Architecture and facies distribution of organic-clastic lake fills in the fluvio-deltaic Rhine-Meuse system, The Netherlands Ingwer J.

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1 Arhiteture and faies distribution of organi-lasti lake fills in the fluvio-deltai Rhine-Meuse system, The Netherlands Ingwer J.Bos Supplement 1. Duration and harateristis of fluvial regime disharge and sediment transport related to mouth-bar deposition in organi-lasti lake fills There is a strong relation between the harateristis of fluvial hannels sediment supply and period of ativity and the sediment bodies they produe upon debouhing into, for example, a lake. In order to alulate minimum timesales for delta sedimentation from alluvial arhiteture e.g., width/thikness ratio, deposited sediment volume - a number of omputations have to be made, primarily based on fluid dynamis. The relevant equations (numbers refer to those as used by Kleinhans 2005) are disussed below and are embedded in a more fundamental ontext in a publiation by Kleinhans (2005). A brief overview of the parameters used in the model (Supplement 3) is given in Table 1. Flow omputations Water flow through a hannel an be haraterized by a set of parameters suh as disharge, flow veloity, hydrauli roughness, Reynolds and Froude numbers and bed shear stress. Disharge (Q) is the produt of the hannel width (W), hannel depth (h) and the flow veloity (u) averaged over the width and depth of the hannel: Q = hwu The hydrauli radius instead of water depth is used to aount for the effet of banks on the water depth and is expressed as R Wh = (2) h W + 2 h The flow veloity, averaged over the depth and width, is given by the Dary-Weisbah equation: (1) u = 8ghS f (3) where g = the aeleration due to gravity, h is depth (hydrauli radius) and S = water surfae slope or hannel bed surfae, given that the flow is steady and uniform. f = the frition fator, whih is a measure for the hydrauli roughness. Hydrauli roughness is very relevant for flow alulations as it determines the water depth. However, it is hard to determine as it depends on omplexly interating variables suh as flow turbulene and roughness elements on the hannel bed (e.g., grains and bed forms). A widely used preditor for the frition fator is the White-Colebrook frition law: 8 f h h = 5.74 log = 5.74 log k s k s where k s = Nikuradse roughness length, whih depends on harateristis of the grain-size distribution (e.g., D 50 ) or on bed-form height. The Reynolds and Froude numbers desribe two elementary harateristis of flow. The Reynolds number differentiates between laminar and turbulent flow and relates to the flow veloity (u), water depth (h) and the fluid visosity (υ) as (8) uh Re f = υ (14) For Re f > 500, flow is turbulent, whih is valid for all rivers. The Froude number indiates whether flow is subritial (Fr < 1) or superritial (Fr > 1).

2 Fr = u gh (15) where u = ritial flow veloity. Table 1. overview of the input and alulated parameters in the model (Supplement 3). symbol units line desription Parameters and variables g m/s2 Gravity W m Width of hannel h m Depth of hannel S m/m Slope upstream hannel k s m Nikuradse roughness length kg/m3 Fluid density Centigrad e Fluid temperature - Dynami visosity - Kinemati visosity D 50 m Median grain size D 90 m 90 th perentile grain size kg/m3 Sediment density λ Porosity Disharge alulations Rh m Hydrauli radius (eq. 2 Kleinhans) - Width/depth ratio f - Frition fator (eq. 8 Kleinhans) u m/s Veloity (eq. 3 Kleinhans) Fr - Froude number (eq. 15 Kleinhans) Re - Reynolds number (eq. 14 Kleinhans) Qw m3/s Disharge (eq. 1 Kleinhans) Bed-load transport f' - Grain frition fator (eq. 8 Kleinhans) τ' Pa Grain shear stress (eq. 17 Kleinhans) θ' - Shields parameter (grain related) (eq. 22 Kleinhans) - Shields riterion for inipient motion Φ b - Non-dimensional transport rate (eq. 30 Kleinhans) R - Relative submerged density (in eq. 20 Kleinhans) m2/s Speifi volumetri transport rate q b m3/ Volumetri transport rate - Water/sediment ratio - Total/bedload ratio Total load transport (suspension dominated) τ Pa Total shear stress (eq. 16 Kleinhans) θ - Shields parameter (total) (eq. 22 Kleinhans) Φ s - Non-dimensional total transport rate (eq. 37 Kleinhans) m2/s Speifi volumetri transport rate (eq. 29 Kleinhans) q s m3/ Volumetri transport rate - Water/sediment ratio Erosion/sedimentation m2 m3 m3 Deposited sediment delta surfae Deposited sediment delta volume (sand) Deposited hannel-belt volume (sand) Time-sale of formation assuming bed-load Delta volume/bed-load flux CB volume/bed-load flux Time-sale of formation assuming suspended load Delta volume/total sediment flux (~eq. 54 Kleinhans) CB volume/sediment flux

3 The bed shear stress affets sediment transport and is defined as τ = ρu * 2 = ρgh sin S (16) in whih ρ = fluid density (1000 kg/m 3 for fresh water), u* = flow veloity and S = hannel gradient. If u is written as the Dary-Weisbah equation (eq. 3), the bed shear stress relates to the hydrauli roughness as follows 1 2 τ = ρf u (17) 8 The bed shear stress may be divided in two omponents: bed-form related and grain-related. Of these two, only grain-related bed shear stress is relevant for sediment transport, whih an be alulated from equation (17) where the frition fator (f) is defined by the White-Colebrook frition law (eq. 8). The hydrauli roughness length is ommonly hosen as k s = 2.5D 50 (Kleinhans 2005). Sediment mobility Preferentially, non-dimensional variables and parameters are used to desribe bed-load sediment transport. These variables either desribe the flow or the sediment size. The grain size is desribed by * D = D 3 50 Rg 2 υ (20) where R = (ρ s ρ)/ρ is relative submerged density, ρ = the liquid density and ρ s is the sediment density (2650 kg/m3 for quartz sand). Commonly applied flow parameters are based on urrent veloity, shear stress (τ) and grain shear stress (τ, only skin frition). The shear stress is represented by the non-dimensional Shields parameter : θ = τ ( ρ s ρ ) gd50 (22) whih also is valid for grain shear stress (θ ). Sediment transport Non-dimensional sediment transport is defined as φ = ( ) D Rg q b or s 50 (29) wherein q b or s = bed load or suspended-load sediment transport rate (m 2 /s, ubi m per m width per seond) exluding pore spae. A preditor for bed-load sediment transport near the beginning of motion was derived by Meyer-Peter and Mueller (1948) φ = b ( θ ' θ ) r (30) A well-known preditor for suspended-load sediment transport has been published by Engelund and Hansen (1967) and is given below φ s = 0.4 θ f 2.5 (37)

4 wherein Φ s = non-dimensional suspended-load sediment transport and f = Dary-Weisbah oeffiient related to the total roughness. Timesale of hannel and delta formation The minimum timesale of delta/hannel formation is defined by T V s s = 1 λ ( ) Q s (54) wherein V s = volume of sediment (inluding pores), whih is either eroded from a hannel or deposited in a delta and Q s = (q b + q s )W s with W s = width that part of the hannel floor that transports sediment (Kleinhans 2005).

5 Input parameters and variables W = 180 m. This is the minimum width of the hannel belt and onsequently the maximum width of the palaeohannel, whih is measured on a reent geologial-geomorphologial map of the area (Fig. 5B in main manusript). h = 8 m. Only 3 orings penetrated the hannel belt of the Angstel, reovering hannel-belt deposits that were 6.0, 9.1 and 10.3 m thik. S = 3.6 m/km. The slope of the upstream hannel was derived from the Gradient of the Top of Sand (GTS) of the hannel belt deposits of the Aa and Angstel (Fig. 1). Berendsen (1982) showed that GTS lines an be used to approximate the gradient of palaeohannels. We seleted all orings that reorded the top of Aa or Angstel hannel-belt deposits (n=103). Within setions of 2 km along the palaeohannel as measured along abandoned hannel deposits the point with highest deteted hannel-belt sediment was seleted. These points (n=10) were plotted as a funtion of the distane from Utreht along the paleo hannel. The gradient of the trendline was used as gradient of the palaeohannel. Although R 2 of the trend line is relatively low (0.27), a gradient of 3.6 m/km is not unusual for hannels in distal parts of delta plains. Values between 3.0 and 10 m/km (Makaske et al. 2007; Törnqvist et al. 1993) were reported for palaeohannels in the Rhine-Meuse delta. GTS-line Aa-Angstel, the feeding hannel of the Aetsveldse lasti lake fill 0 elevation (m relative to Duth O.D., ~ MSL) y = x R 2 = distane from Utreht (km) Figure 1. GTS-line of the Aa-Angstel. λ ~ 34% for Holoene hannel-belt sediment in the Rhine-Meuse delta (Weerts 1996). Water temperature = 10.4 C. This is the average (based on daily measurements), whih are the earliest doumented measurements (Rijkswaterstaat 2009) of water temperature in the Rhine. Referenes BERENDSEN, H.J.A., 1982, De genese van het landshap in het zuiden van de provinie Utreht, een fysish geografishe studie: Published PhD Thesis Utreht University. Utrehtse Geografishe Studies 10, Utreht, 256 p. ENGELUND, F., and HANSEN, E., 1967, A monograph on sediment transport in alluvial streams: Kobenhavn, Denmark, Teknisk Forlag. KLEINHANS, M.G., 2005, Flow disharge and sediment transport models for estimating a minimum timesale of hydrologial ativity and hannel and delta formation on Mars: Journal of Geophysial Researh, v. 110, Doi E12003.

6 MAKASKE, B., BERENDSEN, H.J.A., and VAN REE, M.H.M., 2007, Middle Holoene avulsion-belt deposits in the entral Rhine-Meuse delta, The Netherlands: Journal of Sedimentary Researh, v. 77, p MEYER-PETER, E., and MUELLER, R., 1948, Formulas for bed-load transport: Proeedings 2nd Meeting of the International Assoiation for Hydrauli Strutural Researh, p RIJKSWATERSTAAT, 2009, Temperatuur in o C in oppervlaktewater. Soure: DONAR database, available at TÖRNQVIST, T.E., VAN REE, M.H.M., and FAESSEN, E.L.J.H., 1993, Longitudinal faies arhitetural hanges of a middle Holoene anastomosing distributary system (Rhine-Meuse delta, The Netherlands). Sedimentary Geology, v. 85, p WEERTS, H.J.T., 1996, Complex onfining layers. Arhiteture and hydrauli properties of Holoene and Late Weihselian deposits in the fluvial Rhine- Meuse delta, The Netherlands: Published PhD Thesis Utreht University. Neth. Geogr. Stud. 213, Utreht, 189 p.

UNIT 1 OPEN CHANNEL FLOW 2 MARK QUESTIONS AND ANSWERS

UNIT 1 OPEN CHANNEL FLOW 2 MARK QUESTIONS AND ANSWERS DEPARTMENT: CIVIL ENGINEERING SEMESTER: IV- SEMESTER SUBJECT CODE / Name: CE53 / Applied Hydrauli Engineering 1. Define open hannel flow with examples. Examples: UNIT 1 OPEN CHANNEL FLOW MARK QUESTIONS