Environmental Hydraulics: Stratified Flows by Flemming Bo Pedersen (auth.)

By Flemming Bo Pedersen (auth.)

The current lecture notes hide a primary path in th~ most typical kinds of stratified flows encountered in Environ­ psychological Hydraulics. lots of the flows are buoyancy flows, i.e. currents within which gravity acts on small density alterations. half I offers the fundamental ideas of stagnant, densit- stratified water, and of flowing non-miscible stratified fluids. The similarity to the (presumed) recognized open channel move, topic to a discounted gravity, is illustrated. half II treats the miscible density stratified flows. In outlining the governing equations, the robust coupling among the turbulence (the blending) and the suggest circulation is emphasised. The presentation and discussions of the fundamental governing equa­ tions are by means of illustrative examples. Separate chapters are dedicated to Dense backside Currents, unfastened Penetrative Convec­ tion, Wind-driven Stratified circulate, Horizontal Buoyancy movement and Vertical jet/plumes. half III provides a few examples of sensible difficulties solved at the foundation of data given within the current lecture notes. it's the author's event that the subjects handled in bankruptcy eight and within the next chapters are specially good­ suited to self-tuition, through a study-circle. ACKNOWLEDGEMENT the writer has benefited through the precious support of his col­ legues on the Institute of Hydrodynamics and Hydraulic Engin­ eering, the Technical college of Denmark, specially our librarian Mrs. Kirsten Dj¢rup, our secretary Mrs. Marianne Lewis and our technical draftsman Mrs. Liselotte Norup.

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5) 0 PR(1+6) ,has been introduced. The depth integrated continuity equations are illustrated by examples in the following. We consider a fjord (Fig. 2) with a fresh water runoff R from a river located at the upstream end. On its way out of the fjord, the fresh water is continuously diluted by sea-water from below, for instance due to wind generated entrainment. Fig. 2 A fjord with entrainment (higly distorted scale) . 7) Q (where B is the interfacial width of the fjord). 9) (where is the fresh water mass deficit).

1-... Initial winddrivPn flow _t,. fntprnal wav .. iRJ • IR i' constant V.... lical buoyant constant Plum.. ij J.. ts 1~1~-----------L~2----------~I~---------'~OnO----=F'2~4~~~~~--~~'02 10-3 1010A' 35 4. e. - as far as turbulent flow is concerned - with a production of turbulent kinetic energy, which in a homogeneous flow is dissipated into heat. In a stratified flow, part of this turbulent kinetic energy is used to mix the flowing water with the ambient water. Let us briefly illustrate this mixing process in a dense bottom current, see Fig.

11 ) Although terrifying to look at, the energy equation for the mean motion simply states that the change in kinetic energy is due to the work done by the internal and external forces. The first two terms are the local and the convective rate of change of kinetic energy, respectively. The third term is the work done per unit time by the Reynolds' stresses v vj). 11) - shallow flows). 4. The physical interpretation of Eq. 13) is: The energy transferred from the mean flow (last term) is partly used for production of turbulent kinetic energy (PROD) and partly transferred to the ambient fluid (first term on the right hand side).

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