This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in Q 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule. In Q 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in $3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in 0 3. The two-dimensional energy-conserving flow is investigated further in Q 4, and finally a close approximation to the shape of the interface is obtained. In Q 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In $6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.

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Gravity currents and related phenomena

In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing

: SUTRA (Saturated-Unsaturated Transport) is a computer program which simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. The mathematical model employs a two-dimensional hybrid finite-element and integrated-finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated by SUTRA: (1) fluid density-dependent saturated or unsaturated ground-water flow, and either; (2a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay, or, (2b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA provides, as the primary calculated result, fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA may also be used to simulate simpler subsets of the above process. Additional keywords: Fluid flow; Radial flow; FORTRAN. (Author)

SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport.

Results of recent theoretical studies are used as a basis for a new two-parameter system of estuarine classification. The classes are delineated by the magnitudes of the relative stratification and circulation parameters associated with changes in the salt balance mechanism. The theoretical results depend on a knowledge of the eddy coefficients of viscosity and diffusivity. Tentative relationships between these coefficients and the bulk parameters of tidal current, river flow, and geomorphology, which are obtained from experimental data, may be used to determine the salinity and net current distributions in partially mixed and well-mixed coastal plain estuaries.

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New dimensions in estuary classification1

Sea salt aerosol (SSA) exerts a major influence over a broad reach of geophysics. It is important to the physics and chemistry of the marine atmosphere and to marine geochemistry and biogeochemistry generally. It affects visibility, remote sensing, atmospheric chemistry, and air quality. Sea salt aerosol particles interact with other atmospheric gaseous and aerosol constituents by acting as sinks for condensable gases and suppressing new particle formation, thus influencing the size distribution of these other aerosols and more broadly influencing the geochemical cycles of substances with which they interact. As the key aerosol constituent over much of Earth's surface at present, and all the more so in pre-industrial times, SSA is central to description of Earth's aerosol burden.

Sea Salt Aerosol Production: Mechanisms, Methods, Measurements, and Models - A Critical Review

Field experiments were conducted in Lake Balaton, a large (surface area, 600 km2) but shallow (mean depth, 3.2 m) lake in Hungary, to quantify the resuspension and deposition of bottom sediment due to episodic storm events. Measurements were made of windspeed and direction, surface waves, mean water velocity, and suspended sediment concentration. During significant wind events, the computed bottom stress due to surface waves dominated that due to the mean current, and therefore surface waves were assumed to be the major cause of sediment resuspension. A simple model for the depth-averaged suspended sediment concentration based on surface wave height was calibrated with about 10 h of data collected during one storm event and verified against 15 d of data collected at the same site. The success of the suspended sediment model, which assumes that the bottom sediment was noncohesive, is surprising since the bottom material was composed predominantly of sediment in the clay and fine-silt size ranges. This fit may indicate the presence of a thin surface layer of loosely bound sediment that is continuously involved in resuspension. The suspended sediment model could easily be integrated into a water quality model (e.g. to predict light attenuation), provided that lateral transport is negligible, or it could be used to provide the bottom boundary condition for a more general suspended sediment transport model in which advective transport is included. Due to their small fall velocities, finegrained particles (i.e. those in the silt and clay size ranges) are transported easily by flows. An understanding of the dynamic behavior of these particles is particularly important in shallow lakes and estuaries since there they may repeatedly settle to the bot

https://aslopubs.onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1990.35.5.1050

Dynamic behavior of suspended sediment concentrations in a shallow lake perturbed by episodic wind events

Coefficients of longitudinal and lateral dispersion were measured for steady uniform laminar flow through an isotropic porous medium. A unique experimental method for measuring lateral dispersion is described. It is found that the ratio of the coefficient of longitudinal dispersion D1 to the coefficient of lateral dispersion D2 is given by where λ and n are dimensionless coefficients dependent upon the pore-system geometry, and [real ] is the Reynolds number based on the seepage velocity, the average grain diameter, and the kinematic viscosity.

Longitudinal and lateral dispersion in an isotropic porous medium

Theories are developed for the time dependent vertical temperature distribution in a deep lake during the yearly cycle of solar heating and cooling. A portion of the incoming solar radiation is assumed to be absorbed at the water surface, whereas the remainder is absorbed exponentially beneath the surface. Heat is also conducted downward by molecular diffusion. A heat flux balance at the water surface, which accounts for back radiation and evaporative heat loss, is formulated as a boundary condition. The linear, second-order heat transfer equation is solved by superposition of solutions for the surface absorbed radiation and the internally absorbed radiation. Analytical solutions are given for three different assumptions regarding the time dependence of the incoming radiation and the surface heat losses. At certain times, the resulting temperature and density distribution in the epilimnion are unstable. Under these conditions convective mixing and turbulent diffusion are accounted for by generating a surface mixed layer of uniform temperature. The depth of the surface mixed layer is determined by a thermal energy balance. The theory shows good agreement with field observations of temperature distributions in Lake Tahoe. Experiments are performed using artificial insolation (mercury vapor and infrared lamps) on a laboratory tank. We conclude that it is possible to simulate the development of thermal stratification under laboratory conditions.

Thermal stratification in lakes: Analytical and laboratory studies

Longitudinal dispersion and permeability tests were performed in the Darcy flow regime using uniform porous media consisting either of spheres or sand grains.

Dispersion-Permeability Correlation in Porous Media

A technique is developed for accounting for the contribution of free convection to the evaporation from a cooling pond. Established formulas for forced (wind-driven) evaporation are corrected for convective effects and used in a formula for surface energy balance to estimate heat fluxes and surface temperatures of cooling ponds. The resulting expression for total heat loss agrees with observed cooling pond performance better than other formulas presently in use. Surface heat loss coefficients may be derived from the new heat loss formula for use in calculating temperature rises induced by heated discharges.

Donald R. F. Harleman

Papers

Dynamic behavior of suspended sediment concentrations in a shallow lake perturbed by episodic wind events

Longitudinal and lateral dispersion in an isotropic porous medium

Thermal stratification in lakes: Analytical and laboratory studies

Dispersion-Permeability Correlation in Porous Media

Surface heat loss from cooling ponds