ALBERT

Description: The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in a thin pycnocline were studied numerically within the framework of the Navier–Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly non-linear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of instability. The dependence of loss of energy on the wave amplitude is not monotonic. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

Description: A modelling system - THREETOX - has been developed to simulate the transport and mixing of cooling water in both freshwater and marine environment. A 3D hydrostatic free-surface model describes the heat dispersion in the far-field, whereas an integral buoyant jet model coupled with a far-field model is applied to the near-field. The equations of hydrodynamics of the far-field model are completed by equations for heat and salt transport, and by the k - ε turbulence model. Special attention is paid to the parameterization of heat fluxes between water and atmosphere and between water and bottom sediments. Wetting and drying (WAD) processes were built into the model to describe areas where tide and floods play a dominant role. The model was enhanced by processes describing the effects of ship traffic on the dispersion of the discharged heat in stagnant canals. The sigma coordinate in the upper layer can be combined in the lower layer with a second sigma coordinate system or with a z coordinate system. An orthogonal curvilinear horizontal grid with two-way nesting capabilities has been used to describe the area of interest accurately. A high order advection scheme has been applied in the model. Several examples of the application and validation of the THREETOX model are presented. Studies were performed on the dispersion of cooling water, discharged by various power plants in the Netherlands located at different types of aquatic systems, varying from rivers, canals to tidal river reaches. Copyright © 2008 John Wiley & Sons, Ltd.

Description: The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in thin pycnocline were studied numerically within the framework of the Navier-Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves the trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly nonlinear waves without trapped cores, (ii) stable strongly nonlinear waves with trapped cores, and (iii) shear unstable strongly nonlinear waves. The wave phase shift grows as the amplitudes of the interacting waves increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum runup amplitude over the sum of the amplitudes of colliding waves almost linearly increases with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The waves of class (ii) with a normalized on thickness of pycnocline amplitude lose fluid trapped by the wave cores in the range approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of three-dimensional instability and turbulence. The dependence of loss of energy on the wave amplitude is not monotonous. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.