Contents Preface xi Acknowledgments xiii Chapter 1 Concepts and Definitions 1.1 The Role of Hydro... more Contents Preface xi Acknowledgments xiii Chapter 1 Concepts and Definitions 1.1 The Role of Hydrology and Hydraulic Engineering in Environmental Management I 1.1.1 Overall Framework for Environmental Management 2 1.1.2 Using the Water Environment for Waste ...
Mixing and transport processes in many stratified lakes are largely determined by the propagating... more Mixing and transport processes in many stratified lakes are largely determined by the propagating internal wave field excited by surface wind events. The onset of an applied wind stress is initially balanced internally by a baroclinic pressure gradient associated with a basin-scale tilt in the isopycnals. As the wind relaxes, the internal non-equilibrium degenerates into an evolving internal wave filed.
Under certain tidal conditions, a saline underflow originating in the Pacific Ocean moves into La... more Under certain tidal conditions, a saline underflow originating in the Pacific Ocean moves into Lake Ogawara, Japan. The underflow consists of a uniform saline bottom layer that is slightly warmer than the ambient and an interfacial shear layer in which the velocity and density are decreased. Within the experimental area the underflow is confined to a channel approximately 1 km wide and is essentially two-dimensional. The underflow had a bulk Richardson number, defined in terms of the mean properties, between 1 and 2. The rate of entrainment into the bottom layer was calculated using two distinct methods. The first method used the change in the maximum salinity of the underflow measured at two stations along the path of the underflow to infer the amount of ambient water entrained. The second method made direct measurements of vertical mass fluxes with a profiler. The agreement between the two methods was excellent. The measured entrainment coefficients were consistent with the derived entrainment law. The turbulent structure of the flow was mapped for a 3-h quasi-steady period of the flow. Turbulence is predominantly generated on the bottom boundary and is transported vertically to the density interface where it leads to mixing.
Destratification techniques are often used to improve water quality in reservoirs. The majority o... more Destratification techniques are often used to improve water quality in reservoirs. The majority of investigations have concentrated on the use of bubble aerators; however, an interesting alternative is the use of mechanical mixing systems consisting of a large propeller immersed in the water column. A laboratory study of such a system was used to examine the efficiency of energy conversion from mechanical energy to buoyancy flux as a function of impeller diameter, the speed of rotation, and the degree and type of stratification. The results were shown to depend on a generalized Froude number with the peak efficiency of energy conversion as high as 12%. A direct scaling mechanism enabling the results found in the laboratory model to be applied to a prototype situation was achieved via the application of derived scaling parameters. A simple design methodology for prototype versions of mechanical mixing systems based on this study is suggested.
A new Lagrangian, dynamic river model is described. The model solves the coupled one-dimensional ... more A new Lagrangian, dynamic river model is described. The model solves the coupled one-dimensional hydrostatic flow equations separately in a main river channel and in adjacent floodplains using a two-stage predictor-corrector scheme. The lateral interaction between the main channel and floodplains, due to both advective exchange arising from lateral pressure gradients and turbulent exchange due to lateral shear, is included. The Lagrangian moving grid eliminates numerical diffusion and oscillations commonly experienced in Eulerian models, and can accurately simulate wave propagation and nonlinear steepening until wave breaking. The Lagrangian moving grid is dynamically adaptive, providing variable resolution as the moving fluid parcel’s length changes, either because the cross-sectional flow area or the flow depth changes as the wave moves down a channel of variable cross section. The model also allows flows over dry beds and moving boundaries to be handled efficiently. The model was successfully validated...
A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is... more A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predict...
Field and laboratory experiments were performed to investigate the mixing induced by energetic po... more Field and laboratory experiments were performed to investigate the mixing induced by energetic point-source bubble plumes in water columns of arbitrary stable stratification. Published data from various sources were also used in the present study to increase the parameter range. It was found that the bubble-plume surface signatures were marked by a central unsteady core consisting of an air-water mixture, surrounded by an annular up-thrusting flow consisting of water only. Outside this, the rising plume water spread radially, plunged below the surface, and then flowed outward as an intrusive gravity current at a level of neutral buoyancy. By equating the observed arbitrary stratification to a linear profile of equal potential energy, the radial extent of the plunge point and the net detrainment rate could be parameterized using natural scales of the problem. These formulas were verified using field and laboratory data, and may thus be used in air-diffuser design procedures.
Two detailed field experiments were performed to investigate the spreading dynamics of axisymmetr... more Two detailed field experiments were performed to investigate the spreading dynamics of axisymmetric, inertia-buoyancy controlled, intrusive gravity currents in linearly stratified environments. The appropriate intrusions were successfully generated using deep-set point-source bubble plume devices installed within different thermally-stratified reservoirs. The intrusive flows were found to progress at a rate predicted from a simple inertia-buoyancy force balance with the intrusion thickness decreasing with distance from the source. The results imply that shear waves of all modes were generated at the intrusion nose and able to propagate away to modify the flow field. Turbulent activity, internal to the intrusions, was found not to influence the spreading characteristics. Scaling arguments and the experimental findings were also used to derive a parameter describing the initial intrusion dynamics. By combining the current findings with previously published results for intrusions progressing in the viscous-buoyancy regime, a relation describing the distance at which viscous forces become dominant was derived.
The Swan River is typical of the estuaries in southwest Australia. A shallow (5 m) sill near the ... more The Swan River is typical of the estuaries in southwest Australia. A shallow (5 m) sill near the entrance controls fluid exchange between the estuary and the ocean. The main estuarine basin is relatively deep and wide and is in turn bounded at the upstream end by a shallower (2 m) secondary sill. An understanding of the dynamics associated with the circulation and response of the deep basin over intertidal time scales was required to predict the dispersal of nutrients and provide data to validate numerical models of the system. The dynamics of the deep basin were documented with several C-T-D-DO transects during intensive summer and winter experiments. A variety of internal features including lee waves, undular bores, and basin scale seiching were observed over a tidal cycle. The circulation pattern and the basin response are shown to depend on the intraction between the tidal dynamics, the sill control, and the stratification produced by the gravitational overflow. A one-dimensional, three-layered analytical model was constructed to explain the basin response.
An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagat... more An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagation of long interfacial gravity waves in the presence of a strong, space–time varying background. Provision is made in the derivation for a spatially varying lower depth so that some topographic effects can also be included. The extended KdV model is applied to some simple scenarios in basins of constant and varying depths, using approximate expressions for the variable coefficients derived for the case when the background field is composed of a moderate-amplitude ultra-long wave. The model shows that energy can be transferred either to or from the evolving wave packet depending on the relative phases of the evolving waves and the background variation. Comparison of the model with laboratory experiments confirms its applicability and usefulness in examining the evolution of weakly nonlinear waves in natural systems where the background state is rarely uniform or steady.
Contents Preface xi Acknowledgments xiii Chapter 1 Concepts and Definitions 1.1 The Role of Hydro... more Contents Preface xi Acknowledgments xiii Chapter 1 Concepts and Definitions 1.1 The Role of Hydrology and Hydraulic Engineering in Environmental Management I 1.1.1 Overall Framework for Environmental Management 2 1.1.2 Using the Water Environment for Waste ...
Mixing and transport processes in many stratified lakes are largely determined by the propagating... more Mixing and transport processes in many stratified lakes are largely determined by the propagating internal wave field excited by surface wind events. The onset of an applied wind stress is initially balanced internally by a baroclinic pressure gradient associated with a basin-scale tilt in the isopycnals. As the wind relaxes, the internal non-equilibrium degenerates into an evolving internal wave filed.
Under certain tidal conditions, a saline underflow originating in the Pacific Ocean moves into La... more Under certain tidal conditions, a saline underflow originating in the Pacific Ocean moves into Lake Ogawara, Japan. The underflow consists of a uniform saline bottom layer that is slightly warmer than the ambient and an interfacial shear layer in which the velocity and density are decreased. Within the experimental area the underflow is confined to a channel approximately 1 km wide and is essentially two-dimensional. The underflow had a bulk Richardson number, defined in terms of the mean properties, between 1 and 2. The rate of entrainment into the bottom layer was calculated using two distinct methods. The first method used the change in the maximum salinity of the underflow measured at two stations along the path of the underflow to infer the amount of ambient water entrained. The second method made direct measurements of vertical mass fluxes with a profiler. The agreement between the two methods was excellent. The measured entrainment coefficients were consistent with the derived entrainment law. The turbulent structure of the flow was mapped for a 3-h quasi-steady period of the flow. Turbulence is predominantly generated on the bottom boundary and is transported vertically to the density interface where it leads to mixing.
Destratification techniques are often used to improve water quality in reservoirs. The majority o... more Destratification techniques are often used to improve water quality in reservoirs. The majority of investigations have concentrated on the use of bubble aerators; however, an interesting alternative is the use of mechanical mixing systems consisting of a large propeller immersed in the water column. A laboratory study of such a system was used to examine the efficiency of energy conversion from mechanical energy to buoyancy flux as a function of impeller diameter, the speed of rotation, and the degree and type of stratification. The results were shown to depend on a generalized Froude number with the peak efficiency of energy conversion as high as 12%. A direct scaling mechanism enabling the results found in the laboratory model to be applied to a prototype situation was achieved via the application of derived scaling parameters. A simple design methodology for prototype versions of mechanical mixing systems based on this study is suggested.
A new Lagrangian, dynamic river model is described. The model solves the coupled one-dimensional ... more A new Lagrangian, dynamic river model is described. The model solves the coupled one-dimensional hydrostatic flow equations separately in a main river channel and in adjacent floodplains using a two-stage predictor-corrector scheme. The lateral interaction between the main channel and floodplains, due to both advective exchange arising from lateral pressure gradients and turbulent exchange due to lateral shear, is included. The Lagrangian moving grid eliminates numerical diffusion and oscillations commonly experienced in Eulerian models, and can accurately simulate wave propagation and nonlinear steepening until wave breaking. The Lagrangian moving grid is dynamically adaptive, providing variable resolution as the moving fluid parcel’s length changes, either because the cross-sectional flow area or the flow depth changes as the wave moves down a channel of variable cross section. The model also allows flows over dry beds and moving boundaries to be handled efficiently. The model was successfully validated...
A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is... more A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predict...
Field and laboratory experiments were performed to investigate the mixing induced by energetic po... more Field and laboratory experiments were performed to investigate the mixing induced by energetic point-source bubble plumes in water columns of arbitrary stable stratification. Published data from various sources were also used in the present study to increase the parameter range. It was found that the bubble-plume surface signatures were marked by a central unsteady core consisting of an air-water mixture, surrounded by an annular up-thrusting flow consisting of water only. Outside this, the rising plume water spread radially, plunged below the surface, and then flowed outward as an intrusive gravity current at a level of neutral buoyancy. By equating the observed arbitrary stratification to a linear profile of equal potential energy, the radial extent of the plunge point and the net detrainment rate could be parameterized using natural scales of the problem. These formulas were verified using field and laboratory data, and may thus be used in air-diffuser design procedures.
Two detailed field experiments were performed to investigate the spreading dynamics of axisymmetr... more Two detailed field experiments were performed to investigate the spreading dynamics of axisymmetric, inertia-buoyancy controlled, intrusive gravity currents in linearly stratified environments. The appropriate intrusions were successfully generated using deep-set point-source bubble plume devices installed within different thermally-stratified reservoirs. The intrusive flows were found to progress at a rate predicted from a simple inertia-buoyancy force balance with the intrusion thickness decreasing with distance from the source. The results imply that shear waves of all modes were generated at the intrusion nose and able to propagate away to modify the flow field. Turbulent activity, internal to the intrusions, was found not to influence the spreading characteristics. Scaling arguments and the experimental findings were also used to derive a parameter describing the initial intrusion dynamics. By combining the current findings with previously published results for intrusions progressing in the viscous-buoyancy regime, a relation describing the distance at which viscous forces become dominant was derived.
The Swan River is typical of the estuaries in southwest Australia. A shallow (5 m) sill near the ... more The Swan River is typical of the estuaries in southwest Australia. A shallow (5 m) sill near the entrance controls fluid exchange between the estuary and the ocean. The main estuarine basin is relatively deep and wide and is in turn bounded at the upstream end by a shallower (2 m) secondary sill. An understanding of the dynamics associated with the circulation and response of the deep basin over intertidal time scales was required to predict the dispersal of nutrients and provide data to validate numerical models of the system. The dynamics of the deep basin were documented with several C-T-D-DO transects during intensive summer and winter experiments. A variety of internal features including lee waves, undular bores, and basin scale seiching were observed over a tidal cycle. The circulation pattern and the basin response are shown to depend on the intraction between the tidal dynamics, the sill control, and the stratification produced by the gravitational overflow. A one-dimensional, three-layered analytical model was constructed to explain the basin response.
An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagat... more An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagation of long interfacial gravity waves in the presence of a strong, space–time varying background. Provision is made in the derivation for a spatially varying lower depth so that some topographic effects can also be included. The extended KdV model is applied to some simple scenarios in basins of constant and varying depths, using approximate expressions for the variable coefficients derived for the case when the background field is composed of a moderate-amplitude ultra-long wave. The model shows that energy can be transferred either to or from the evolving wave packet depending on the relative phases of the evolving waves and the background variation. Comparison of the model with laboratory experiments confirms its applicability and usefulness in examining the evolution of weakly nonlinear waves in natural systems where the background state is rarely uniform or steady.
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Papers by Jorg Imberger