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

A two-dimensional model of flow and bed topography in sinuous channels with erodible boundaries is developed and applied in order to investigate the mechanism of meander initiation. By reexamining the problem recently tackled by Ikeda, Parker & Sawai (1981), a previously undiscovered ‘resonance’ phenomenon is detected which occurs when the values of the relevant parameters fall within a neighbourhood of certain critical values. It is suggested that the above resonance controls the bend growth, and it is shown that it is connected in some sense with bar instability. In fact, by performing a linear stability analysis of flow in straight erodible channels, resonant flow in sinuous channels is shown to occur when curvature ‘forces’ a ‘natural’ solution represented by approximately steady perturbations of the alternate bar type. A comparison with experimental observations appears to support the idea that resonance is associated with meander formation.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112085002440

A unified bar–bend theory of river meanders

Following ideas developed in the field of hydrodynamic stability of laminar flows (Stuart 1971) a predictive theory is proposed to determine the development of finite-amplitude alternate bars in straight channels with erodible bottoms. It is shown that an ‘equilibrium amplitude’ of bedforms is reached as t → ∞ within a wide range of values of the parameter (β − βc)/βc, where t is the time, β is the width ratio of the channel and βc is its ‘critical’ value below which bars would not form. The theory leads to relationships for the maximum height and the maximum scour of bars which compare satisfactorily with the experimental data of various authors. Moreover the experimentally detected tendency of the bed perturbation to form diagonal fronts is qualitatively reproduced.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087002064

Finite-amplitude alternate bars

[1] This contribution investigates the morphodynamic equilibrium of funnel-shaped well-mixed estuaries and/or tidal channels. The one-dimensional de Saint Venant and Exner equations are solved numerically for the ideal case of a frictionally dominated estuary consisting of noncohesive sediment and with insignificant intertidal storage of water in tidal flats and salt marshes. This class of estuaries turns out to be invariably flood dominated. The resulting asymmetries in surface elevations and tidal currents lead to a net sediment flux within a tidal cycle which is directed landward. As a consequence, sediments are trapped within the estuary and the bottom profile evolves asymptotically toward an equilibrium configuration, allowing a vanishing net sediment flux everywhere and, in accordance with field observations, a nearly constant value of the maximum flood/ebb speed. Such an equilibrium bed profile is characterized by a concavity increasing as the estuary convergence increases and by a uniquely determined value of the depth at the inlet section. The final length of the estuary is fixed by the longitudinal extension of the very shallow area which tends to form in the landward portion of the estuary. Note that sediment advection is neglected in the analysis, an assumption appropriate to the case of not too fine sediment.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JC000468

Long‐term evolution and morphodynamic equilibrium of tidal channels

Perturbations of channel geometry (like variations of channel curvature or channel width) in meandering rivers give rise to morphodynamic effects which display themselves through the development of large-scale perturbations of bottom topography in the form of stationary bars developing in the longitudinal direction. The latter may then drive the lateral migration of the channel by enhancing bank erosion at bar pools: through this mechanism local perturbations of channel geometry may affect the planimetric development of meandering rivers on large timescales. The problem tackled herein is whether such morphodynamic influence is invariably felt downstream as the commonly employed model of river meandering would suggest. In order to solve this problem, we derive the exact solution of the linearized form of the mathematical problem of river morphodynamics. Linear analysis had pointed out the existence of a resonance phenomenon: in a linear (hence ideal) context, resonance occurs when the meander wavenumber and the width ratio of the channel take values (λ R and β R , respectively) such as to force free spatial modes of the system consisting of free bars which neither grow nor decay either in time or in space. Channels characterized by values of the width ratio β larger (smaller) than β R are called super- (sub-)resonant. The present solution, which applies to channels with constant width and arbitrary curvature distribution, shows that two distinct scenarios may occur: downstream influence is associated with sub-resonant channels and vice versa dominant upstream influence occurs in super-resonant channels. Small-amplitude waves of bottom topography are shown to migrate downstream in the former case and may migrate upstream in the latter, as resonance also defines the threshold conditions below (above) which small-amplitude alternate bar perturbations (may) migrate downstream (upstream). These results have several implications. In the present paper we examine the overdeepening phenomenon whereby abrupt variations of channel curvature, as in sequences of straight and constant curvature reaches, lead to sequences of stationary alternate bars with amplitude decaying in the longitudinal direction. We show that, along with downstream overdeepening, an upstream overdeepening scenario is predicted in the super-resonant regime. Implications of the upstream influence on planimetric development of meandering rivers are investigated in Part 2.

Downstream and upstream influence in river meandering. Part 1. General theory and application to overdeepening

We revisit the problem of one-dimensional tide propagation in convergent estuaries considering four limiting cases defined by the relative intensity of dissipation versus local inertia in the momentum equation and by the role of channel convergence in the mass balance. In weakly dissipative estuaries, tide propagation is essentially a weakly nonlinear phenomenon where overtides are generated in a cascade process such that higher harmonics have increasingly smaller amplitudes. Furthermore, nonlinearity gives rise to a seaward directed residual current. As channel convergence increases, the distortion of the tidal wave is enhanced and both tidal wave speed and wave lenght increase. The solution loses its wavy character when the estuary reaches its “critical convergence”; above such convergence the weakly dissipative limit becomes meaningless. Finally, when channel convergence is strong or moderate, weakly dissipative estuaries turn out to be ebb dominated. In strongly dissipative estuaries, tide propagation becomes a strongly nonlinear phenomenon that displays peaking and sharp distortion of the current profile, and that invariably leads to flood dominance. As the role of channel convergence is increasingly counteracted by the diffusive effect of spatial variations of the current velocity on flow continuity, tidal amplitude experiences a progressively decreasing amplification while tidal wave speed increases. We develop a nonlinear parabolic approximation of the full de Saint Venant equations able to describe this behaviour. Finally, strongly convergent and moderately dissipative estuaries enhance wave peaking as the effect of local inertia is increased. The full de Saint Venant equations are the appropriate model to treat this case.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JC900015

Giovanni Seminara

Papers

A unified bar–bend theory of river meanders

Finite-amplitude alternate bars

Long‐term evolution and morphodynamic equilibrium of tidal channels

Downstream and upstream influence in river meandering. Part 1. General theory and application to overdeepening

On tide propagation in convergent estuaries