Hydrology of catchments, rivers and deltas (CIE5450)

Transcription

1 Hydrology of catchments, rivers and deltas (CIE5450) Prof.dr.ir. Savenije Lecture Salinity and tides in alluvial estuaries

2 Salinity and Tides in Alluvial Estuaries by Hubert H.G. Savenije Delft University of Technology

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4 Contents Estuary shape 5 new equations The role of the phase lag The role of tidal damping/amplification New versus Classical equations

5 Estuary Shape

6 Incomati Gent Schelde

7 Geometry of the Schelde estuary A B h A' B' h' B B 0 exp x b km Geometry of the Incomati estuary A h 0 B 0 exp x b A B h A' B' h' km

8 Equation Name Newly derived equation "Classical" equation Phase Lag equation Geometry-Tide relation Scaling equation Damping equation Green s eq. (1937) Celerity equation Mazure's equation (1837) d d H x tan = H E b b 2 c(1 b) (1 b) = r S h (1 b) r b cos( ) S 1 h c sin( ) g 1 1+ = H f ' c sin b sin hc h r b r S d H d x S h c 1 = H 2b 2 1 sin 2 c R' 1 c gh / 1 c 2 gh rs 2 1 b rs gh gh c cos c 2 2 f f

9 Most important differences Inclusion of Phase lag ε between HW and HWS Inclusion of tidal damping δ

10 The Phase Lag between HW and HWS

11 Standing wave ε=0 Mixed wave 0<ε<π/2 U sin( t ) Z cos(t) h Progressive wave ε=π/2

12 Phase Lag equation Conditions at HW: dh/dt=0, V=υsinε, dv/dt=ωυcosε Subst. in Lagrangean Continuity Equation: tan = c(1 b b) b 2 (1 b) (Savenije, 1993)

13 Tidal Damping and Amplification

14 Tidal damping and amplification 2 Tidal range in the Schelde y 0 y Q=41 calc Q=41 obs Q=0 calc Q=100 calc km

15 Tidal damping and amplification 1.5 Tidal range in the Incomati y 0 1 y calc obs km

16 Tidal damping and amplification 1. Combination of continuity and momentum balance equation h 2. Impose constraint for HW: 0 and V=υsinε 3. Impose constraint for LW: 0 and V=-υsinε t 4. Subtract the two envelopes 5. Yields: t h 1 d = d x 1 b f sin ' hc / 1+ g c sin (Savenije, 1998)

17 Tidal damping and amplification y hc f b x y y sin ' 1 = d d 1 α=o(0.1) If y>0.5 : linear amplification of damping If y<0.1 : exponential damping

18 The Geometry-Tide relation

19 The geometry-tide relation 1. Lagrangean version of Continuity equation 2. Integration between LW and HW 3. Taylor series expansion for E/b<1 H E = r h S b (1 cos( b) ) (Savenije, 1993)

20 The Scaling equation Combination of the geometry-tide relation with the Phase-Lag equation yields the Scaling Equation r S 1 h c sin( ) (Savenije & Veling, 2005)

21 Relation between wave celerity and tidal damping

22 Tidal propagation in the Schelde travel time (min) HW LW classic Classical equation c 0 1 gh distance (km) Tidal range in the Schelde 2 y Q=41 calc Q=41 obs Q=0 calc Q=100 calc y H H km

23 Tidal propagation in the Incomati travel time (min) classic HWS LW S Classical equation c 0 1 gh distance (km) Tidal range in the Incomati 1.5 y calc obs y H H km

24 The Celerity equation 1. Allow amplification and damping of the tide 2. Assume that the scaled tidal wave propagates undeformed 3. Assume η/h<1 4. Method of Characteristics 5. Solution for HWS and LWS 2 1 sin 2 R c gh / 1 rs 2 1 c ' b (Savenije & Veling, 2005)

25 Tidal propagation Incomati 600 travel time (min) TA classic HWS LW S HWS LW S distance (km) Tidal propagation in the Schelde 500 travel time (min) HW LW HW LW classic F&A distance (km)

26 Comparing the new Equations with their Classical Counterparts

27 Equation Name Newly derived equation "Classical" equation Phase Lag equation Geometry-Tide relation Scaling equation Damping equation Celerity equation Mazure's equation b b 2 tan = c(1 b) (1 b) H E = r S h (1 b) r b cos( ) S 1 h c sin( ) d H g 1 sin 1+ = H f ' d x c sin b hc c 1 r sin 2 gh / c ' b 2 R S gh cos f h r b r S d H d x c 2 S h c 1 = H 2b c 2 c 2 1 r S gh gh f

28 Equation Name Phase Lag equation Geometry-Tide relation Scaling equation Damping equation Celerity equation Mazure's equation Assumption made for Classical equation either ε=0 or ε=π/2 ε=0 and δ=0 ε=π/2 ε=π/2 and f =0 ε=π/2 or δ=0 ε=0 "Classical" equation h r b r S d H d x c 2 S h c 1 = H 2b 1 r S gh gh c 2 f

29 Conclusions The new equations demonstrate substantial differences with classical counterparts They are more general versions of the classical equations (which are special cases) They are consistent with each other (which the classical equations are not) The phase lag plays a key role and is the most important estuary parameter

30 Thank You for your attention

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32 Some useful estuary equations h b 1b cos H E continuity equation (Savenije, 1993) b tan 1 bc from continuity equation (Savenije, 1993) sin F the Scaling Equation h c (Savenije & Veling, 2005)

33 References: Savenije, H.H.G. and E.J.M. Veling, The relation between tidal damping and wave celerity in estuaries. Journal of Geophysical Research. In print. Horrevoets, A.C., H.H.G. Savenije, J.N. Schuurman, and S. Graas, The influence of river discharge on tidal damping in alluvial estuaries. Journal of Hydrology, 294(4): Savenije, H.H.G., A simple analytical expression to describe tidal damping or amplification, Journal of Hydrology, Vol.243, Iss.3-4, pp Savenije, H.H.G., "Analytical expression for tidal damping in alluvial estuaries", Journal of Hydraulic Engineering, Vol. 124, No. 6, pp , Savenije, H.H.G., "Predictive model for salt intrusion in estuaries", Journal of Hydrology, 148: , Elsevier, Amsterdam, The Netherlands, Savenije, H.H.G., "Determination of estuary parameters on the basis of Lagrangian analysis", Journal of Hydraulic Engineering, Vol. 119, No. 5: , ASCE New York, USA, 1993.

34 References: Savenije, H.H.G., "Composition and driving mechanisms of longitudinal tidal average salinity dispersion in estuaries", Journal of Hydrology, 144: , Elsevier, Amsterdam, The Netherlands, Savenije, H.H.G. and Pagès, J., "Hypersalinity, a dramatic change in the hydrology of Sahelian estuaries", Journal of Hydrology, 135: , Elsevier, Amsterdam, The Netherlands, Savenije, H.H.G., "Lagrangean solution of St. Venant's equations for an alluvial estuary", Journal of Hydraulic Engineering, Vol. 118, No. 8: , ASCE New York, USA, Savenije, H.H.G., "Salt intrusion model for High Water Slack, Low Water Slack and Mean tide, on spreadsheet", Journal of Hydrology, 107:9-18, Elsevier, Amsterdam, The Netherlands, Savenije, H.H.G., "Influence of Rain and Evaporation on Salt Intrusion in Estuaries", Journal of Hydraulic Engineering, 88: , ASCE New York, USA, Savenije, H.H.G., "A one-dimensional model for salinity intrusion in alluvial estuaries", Journal of Hydrology, 85: , Elsevier, Amsterdam, The Netherlands, 1986.

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