By Flemming Bo Pedersen (auth.)
The current lecture notes disguise a primary path in th~ most typical sorts 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 transformations. half I provides the fundamental strategies of stagnant, densit- stratified water, and of flowing non-miscible stratified fluids. The similarity to the (presumed) recognized open channel movement, topic to a discounted gravity, is illustrated. half II treats the miscible density stratified flows. In outlining the governing equations, the powerful 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 stream and Vertical jet/plumes. half III offers a few examples of sensible difficulties solved at the foundation of data given within the current lecture notes. it's the author's adventure that the themes handled in bankruptcy eight and within the next chapters are particularly good suited to self-tuition, by way of a study-circle. ACKNOWLEDGEMENT the writer has benefited through the dear support of his col legues on the Institute of Hydrodynamics and Hydraulic Engin eering, the Technical college of Denmark, particularly our librarian Mrs. Kirsten Dj¢rup, our secretary Mrs. Marianne Lewis and our technical draftsman Mrs. Liselotte Norup.
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Extra resources for Environmental Hydraulics: Stratified Flows
There are still three terms to mention in the energy equation for the mean motion, namely the work done by the pressure and gravity forces, and finally the last term which is the viscous dissipation, which may be neglected for high Reynolds' numbers. In the example to follow we wish to demonstrate in a simple case how the combined energy and momentum equation yields an expression for PROD (the production of turbulent kinetic energy). We consider a homogeneous lake in the inertial phase just after a constant wind stress has been imposed on the surface, Fig.
Gy cos ,w W PROD (see Eq. 41). 2) It has often been found that this conventional flux Richardson number is a constant. e. VE/V .... IF /::, 2, see Fig. 6). On the other hand, when the flow is associated with high values of the densimetric Froude number, the entrainment increases at a continuously decreasing rate with the densimetric Froude number, and furthermore the rate of increase in potential energy becomes negligible (just consider a jet where POT is zero). Hence the hypothesis of the constant flux Richardson number has its limit.
The energy transferred per unit area to the neighbouring elements amounts to Io a y -~- on (T v ) dn s - T. 1 U. 26) (as the velocity at the wall is zero). The energy transferred from the mean flow to the turbulence is (per unit area) v (as h/an s aT an dn + T W y T. 1 = Vy (T W +T . )/y is constant). Hence, we find 1 PROD" SU b" = T. 28) as postulated above. The terms 1/2 p (aV2) V E are the major contributions to PROD in supercritical flows. In this flow range the velocity distribution is approximately as illustrated in Fig.
Environmental Hydraulics: Stratified Flows by Flemming Bo Pedersen (auth.)