Internal Hydraulic Jumps Research Articles

Marine Tailings Disposal Simulation

The disposal of mine tailings in deep water body requires comprehensive assessment of the potential environmental impacts, and estimates of the effective storage capacity of the bottom bathymetry for accommodating the anticipated volume of disposed tailings over the life of a mine. A mathematical simulation model was developed for this purpose to predict the distribution and long-term deposition patterns of tailings in a fjord. The model describes the mechanics of the tailings slurry flow along the bottom of the receiving water body and the settling of suspended particles, as well as the redistribution of the deposited sediments due to slumping of unstable slopes. Specific processes simulated in the model also include entrainment at the top of the density current, entrainment associated with internal hydraulic jumps in areas of changing bottom slopes, hindered settling and coagulation of suspended particles, and sediment deposition and bathymetric changes resulting from the deposition of large quantities of tailings. Long-term tailings deposition patterns are predicted by analyzing the flow of the tailings slurry in a series of time increments, from a few months to a year. The bathymetry is assumed to remain unchanged within each time increment, and the model first simulates the steady-state flow field for the tailings slurry along the bottom and the resulting deposition rates for several sizes of suspended particles. Then the estimated tailings deposition rates are combined with slope stability considerations to predict the new bathymetry of the receiving water body. Data from several operating marine tailings disposal systems were reviewed to assess the applicability of specific relationships used in the model. The model was calibrated using data from one of the most extensively studied marine tailings disposal systems, the Island Copper mine in Rupert Inlet of Vancouver Island, British Columbia. Comparison of simulated tailings deposition patterns in Rupert Inlet with data from field observations and measurements suggests that calibration of the model is satisfactory and provides confidence in the capability of the model to predict deposition patterns and suspended sediment concentrations for proposed mines.

Internal hydraulic jumps at T-junctions

This paper presents a theoretical investigation of the occurrence of hydraulic jumps in two-layer systems induced by extraction of fluid from the upper layer. The physical configuration consists of a horizontal main pipe along which air and water flow, and a vertically upward side arm. An hydraulic model based on the momentum principle assuming that the fluids do not mix is developed that leads to at least two possible conjugate states for any given two-layer flow. A method of determining the amount of gas which must be extracted into the side arm for a jump to occur is developed and predictions shown to be in reasonable agreement with observation. Unusually, it is shown that above this critical gas take-off value two possible states remain energetically feasible.

Tidal dynamics and associated features of the northwestern shelf of the Alboran Sea

Current meter records from several stations in the northwestern Alboran Sea have been examined, to determine the structure of the tide on the Spanish Continental shelf. Tidal activity is restricted mainly to the westernmost area, where an inflowing jet of Atlantic water through the Strait of Gibraltar is observed almost permanently. A remarkable baroclinic tide, dominated by the interfacial mode, exists in this area. The geographic location of the jet and associated front, which exhibits low frequency fluctuations, controls the intensity of the baroclinic tide: the influence of the spring-neap tidal cycle is also noticeable. A study of the propagation of this internal tide confirms it as a feature related to the density front. During certain tidal cycles, internal hydraulic jumps appear to be formed somewhere over the shelf, shortly after high tide; later, they decay releasing undular internal bores. Internal waves originating from the Gibraltar Strait (generated at Camarinal Sill) are detected regularly at the outer and westernmost station of our study area. All these features become less distinctive in an easterly direction.

Effect of diurnal temperature variation on the hydraulics of clarifiers

This study was carried out to obtain data on the behaviour of thermally induced density currents in primary rectangular clarifiers so that better models can be developed for these units. This note deals with the case when the influent is cooler than the ambient temperature in the tank. The experiments were made in a model with a scale of about 1:20 compared to the typical full-scale clarifier. Temperature surveys and dye tests were carried out for turbulent flow and temperature differences between influent and effluent that were equivalent to ±0.2 °C in the prototype on a diurnal basis. The results indicate six flow regimes that follow a decrease in influent temperature: (i) denser wall jet; (ii) splash at the end wall; (iii) moving internal hydraulic jump; (iv) submerged internal hydraulic jump; (v) splash at the influent baffle; and (vi) stratified flow. A comparison of the test data with those available in the literature showed that the entrainment equations involving the Richardson number are adequate for modelling, but the classical hydraulic jump equations need modifications for the effect of entrainment. Key words: clarifiers, rectangular, primary, model, density currents, internal hydraulic jumps, unsteady flow, denser wall jets.

Tidal and atmospheric forcing of the upper ocean in the Gulf of California: 1. Sea surface temperature variability

Two years of satellite infrared imagery (1984–1986) are used to examine the sea surface temperature (SST) variability in the northern Gulf of California. Empirical orthogonal functions (EOFs) of the temporal and spatial SST variance for 20 monthly mean images show that the dominant SST patterns are generated by spatially varying tidal mixing in the presence of seasonal heating and cooling. These patterns are modified in the fall and winter when shelf temperatures south of Tiburon Island cool in response to upwelling‐favorable winds. These same winds bring cold, dry air from off the continental United States, causing local cooling of the shallow northern shelf. During the rest of the year, the broad, shallow shelves are warmer than offshore. The seasonally reversing temperature patterns are consistent with recent hydrographic observations which show a cyclonic surface circulation in the summer and a weaker anticyclonic circulation during the rest of the year. Atmospheric forcing of the northern gulf appears to occur over large spatial scales. Area‐averaged SSTs for the Guaymas Basin, island region, and northern basin show significant fluctuations which are highly correlated. These fluctuations in SST correspond to similar fluctuations in the air temperature which are related to synoptic weather events over the gulf. During periods of particularly low wind speeds, the air temperature over the gulf increases dramatically. By afternoon, intense heating of the sea surface results in the appearance of warm SST anomalies in the satellite data. These SSTs are approximately 2°C warmer than surrounding SSTs and most likely occur as a result of a spatially varying wind field. A regression analysis of the SST relative to the fortnightly tidal range shows that tidal mixing occurs over the sills in the island region as well as on the shallow norther shelf. Mixing over the sills, however, occurs as a result of large breaking internal waves or internal hydraulic jumps which mix water over the upper 300–500 m. This mixing pumps heat away from the surface, deep into the water column, there by maintaining the cool SSTs. Since mixing occurs over greater depths in the island region, the temperatures there are much colder than those generated by tidal mixing on the shallow shelves, resulting in the persistent pool of cool water evident in the satellite data. This cooler water is mixed horizontally by the basin‐scale circulation, lowering the SSTs over much of the northern gulf. These reduced SSTs have a large impact on the surface heat flux by lowering the saturation vapor pressure of the air. As a result, the amount of heat lost to the atmosphere through the latent or evaporative heat flux is reduced. This may explain why the Gulf of California gains heat on an annual average rather than losing heat as occurs in the Mediterranean and Red seas where tidal mixing is not significant.

Internal Wave Activity in Rotterdam Waterway

A variety of internal wave mechanisms is observed in the partially mixed Rotterdam Waterway estuary due to the interaction between stratified tidal flow and topography. The topographically generated waves include lee waves, resonant trapped waves and critical layers, freely propagating waves, breaking internal hydraulic jumps at the banks, and rotor formation. Acoustic images and profiles of density and velocity are presented. The acoustic images are explained on the basis of basic internal wave theory. Mathematical models tend to ignore smallscale internal wave activity as a source of turbulent kinetic energy. The paper investigates whether it is justified to do so on the scale of the topography. On the basis of an estimate of the internal wave‐induced production of turbulent kinetic energy it is concluded that for the observed internal waves this source of energy may not always be neglected when compared with the production by the background flow, in particular when first‐mode short internal waves are i...

Internal hydraulics of a sediment-stratified channel flow

Mudflats along the macrotidal Yellow Sea coast of South Korea are incised by numerous channels that act as drainage and sediment dispersal routes, primarily during ebb flows. Observations in two channels at maximum ebb revealed stable vertical distributions of suspended sediment (density) capped by a lutocline at mid-depth, across which suspended-sediment-related density varied rapidly. Internal responses, as revealed by turbidity and velocity data, varied with flow, suspended sediment, and morphology. At one location, upstream-propagating lowest mode internal waves with period T = 140 s were observed. Superimposed on the interfacial waves were higher frequency Kelvin-Helmholtz billows, apparently related to mean flow shear. Visual observations indicated that billows filled the channel from surface to bottom. At the second location, an undulatory jump consisting of a series of surges was observed. Each surge resembled the head of a turbidity current. Kelvin-Helmholtz billows were present, but only at surge crests and troughs. Internal hydraulic jumps, sediment spilling from feeder channels, and collapse of instabilities may contribute to wave generation. A range of bottom sediment sizes permits the development of a stable stratification within the bottom boundary layer beneath a lutocline. A simple numerical model shows that the lutocline is the upper limit of a boundary layer with a thickness proportional to mean flow velocity and to the intensity of suspended-sediment stratification within the layer. Billows appear to enhance resuspension of sediment, thereby increasing the sediment load and thickness of the boundary layer. Locations of hydraulic jumps appear to be sites of deposition.

Internal hydraulic jumps and solitons at a shelf break region on the Australian North West Shelf

A large‐amplitude, shoreward propagating, semidiurnal internal tide has previously been observed at a shelf break region on the Australian North West Shelf. This paper discusses detailed observations of the wave shape as the internal tide shoals over the shelf slope, near the shelf break. The leading face of the internal tide is seen to steepen and form an internal hydraulic jump. The properties of the jump are well described by a two‐layer hydraulic jump model in which the nearly uniform background temperature (density) profile is strongly distorted by the internal tide to an approximately two‐layer stratification just before a jump. The height of the jumps reaches 60 m in 123 m water depth, and the jumps contribute significantly to the strong dissipation of the internal tide that has previously been observed in this region. Following some of the jumps, packets of ∼ 12 internal waves of 20 min period are observed. These are described as solitons, and it is found that a second‐order theory (in wave amplitude) is necessary to describe the wavelength and phase speed. These waves also play an important role in the energy dissipation of the internal tide.

87:6092 Internal hydraulic jumps and solitons at a shelf break region on the Australian north west shelf: Holloway, P.E., 1987. J. geophys. Res., 92(C5):5405–5416

87:6092 Internal hydraulic jumps and solitons at a shelf break region on the Australian north west shelf: Holloway, P.E., 1987. J. geophys. Res., 92(C5):5405–5416

The hydraulics of two flowing layers with different densities

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.

Internal Hydraulic Jump Within Gradually Expanding Channel

Internal Hydraulic Jump Within Gradually Expanding Channel

Reverse Flow in Internal Hydraulic Jump and It's Contribution to Mixing Mechanism

Reverse Flow in Internal Hydraulic Jump and It's Contribution to Mixing Mechanism

Internal Hydraulic Jump in Stratified Counterflow

Based on a Boussinesq approximation of the governing momentum equations for an internal hydraulic jump in a two-layer counterflow, two important properties of an equal counterflow are demonstrated analytically. Corresponding to a given supercritical upstream state, there can be either two possible downstream conjugate states within the physically realizable range, or none at all. Further, the energy loss criterion across the jump is always satisfied. Consequently, the uniqueness of the downstream state cannot be determined by energy considerations, as done previously for the internal jump in a coflowing stratified flow. Physical arguments, coupled with some experimental observations indicate strongly that the conjugate state closer to the upstream state is the one that will be physically realized. The concept presented herein has been successfully applied to the study of stability and mixing of buoyant discharges in shallow water.

On the question of non-uniqueness of internal hydraulic jumps and drops in a two-fluid system

Conjugate states to a given two-layer flow of stable configuration confied on top and bottom by horizontal walls are studied in detail. There are at most two such states possible from energy considerations. Uniqueness is established by studying the total problem in which the agency responsible for causing shocks is also included. By establishing a suitable correspondence between the rigid top and free surface cases for purely internal shocks, uniqueness of the conjugate state for the latter case is also established. DOI: 10.1111/j.2153-3490.1973.tb00640.x

On the question of non-uniqueness of internal hydraulic jumps and drops in a two-fluid system

Conjugate states to a given two-layer flow of stable configuration confied on top and bottom by horizontal walls are studied in detail. There are at most two such states possible from energy considerations. Uniqueness is established by studying the total problem in which the agency responsible for causing shocks is also included. By establishing a suitable correspondence between the rigid top and free surface cases for purely internal shocks, uniqueness of the conjugate state for the latter case is also established.DOI: 10.1111/j.2153-3490.1973.tb00640.x

Dilution of Buoyant Two-Dimensional Surface Discharges

The flow of heated water from an open channel into a reservoir containing colder and essentially stagnant water has been studied in a laboratory flume. The basic mechanisms which produce mixing between heated discharge and cold water at the transition from a shallow to a deep channel have been documented. Experimental data on internal wave formation and on mixing involving various kinds of internal hydraulic jumps are presented in dimensionless form. A typical example showing the distribution of eddy diffusivities in the presence of a temperature gradient illustrates the mixing process outside the immediate outlet area. The information obtained supports the speculation that dilution of thermal plumes in many prototype situations must be produced mainly by horizontal mixing.

Internal Hydraulic Jump in Co-Current Stratified Flow

Yih and Guha made an important contribution to the study of the internal hydraulic jump of two-layered flow. They did not give criteria for the existence of internal hydraulic jumps nor an explicit form of the energy loss of a jump. Criteria for internal hydraulic jumps are presented herein.