Showing papers in "Journal of Hydraulic Engineering in 1969"
TL;DR: In this article, the authors considered local scour caused by the horseshoe vortex system which forms at the base of the piers and proposed design criteria for blunt-nosed piers under the conditions of clear-water scour and scour with continuous sediment motion.
Abstract: Local scour caused by the horseshoe vortex system which forms at the base of the piers is considered. Piers which induce a pressure field strong enough to cause the formulation of the horseshoe vortex system are termed blunt nosed; all others being classed as sharp-nosed piers. The condition of the sediment transported into and out of the scour hole forms the basis for the further classification of the scour process into clear-water scour and scour with continuous sediment motion. The pier Reynolds number is shown to be an important variable describing the strength of the horseshoe vortex system. Further, the equilibrium scour depth depends on the initial sediment transport condition for a steady uniform flow with fully developed bed material transport. Design criteria are proposed for blunt-nosed piers under the conditions of clear-water scour and scour with continuous sediment motion. Several deviations from the above ideal design conditions are discussed; methods for design in these cases are suggested.
291 citations
TL;DR: In this paper, the relationship between high-intensity rainfall values for durations up to 2 hours and return periods up to 100 years is expressed by means of depth-duration and depth-frequency ratios.
Abstract: Rainfall-duration-frequency estimates for engineering purposes are usually subject to large sampling errors and extensive generalizations of the basic data are therefore advantageous from the point of view of estimation efficiency. Relationships between high-intensity rainfall values for durations up to 2 hr and return periods up to 100 years are appropriately expressed by means of depth-duration and depth-frequency ratios. These ratios are shown to have surprisingly consistent values in such diverse places as Alaska, Hawaii, Puerto Rica, South Africa and Australia, as well as the contiguous United States, and it is suggested that a physical explanation exists for such consistencies. The data may be conveniently generalized with one of several alternative depth-duration-frequency functions which should be useful for estimates in regions of limited data.
170 citations
TL;DR: In this article, a theoretical development of the Navier-Stokes equation through analysis of the dimensionless form of Navier Stokes equation is presented, which shows that energy losses at high-flow velocities in porous medium are a result of convective acceleration effects not turbulent effects.
Abstract: Many investigators are concerned about the validity of the Forchheimer equation which represents the relationship between the velocity of flow and pressure gradient in porous media. A theoretical development of this equation through analysis of the dimensionless form of the Navier-Stokes equation is presented. It shows that energy losses at high-flow velocities in porous medium are a result of convective acceleration effects not turbulent effects. In addition, two dimensionless terms representing the flow behavior are defined and evaluated. It is shown that a constant could be used to represent the geometric properties of the medium and that a characteristic length representative of the flow exist. Both of these quantities are easily evaluated through hydraulic measurements of gradients and flow velocities. Experimental data from many sources were used to evaluate the theoretical results.
157 citations
TL;DR: In this paper, the maximum depth at wave crest, minimum depths at wave trough, wave period and wave velocity of spontaneously developed roll-wave trains were measured in a laboratory channel.
Abstract: The maximum depth at wave crest, minimum depth at wave trough, wave period and wave velocity of spontaneously developed roll-wave trains were measured in a laboratory channel. Channel slope (\IS\N\DO\N) was varied from 0.05 to 12, normal depth (\Ih\N\Dn\N) was varied by a factor of two, and the Froude number of the undistrubed flow (F) ranged from 3.5 to 5.6. For each of the four properties, a single development curve resulted for all \Ih\N\Dn\N, with \IS\N\DO\N and F fixed. The spatial rate of growth of the average maximum depth increased as F was increased by increasing \IS\N\DO\N. The growth rate decreased as \IS\N\DO\N was increased and F was held fixed. Substantial growth occurs when one wave overtakes and combines with another wave. Growth also occurs without wave overtaking. Spontaneously developed roll waves are shown to be related to periodic permanent roll waves. Methods of applying the laboratory results to other channels with inlet conditions similar to that of the laboratory channel are presented.
108 citations
TL;DR: One-dimensional equations of continuity, momentum, and energy for unsteady, spatially varied flow in a fixed-bed open channel of arbitrary configuration are derived from the point forms of the corresponding hydrodynamic equations by integrating the latter over a deforming region of space comprising a slice of differential thickness across the flow with a top always coincident with the fluctuating water surface as discussed by the authors.
Abstract: One-dimensional equations of continuity, momentum, and energy for unsteady, spatially varied flow in a fixed-bed open channel of arbitrary configuration are derived from the point forms of the corresponding hydrodynamic equations by integrating the latter over a deforming region of space comprising a slice of differential thickness across the flow with a top always coincident with the fluctuating water surface. To bring the equations to the form of Saint Venant in fixed and accelerating reference frames, departures from hydrostatic pressure conditions in a cross section due to lateral acceleration, viscous deformation, and turbulent Reynolds stresses are reproduced exactly; the rate of energy dissipation in a cross section is uniquely related to wall shear over the wetted perimeter; the term accounting for lateral discharge depends upon its nature; bulk outflow is considered.
105 citations
TL;DR: Simplified methods of calculating hydraulic transients are presented in this article, with techniques for increasing the computing time interval over that permitted by the characteristics method, and Lumping and interpolation methods are compared with mixed implicit and characteristics methods.
Abstract: Simplified methods of calculating hydraulic transients are set forth, with techniques for increasing the computing time interval over that permitted by the characteristics method. Lumping and interpolation methods are compared with mixed implicit and characteristics methods. Complex boundary conditions are treated, including a spring-mass system with coulomb friction, an accumulator with inertia and fluid friction, pump failures, and column separation.
91 citations
TL;DR: The Shields diagram is widely accepted as a criterion for the beginning-of-bed movement of uniform non-cohesive sediment on a flat bed as mentioned in this paper, but the wide scatter of points on some recent revisions of the diagram is evidence that subjective assessment of beginning of bed movement is unsatisfactory.
Abstract: The well-known Shields diagram (originally published in 1936) is widely accepted as a criterion for the beginning of bed movement of uniform non-cohesive sediment on a flat bed. However, the wide scatter of points on some recent revisions of the diagram is evidence that subjective assessment of beginning of bed movement is unsatisfactory. Physically, the difficulty is caused by the fact that near the so-called beginning of movement only the peaks of the turbulent fluctuations are competent to displace grains. Because these fluctuations are statistically distributed, rare grain movements can take place even at low values of the mean (time-average) shear. If for a given area of bed the number of grains displaced per unit time is plotted against mean shear, the curve will be quite flat at its lower end, so that it is virtually impossible to decide where to draw a line and call it beginning of movement. To say this is not necessarily to imply that a threshold of shear does not exist.
90 citations
TL;DR: In this paper, the authors used a two-dimensional segmented mathematical model of the estuary to depict the probable distribution of a pollutant in a tidal segment of a estuary centered on the outfall.
Abstract: The fate of a pollutant introduced into an estuary depends upon the relative density of the effluent and the receiving water, the vertical density structure of the estuary, the strength of the tidal currents, the nontidal circulation pattern, and the intensity of turbulent diffusion. Effluents having lower density than the receiving waters, and discharged from an outfall on the bottom, ascend to the surface as a buoyant plume, entraining diluting water en route. Tidal currents advect the polluted volume as an oscillating plume, and turbulent diffusion leads to further dilution of the pollutant. Numerical solutions to time dependent theoretical advection-diffusion equations can be used to depict the probable distribution of a pollutant in a tidal segment of the estuary centered on the outfall. Exchange of pollutant between tidal segments in the estuary and the ultimate flushing of the pollutant from the estuary are best treated using a two-dimensional segmented mathematical model of the estuary.
83 citations
TL;DR: In this article, a new predictor for friction factors of flows in sand-bed channels is developed, based on a dimensional analysis to obtain the form of the quantities entering the relation between the geometry of the bed features, flow properties, and the equivalent shear stress due to the form-drag of the ripples, dunes, etc.
Abstract: A new predictor is developed for friction factors of flows in sand-bed channels. A dimensional analysis is pursued to obtain the form of the quantities entering the relation between the geometry of the bed features, the flow properties, and the equivalent shear stress due to the form-drag of the ripples, dunes, etc. Theoretical considerations of the bed stability lead to expressions for the length and height of the bed features in terms of the properties of the bed sediment and flow. These are introduced into the expression yielded by the dimensional analysis, and the resulting frictional relation is quantified with field and laboratory data. The graphical relation of Lovera and Kennedy is used to obtain the flat-bed friction factor. The predictor is evaluated using field data not included in preparation of the graphical relation between the bed-form friction factor, Froude number, and relative roughness. The depth-discharge relations predicted are found to be in good agreement with the measured data.
74 citations
TL;DR: In this article, a procedure for an analytic determination of sand discharge in streams is presented especially adaptable to computer programming, requiring only a modicum of input or given data from which the sand discharge fractions are both separately and in combination completely described quantitatively and in distribution from bed to water surface.
Abstract: A procedure for an analytic determination of sand discharge in streams is presented especially adaptable to computer programming, requiring only a modicum of input or given data from which the sand discharge fractions are both separately and in combination completely described quantitatively and in distribution from bed to water surface. It has been tested by application and comparison with observed data in all types of rivers, small to large, under a full range of flow conditions, and to model flume experiments conducted under widely varying flow conditions with bed sands varying widely in size and size distribution. It is considered that the results by this procedure are sufficiently accurate to warrant its use in many types of studies involving quantitative sand transport, design of channels, channel regulation works, and the assessment of probable effects of channel modifications.
71 citations
TL;DR: The appearance of the computer has had a great influence on computations for the prediction of the tide, especially at locations at the seaside, which can now be carried out more rapidly and accurately which is of special importance for navigation.
Abstract: Tidal computation on a computer in one- and two-dimensional fields is dealt with. Various systems for one-dimensional computation are mentioned and practical applications for mutual comparison are included. Considered also is the presence of a jump. A two-dimensional computational scheme, recently developed by Leendertse is dealt with, together with a practical application. A short review of modern methods of tidal prediction is given. The appearance of the computer has had a great influence on computations for the prediction of the tide, especially at locations at the seaside. Such predictions can now be carried out more rapidly and accurately which is of special importance for navigation. For the construction of engineering works in tidal areas, accurate tidal predictions of future situations are of great value. They furnish the boundary conditions in tidal computations for future situations.
TL;DR: In this article, hot-film anemometry was used to measure the characteristics of turbulence in hydrodynamically smooth and hydroynamically rough open-channel flow and showed that the relative turbulent intensity of the vertical velocity component was about 60% of the longitudinal, and spectral energy distribution was not significantly affected by the type of flow.
Abstract: Measurements of the characteristics of turbulence in hydrodynamically smooth and hydrodynamically rough open-channel flow using hot-film anemometry technics showed: (a) that the relative turbulent intensity of the vertical velocity component was about 60% of the longitudinal, (b) that the spectral energy distribution was not significantly affected by the type of flow, (c) that most of the turbulent energy is contained in frequencies less than 5 hertz, (d) the macroscale of the turbulence as determined from the autocorrelation function was on the same order as the depth and (e) the ratio of the microscale to depth ranged from 0.1 to 0.2. The measurements were used to verify experimentally the longitudinal direction momentum terms in the Navier-Stokes equation and to determine qualitatively the magnitude of the production, diffusion, and dissipation terms in the energy equation.
TL;DR: In this article, two commonly suggested forms of the equation linking head loss and velocity for flow of water through coarse granular media are the Forchheimer and exponential relations combined with the continuity expression, these relations give the differential equations applicable, within the limits of validity of the parent relations, to actual regions of flow.
Abstract: Two commonly suggested forms of the equation linking head loss and velocity for flow of water through coarse granular media are the Forchheimer and exponential relations. Combined with the continuity expression, these relations give the differential equations applicable, within the limits of validity of the parent relations, to actual regions of flow. The resultant nonlinear partial differential equations are amenable to solution by the numerical technique known as the method of finite elements. This technique has advantages when dealing with complex boundary shapes. Solutions have been obtained for some examples of unconfined flow with boundary conditions similar to those likely to be encountered in practical applications. Experimental work in an open flume has shown that agreement between observed and calculated values of discharge and piezometric head can be obtained when the coefficients in the head loss equations are accurately known.
TL;DR: In this paper, the effects of cross-sectional geometry and velocity distribution on the dispersion process in straight, uniform open channels with large width-to-depth ratio are investigated, and the results apply after the elapse of an initial period during which a constant dispersion coefficient has developed.
Abstract: The effects of cross-sectional geometry and velocity distribution on the dispersion process in straight, uniform open channels with large width-to-depth ratio are investigated. The method of investigation follows Taylor’s approach and thus the results apply after the elapse of an initial period during which a constant dispersion coefficient has developed. The results of the analysis show that under the assumed conditions the longitudinal dispersion coefficient can be described by the general expresion \IK\N = \ICRu\N\D*\N; in which \IR\N = the hydraulic radius, \Iu\N\D*\N = the shear velocity, and \IC\N = a factor. The variation of \IC\N with basic geometric and dynamic parameters is presented in the form of equations and diagrams for two velocity profiles (logarithmic and power law), and two cross-sectional shaped (triangular and circular arc). It is found that \IC\N varies significantly with cross-sectional shape, width-to-hydraulic radius ratio, and the Reynolds number. The calculated values of \IC\N and its pattern of variation are compared to available data for open channels with irregular cross section.
TL;DR: In this article, a method was developed for determining friction factors of open channel flows over flat sand beds in an active state of transport, and the graphical predictor is derived from both field and laboratory data, and is presented in a format similar to that of the Moody pipe-friction diagram.
Abstract: A method is developed for determining friction factors of open channel flows over flat sand beds in an active state of transport. The graphical predictor is derived from both field and laboratory data, and is presented in a format similar to that of the Moody pipe-friction diagram. The variation of friction factor with Reynolds number for constant values of the ratio of hydraulic radius to median sediment size was found to be much different for these flows than for one-phase flows in rigid-boundary conduits.
TL;DR: In this article, a theory is presented to define methods of optimum gate operation for altering flow conditions in an open channel, which is applicable to cases of initiating flow, increasing flow, decreasing flow, or stopping flow in irrigation channels, power channels, forebay channels to pumping stations, etc.
Abstract: A theory is presented to define methods of optimum gate operation for altering flow conditions in an open channel. The analytical procedure prescribes the motion of the control devices in the channel so the transient conditions are known and controlled during the period when the flow is being changed from one given situation to another desired flow condition. The method is applicable to cases of initiating flow, increasing flow, decreasing flow, or stopping flow in irrigation channels, power channels, forebay channels to pumping stations, etc. The theory is developed from the basic differential equations for unsteady flow in a prismatic channel, including frictional losses. Two examples are detailed in this study.
TL;DR: In this article, the mode of formation is the controlling criterion, and such matters as nature of sediment, types of soil, kind of stratification or other detailed concerns are of no moment.
Abstract: Alluvial rivers migrate laterally and longitudinally and, incident thereto, generate new flood plain lands Four types of lands are thus formed: sheet accretion, point bar accretion, eddy accretion and back-swamp accretion The type of flood plain land generated is determined by the nature of the local river migration or movement Incident to river migration, caving banks are formed, and under certain conditions, the caves can be very sudden, extensive, and dangerous to man, should the area involved be developed or urban Studies of river migrations and the resulting flood plain lands represent the most generalized aspect of river hydraulics and sedimentation studies In the present studies, mode of formation is the controlling criterion, and such matters as nature of sediment, types of soil, kind of stratification or other detailed concerns, are of no moment
TL;DR: In this paper, it is shown that the relative importance of diffusion or disperion in different transport problems depends on the steepness of the concentration gradient, and that the term diffusion should be reserved for transport that is associated primarily with time-averaged velocity fluctuations and that dispersion should be used for transport associated with the spatial average of velocity variations.
Abstract: Diffusion and dispersion are basically convective transport mechanisms. The method chosen for representing the convection in a mass balance equation is the determining factor in deciding whether diffusion or dispersion must be included in the conservation equation for a given flow. This principle is illustrated for molecular diffusion, turbulent diffusion, and longitudinal dispersion. In a given flow, the relative importance of diffusion or disperion in different transport problems depends on the steepness of the concentration gradient. It is proposed that the term diffusion be reserved for transport that is associated primarily with time-averaged velocity fluctuations and that dispersion be used for transport associated primarily with the spatial average of velocity variations.
TL;DR: In this article, the radial flow jump involves a force not found in the rectangular jump, and it is shown that the depth and energy loss for a radial jump are less and greater respectively than that for a rectangular jump.
Abstract: Hydraulic jumps involving radial flow, as in diverging stilling basins, have not been properly analyzed. Dynamical considerations disclose that the radial flow jump involves a force not found in the rectangular jump. As a consequence, the sequent depth and energy loss for a radial jump are less and greater respectively than that for a rectangular jump. In addition, experimental findings indicate that the length of the radial jump is less than that of the rectangular jump.
TL;DR: In this paper, experimental data was presented on fluctuating pressures in models of spillway stilling basins and the growth of a pressure pulse as flow passes through the upstream portion of the hydraulic jump.
Abstract: Experimental data is presented on fluctuating pressures in models of spillway stilling basins. Of special interest are data on (1) Variation of pressure fluctuations with location in the basin, (2) variation of fluctuations with discharge, and (3) the growth of a pressure pulse as flow passes through the upstream portion of the hydraulic jump. Pressure fluctuations up to plus or minus 40% of the incident-velocity head were measured during the tests.
TL;DR: In this article, the authors derived mathematical expressions for the effects of evapotranspiration and leakage loss in substantially reducing the baseflow and rendering the stream influent or dry.
Abstract: Baseflow curves are obtained by solving a nonlinear partial differential equation of groundwater flow for different boundary conditions. A theoretical basis is provided for differentiating between these curves for shallow and deep aquifers. Various linearized solutions and their limitations and errors are elucidated. Mathematical expressions are derived for the effects of evapotranspiration and leakage loss in substantially reducing the baseflow and rendering the stream influent or dry. Upward leakage from an underlying artesian aquifer casuses the baseflow to be more sustained and reduces its recession rate. Aquifer recharge of duration T , simulated by a sine function, leads to a baseflow hydrograph which peaks at 0.75 T and becomes parallel to the no-recharge curve after about 1.5 T .
TL;DR: Conformal mapping and the Riemann-Hilbert solution to a wellposed mixed-boundary-value problem are combined in solving the problem of gravity-affected flow from planar sluice gates of arbitrary inclination via a rapidly convergent, iterative procedure using a high-speed digital computer.
Abstract: Conformal mapping and the Riemann-Hilbert solution to a wellposed mixed-boundary-value problem are combined in solving the problem of gravity-affected flow from planar sluice gates of arbitrary inclination. The solution is obtained via a rapidly convergent, iterative procedure using a high-speed digital computer. Primary results include the contraction coefficient and the downstream free-surface configuration. The results compare satisfactorily with the results of other investigators. For the problem as posed, the solution given is exact. The solution requires only a modest amount of computer time.
TL;DR: In this paper, the movement of sand and finely crushed rock in tunnels is investigated and two problems are distinguished and dealt with: (1) the general aspect of sand movement in a horizontal tunnel and (2) the conditions for uniform sand movement with variable slope.
Abstract: The movement of sand and finely crushed rock in tunnels is investigated. A basic assumption is that the amount of transported material per unit time is low. Two problems have been distinguished and dealt with: (1) The general aspect of sand movement in a horizontal tunnel and; (2) the conditions for uniform sand movement in tunnels with variable slope. An analysis, based on present information of erosion in open channels, leads to equations for (1) calculating limiting size of particles being moved; and (2) the variation of cross section necessary to maintain uniform sand transport in long tunnels with variable slope. Coefficients are determined on the basis of laboratory tests and field data.
TL;DR: In this paper, a simple mathematical model of an urban basin presented in 1962 by the British Road Research Laboratory is tested on three urban watersheds in the United States, located in Baltimore, Chicago, and Champaign, Ill.
Abstract: A simple mathematical model of an urban basin presented in 1962 by the British Road Research Laboratory is tested on three urban watersheds in the United States. The basins are located in Baltimore, Chicago, and Champaign, Ill. They contain 0.395, 12.5, and 2290 acres respectively. The model produces a runoff hydrograph by applying rainfall to only the directly connected impervious area of the basin. The basin is described by a time-area diagram and a discharge-storage relationship. The peak discharges of actual and predicted hydrographs are compared for 39 storms and complete hydrographs are shown for 8 of these. To apply the model to a basin, the pattern of impervious areas must be known in detail, as well as the slopes and sizes of all surface and subsurface drains.
TL;DR: In this article, a daily multiple-station streamflow simulator was developed using first order Markov chain and regression analysis techniques to simulate the historical flow records of two gaging stations on the Calapooia River.
Abstract: A daily multiple-station streamflow simulator is developed using a first order Markov chain and regression analysis techniques. Historical flow records of two gaging stations on the Calapooia River in Oregon are analyzed and the hydrographs rearranged to reduce the observed variations of flow within any particular day and between each day. Rearrangement of flows consists of distributing the monthly peak or peaks of the hydrograph about particular days in order that the ascension and recession curves of the arranged flows occur on particular days. Daily flows are simulated on the basis of the statistical properties of the rarranged flows. A dampening factor is contained in the simulator to produce nonhistoric flow sequences with statistical distributions similar to the historic distributions for the annual flows, maximum one-day, three-day and ten-day average flows and the minimum one, seven, 30 and 120-day average flows.
TL;DR: In this article, an analytical solution by Laplace transform is presented for the development region of sediment suspensions in an open-channel flow, which is indistinguishable in accuracy from the computer results.
Abstract: In a recent study, Apmann and Rumer analyzed the nonuniform diffusion of suspended sediment in an open-channel flow. Experiments were performed for the situation in which a uniform open-channel flow enters from a region of rigid bottom to a region of sediment-laden bottom. The gradual development of concentration profiles is studied by measurements across the depth and along the flow direction. Theoretical calculations were also made on the basis of an approximate convective-diffusion equation; and the predicted concentration profiles agreed well with experiments. A numerical method of finite differences was used while the possibility of analytical solutions was apparently overlooked. In view of the significance of their work in extending the validity of the diffusion model for sediment suspensions, it seems worthwhile to present herein an analytical solution by Laplace transform. An approximate formula for the development region is derived from the Laplace inversion integral, which is indistinguishable in accuracy from the computer results.
TL;DR: In this paper, the authors studied turbulent mixing which occurs when sewage is discharged into the sea from a deeply submerged outlet and found that the density distribution across the plume is almost Gaussian.
Abstract: This investigation studied turbulent mixing which occurs when sewage is discharged into the sea from a deeply submerged outlet. The investigation was carried out by discharing fresh water, from circular nozzles of 1/2-in. and 1-in. diam, into quiescent ambient fluid of greater density. The ambient fluid was salt solution of uniform density. The motion in the rising plume is similar to convection over a heated source when the nozzle densimetric Froude number is low. The density at points in the plume was determined by measuring the concentration of the solution using an electrical conductivity probe. It was found that the density distribution across the plume is almost Gaussian.
TL;DR: A computer program for solving the basic equations of unsteady flows in reservoirs and natural rivers is being used by the TVA to solve a variety of open-channel flow problems.
Abstract: A digital computer program for solving the basic equations of unsteady flows in reservoirs and natural rivers is being used by the TVA to solve a variety of open-channel flow problems. The mathematical model, which has been proven with field measurements, is capable of accurately predicting variations in water surface elevations, mean velocities, and flows with respect to time at any point along a stream.
TL;DR: In this paper, the authors consider the effect of different bed configurations on the stability of the flat bed flow and show that two different relationships exist for the two different abilities, and a region of transition exists in between the two relationships where different abilities may overlap.
Abstract: THE OCCURRENCE OF DIFFERENT BED FORMS HAS BEEN CONSIDERED AS AN INSTABILITY IN THE FLAT BED FLOW. A GENERAL FUNCTIONAL RELATIONSHIP HAS BEEN DEVELOPED FOR THE INSTABILITY OF FLAT BED WHEN IT IS REPLACED BY EITHER DUNES OR RIPPLES. THE EXPERIMENTS INDICATE THAT TWO DISTINCT RELATIONSHIPS EXIST FOR THE TWO INSTABILITIES. A REGION OF TRANSITION EXISTS IN BETWEEN THE TWO FUNCTIONS WHERE EITHER INSTABILITY MAY OCCUR. THE STABILITY FUNCTION IS USEFUL TO PREDICT THE OCCURRENCE OF DIFFERENT BED FORMS. /ASCE/
TL;DR: In lakes and reservoirs stable density stratification is caused primarily by the temperature variation with depth, and secondarily by a variable concentration of dissolved and suspended solids as mentioned in this paper, which is caused mainly by the surface layers are heated strongly by the sun, while wind and surface evaporation cause mixing in a surface zone, called the epilimnion.
Abstract: In lakes and reservoirs stable density stratification is caused primarily by the temperature variation with depth, and secondarily by a variable concentration of dissolved and suspended solids. In the summer the surface layers are heated strongly by the sun, while wind and surface evaporation cause mixing in a surface zone, called the epilimnion, which is fairly uniform in temperature. Below this is the thermocline through which the temperature decreases rapidly to that of the lower zone, the hypolimnion, which feels negligible effect of the surface heating. During the fall and winter, the epilimnion cools, often to such an extent that the whole water column overturns and becomes fairly well mixed. In the spring the stratification is gradually reestablished. This is briefly the annual regime of lakes with little inflow or outflow. Man-made reservoirs have thermal regimes similar to lakes, but with the added effects if substantial inflows and outflows, which contribute to the heat and mass balance. Incoming river flows may sometimes spread out on the lake surface, if they are less dense than reservoir water, or may plunge to the bottom or to some intermediate level of neutral buoyancy, where an internal density current is formed. The river water density depends on its concentration of dissolved salts and suspended sediments as well as its temperature.