IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

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Morphologic and facies trends through the fluvial–marine transition in tide-dominated depositional systems: A schematic framework for environmental and sequence-stratigraphic interpretation

Fifty years of hyporheic zone research have shown the important role played by the hyporheic zone as an interface between groundwater and surface waters. However, it is only in the last two decades that what began as an empirical science has become a mechanistic science devoted to modeling studies of the complex fluid dynamical and biogeochemical mechanisms occurring in the hyporheic zone. These efforts have led to the picture of surface-subsurface water interactions as regulators of the form and function of fluvial ecosystems. Rather than being isolated systems, surface water bodies continuously interact with the subsurface. Exploration of hyporheic zone processes has led to a new appreciation of their wide reaching consequences for water quality and stream ecology. Modern research aims toward a unified approach, in which processes occurring in the hyporheic zone are key elements for the appreciation, management, and restoration of the whole river environment. In this unifying context, this review summarizes results from modeling studies and field observations about flow and transport processes in the hyporheic zone and describes the theories proposed in hydrology and fluid dynamics developed to quantitatively model and predict the hyporheic transport of water, heat, and dissolved and suspended compounds from sediment grain scale up to the watershed scale. The implications of these processes for stream biogeochemistry and ecology are also discussed.

Hyporheic flow and transport processes: Mechanisms, models, and biogeochemical implications

Field data are used to study the size distribution of bedload in paved gravel-bed streams. Similarity analysis yields the results that all grain size ranges are of approximately equal transportability when the critical condition for breaking the pavement is exceeded. This result is only approximately correct due to deviations from similarity. However, it is adequate to justify development of a method for calculating total bedload, which requires only the subpavement median grain size rather than the size distribution. A method for calculating bedload size distribution that accounts for deviation from similarity is also developed.

Closure of "Bedload and Size Distribution in Paved Gravel-Bed Streams"

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

[1] According to the Bagnold hypothesis for equilibrium bed load transport, a necessary constraint for the maintenance of equilibrium bed load transport is that the fluid shear stress at the bed must be reduced to the critical, or threshold, value associated with incipient motion of grains. It was shown in a companion paper [Seminara et al., 2002], however, that the Bagnold hypothesis breaks down when applied to equilibrium bed load transport on beds with transverse slopes above a relatively modest value that is well below the angle of repose. An investigation of this failure resulted in a demonstration of its lack of validity even for nearly horizontal beds. The constraint is here replaced with an entrainment formulation, according to which a dynamic equilibrium is maintained by a balance between entrainment of bed grains into the bed load layer and deposition of bed load grains onto the bed. The entrainment function is formulated so that the entrainment rate is an increasing function of the excess of the fluid shear stress at the bed over the threshold value. The formulation is implemented with the aid of a unique set of laboratory data that characterizes equilibrium bed load transport at relatively low shear stresses for streamwise angles of bed inclination varying from nearly 0° to 22°. The formulation is shown to provide a description of bed load transport on nearly horizontal beds that fits the data as well as that resulting from the Bagnold constraint. The entrainment formulation has the added advantage of not requiring the unrealistically high dynamic coefficient of Coulomb friction resulting from the Bagnold constraint. Finally, the entrainment formulation provides reasonable and consistent results on finite streamwise and transverse bed slopes, even those at which the Bagnold formulation breaks down completely.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2001WR001253

Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation

[1] The Bagnold hypothesis has been a major tool in the development of mechanistic models of bed load transport. According to the hypothesis, a necessary constraint for the maintenance of equilibrium bed load transport is that the fluid shear stress at the bed must be reduced to the critical, or threshold value associated with incipient motion of grains. The constraint determines a functional form for the areal concentration of bed load grains as a function of flow parameters. It is shown here, however, that the Bagnold hypothesis breaks down when applied to equilibrium bed load transport on beds with transverse slopes above a relatively modest value that is well below the angle of repose. In particular, under such conditions it is shown that no areal concentration, no matter how large, is sufficient to reduce the fluid shear stress at the bed to the critical value. This failure motivates the abandonment of the Bagnold constraint, even for nearly horizontal beds. The framework presented here, however, provides a natural basis for an entrainment-based model of sediment transport that neither satisfies nor suffers from the drawbacks of the Bagnold constraint.

Bed load at low Shields stress on arbitrarily sloping beds: Failure of the Bagnold hypothesis

Flow and bed topography in a regular sequence of meanders is shown to be strongly influenced by nonlinear effects within a fairly wide range of aspect ratios of the channel and meander wavenumbers. This finding is associated with the behaviour of meanders as nonlinear resonators in a neighbourhood of the resonance conditions discovered by Blondeaux & Seminara (1985). A weakly nonlinear approach valid for relatively small measures of channel curvature and within a neighbourhood of the resonant conditions displays all the typical features of nonlinear resonators, including non-uniqueness of the channel response. The nonlinear structure of forced bars close to resonance is also shown to be related to that of nonlinear free steady bars spatially developing in a straight channel from a non-uniform initial condition. Finally we show how to reconcile the intrinsic nonlinearity of the near-resonant channel response with traditional bend stability theories. Some comparison with a systematic set of experimental observations of Colombini, Tubino & Whiting (1990) provides qualitative support for the present theory but also suggests that strongly nonlinear effects may play a non-negligible role for fairly small values of channel curvature. The main implication of this work is the clear need to revisit the literature on the modelling of flow and bed topography in river meanders, which is mostly based on linear theories.

Weakly nonlinear theory of regular meanders

[1] Bend instability is the process whereby perturbations of the planform distribution of a channel relative to a straight configuration may grow, driven by erosion at concave banks and deposition at convex banks, leading to the development of a meandering pattern. Here we investigate the nature of this instability; that is, we ascertain under what conditions bend instability is convective or absolute. In the former case, an initial nonpersistent, small perturbation localized in space is convected away, eventually leaving the flow domain unperturbed. In the latter case, perturbations spread in both the upstream and downstream directions, eventually affecting the whole flow domain. In convective instabilities, the spatial-temporal development of perturbations is somewhat dependent on the characteristics of the initial perturbation which is required to be persistent in time. On the contrary, absolute instabilities are able to amplify perturbations, even if triggered at some initial time and then ceased. If bend instability is convective, planform information migrates only in one direction, while in the absolute regime, information is propagated in both directions. We show that bend instability is most often, though not invariably, convective at both a linear and nonlinear level. Moreover, the group velocity of perturbations changes sign as the width to depth ratio of the channel crosses some threshold value (the resonant value of Blondeaux and Seminara (1985)): Below (above) resonance, information is propagated downstream (upstream). We discuss the implications that these findings have on the morphological characteristics of meandering rivers (in particular, the sense of skewing of meander bends and the direction of meander migration). We also clarify how the choice of appropriate boundary conditions in numerical simulations of planform evolution is crucially dependent on the nature of bend instability and on its subresonant or superresonant regime.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005JF000416

On the nature of meander instability

Bar instability is recognized as the fundamental mechanism underlying the formation of large-scale forms of rivers. We show that the nature of such instability is convective rather than absolute. Such a result is obtained by revisiting the linear stability analysis of open-channel uniform flow over a cohesionless channel of Colombini et al. (1987) and using the Briggs (1964) criterion to distinguish between the convectively and absolutely unstable temporally asymptotic response to an initial boundary-value perturbation of bed topography. Examining the branch-point singularities of the dispersion relation, which can be determined in closed form, we show that all the existing branch-point singularities characterized by positive bar growth rate ω i , involve spatial branches of the dispersion relation which, for large positive values of ω i , lie in the same half λ-plane, λ denoting the complex bar wavenumber. Hence, the nature of instability is convective and remains so for any value of the aspect ratio, the controlling parameter of the basic instability, as well as for any lateral mode investigated. The latter analytical findings are confirmed by numerical solutions of the fully nonlinear problem. In fact, starting from either a randomly distributed or a localized spatial perturbation of bed topography, groups of bars are found to grow and migrate downstream leaving the source area undisturbed. The actual bars observed in laboratory experiments arise from the spatial-temporal growth of some persistent initial perturbation. The nonlinear development of such perturbations is shown to lead to a periodic pattern with amplitude independent of the amplitude of the initial perturbation. Bars are also found to lengthen and slow down as they grow from the linear into the nonlinear regime, in agreement with experimental observations. The distance from the initial cross-section at which equilibrium is achieved depends on the initial amplitude of the perturbation, a finding which calls for a revisitation of classical laboratory observations reported in the literature.

Giovanni Seminara

Papers

Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation

Bed load at low Shields stress on arbitrarily sloping beds: Failure of the Bagnold hypothesis

Weakly nonlinear theory of regular meanders

On the nature of meander instability

On the convective nature of bar instability