anisotropy and Flow Alignment in Viscous Rock

— A novel class of nonlinear, visco-elastic rheologies has recently been developed by MÜHLHAUS et al.(2002a, b). The theory was originally developed for the simulation of large deformation processes including folding and kinking in multi-layered visco-elastic rock . The orientation of the layer surfaces or slip planes in the context of crystallographic slip is determined by the normal vector the so-called director of these surfaces. Here the model (MÜHLHAUS et al., 2002a, b) is generalized to include thermal effects; it is shown that in 2-D steady states the director is given by the gradient of the flow potential. The model is applied to anisotropic simple shear where the directors are initially parallel to the shear direction. The relative effects of textural hardening and thermal softening are demonstrated. We then turn to natural convection and compare the time evolution and approximately steady states of isotropic and anisotropic convection for a Rayleigh number R a=5.64×10⁵ for aspect ratios of the experimental domain of 1 and 2, respectively. The isotropic case has a simple steady-state solution, whereas in the orthotropic convection model patterns evolve continuously in the core of the convection cell, which makes only a near-steady condition possible. This near-steady state condition shows well aligned boundary layers, and the number of convection cells which develop appears to be reduced in the orthotropic case. At the moderate Rayleigh numbers explored here we found only minor influences in the change from aspect ratio one to two in the model domain.     

The effects of alongshore variation in bottom topography on a boundary current—(topographically induced upwelling)

A theory which describes the constant f-plane flow of a steady inviscid baroclinic boundary current over a continental margin with a bathymetry that varies slowly in the alongshore but rapidly in the offshore directions is developed in the parameter regime (L_D/L)² ≤ Ro 1, where L_D is the internal deformation radius, L the horizontal length scale, and Ro the Rossby number. To lowest order in the Rossby number the flow is along isobaths with speed q_o = V_u(h,z)|Vh|/α, where V_u(h,z) is the upstream speed, α the upstream bottom slope at depth h, and Vh the bottom slope downstream at depth h. The lowest order flow produces a variation in the vertical component of relative vorticity along the isobath as the magnitude and direction of Vh vary in the downstream direction. The variation of vorticity requires a vertical as well as a cross-isobath flow at first order in the Rossby number. The first order vertical velocity is computed from the vorticity equation in terms of upstream conditions and downstream variations of the bathymetry. The density, pressure, and cross-isobath flow at first order in the Rossby number are then calculated. It is shown that in the cyclonic region of current (d/dh(V_u/α) > 0), if the isobaths diverge in the downstream direction ((∂/∂s)|Vh| < 0), then upwelling and onshore flow occur. The theory is applied to the northeastern Florida shelf to explain bottom temperature observations.     

Numerical modelling of wind effects on breaking waves in the surf zone

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k ? ?? turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.     

The damage mechanics of brittle solids in compression

The development of microcrack damage in brittle solids in compression is analyzed, using a simple model. The model is developed from recent detailed analysis of the initiation, propagation and linkage of microfractures from pre-existing cracks, voids, or other inhomogeneities. It describes the evolution of damage with strain and from it a criteria for failure can be established. The results are used to construct failure surfaces in stress space which combine information about brittle failure with data describing the onset of plastic yielding. Such failure surfaces are constructed for a number of rocks and are compared with previously published experimental data.     

Petrology of the Izmir-Karaburun volcanic area (West Turkey)

The Izmir-Karaburun region is located on the West coast of Turkey. In this area volcanic rocks of the late Miocene-Pliocene age outcrop. On the basis of the collected petrographic and geochemical data it has been possible to subdivide these rocks in to three series:a) calc-alkaline series of Karaburun-Koca dag-Izmir (quantitatively the most important). This series is formed by latite-andesites-dacites-rhyodacites.b) Silicic series of Izmir-Lebedos, mainly constituted by alkali rhyolitic rocks.c) Urla series, formed by alkali trachytes and alkali rhyolites, associated with scarce basic lavas of hawaiitic type. A different genesis is assumed for these series. In a first phase the latite-andesitic magma was formed by a partial melting in the lower crust or in the upper mantle. Afterwards a subcrustal magma with alkali basaltic affinity rose slowly through the crust forming an intermediate reservoir and differentiating predominantly towards alkali trachytic terms. Finally silicic magma of Izmir-Lebedos was formed by an anatectic process. It is possible that the fusion has been favoured by the presence of basic magma in the upper crust.     

An application of parametric statistical tests to well-yield data from carbonates of central Pennsylvania

Variation in productivity, yield in gallons per minute per foot of drawndown per foot of saturated thickness, of 80 water wells located in folded and faulted carbonate rocks and shales of Cambro-Ordovician age in central Pennsylvania, was related to six hydroecologic factors. Parametric and nonparametric statistical techniques were applied and results of One Factor Analysis of Variance and Student t-test are presented. Productivity values were transformed to common logarithms, and it was assumed that a log-normal model would reasonably describe the variation in productivity especially as the sample size was increased. These tests showed that the variations in number of fracture traces, rock type, dip of bedrock strata and topography were significant and variation in depth to water table was not significant in accounting for variation in well yield. Student t-test showed that anticlinal wells were significantly different from synclinal wells. However, wells in the same rock type but different structural settings were not significantly different. This shows that variations in rock type and number of fracture traces are more important than other structural variations. Both parametric and nonparametric tests gave identical results, which justifies the use of parametric tests which require normally distributed data.