RIVER AND DELTA SYSTEMS GEO4-4436
Lecture 1: Introduction: Repetition flow, sediment transport and morphodynamics
This course:
- Scales: From particle to planet
- Disciplines: From geology and sedimentology to biogeomorphology and engineering
- Singular causal relationships and systems: Physics, ecology, What do we care if it is a system?
- Methods: Basic modelling, explaining, and reporting
See the effects of interference. We deal with conceptual models with descriptions and hypotheses,
experiments, simulation models (numerical models) which has its own problems, and analytical
models (you do not have to do them yourselves but they will be explained).
Scales:
1. Flow, sediment transport and channel morphodynamics
o Steady uniform flow and backwater effect
o Equilibrium sediment transport
o Exner equation (morphological evolution)
o Effects of changing boundary conditions
o Basics of numerical modelling
2. River patterns: and interactions with species. Partly dependent on the smaller scales.
o Floodplain formation
o Bar patterns
o River patterns
o Effect of changing boundary conditions
o Preservation, sedimentology
3. Bifurcations and avulsion: river displacement. How channels shift over large floodplains.
o Physics of bifurcation stability
o Causes of avulsion
o Accommodation space
4. From source to sink and in between: Erosion (hydrological cycle) and transport towards sea
o Simple cases: mass conservation
o Sediment budgets and transfer through valleys and multiple basins
o Reconstructing allogenic forcing
o Accommodation space
o Fluvial architecture
Part of the job is to look at the global scale. The scales are useful
for river engineering, river management, nature restoration, and
geological resources (sediments, water, oil). Predict effects of
global change. Sustainable use of sinking/drowning deltas.
(NIMBY: Not In My BackYard -> Now In Your BackYard, learning
how to solve poorly defined problems).
Sea level, Sediment and Subsidence must be in equilibrium in a delta. If something changes, the delta
changes. For most deltas, two or three out of these deltas have red flags, so they are problematic.
There is a fourth S which is not for the sustainability of the delta, but for the humans there:
Salinization, which pollutes the ground water.
Question -> hypothesis -> method -> results -> discussion -> conclusion -> new questions
,Causal explanation: reduce a phenomenon to the workings of the underlying mechanisms and relate
a phenomenon to a statistical relation. E.g., in Covid19 you had people that studied the virus
(mechanisms) and people studying the spreading of the virus (statistical relation), which were both
needed.
A simple causal explanation is often not enough. There are multiple causal interactions and
feedbacks. One cause/effect on one delta might have not have the same effect on another delta. So
we look at the whole delta with all the causal interaction and feedbacks, and also the history of
system matters.
Sediment transport is a nonlinear function of flow force
Morphology is in a feedback loop with flow and sediment
transport: Flow is changing the morphology and
morphology is changing the flow. You can not know what
the flow is going to look like, so you need models.
Turbulent flow in rivers:
- Flow strength
- Normal flow
- Flow resistance
- How to account for turbulence
Flow strength parameters:
- u: flow velocity (usually averaged over depth h)
- Q: flow discharge 𝑄 = 𝑢ℎ𝑊 = 𝑢𝐴. Most rivers have a flow velocity of 0.5m/s to 3 m/s, but
their discharges differ a lot. So most of the variation in discharge comes from the depth and
width but little from the velocity.
- τ: flow shear stress: shear of the flow on the bed of the river = 𝜏 = 𝜌𝑔ℎ𝑆. S= gradient and 𝜌 is
fluid density (1000 kg/m3)
- 𝜔 : stream power 𝜔 = 𝜏𝑢
Normal flow: both steady and uniform flow
- steady flow: no change in u over time
- uniform flow: no change in velocity over space
𝑢
Not normal flow: steady nonuniform flow. 𝐹𝑟 =
√𝑔ℎ
- Subcritical flow: slow, Fr<1, downstream control.
Sand and gravel (some slight jumps) river are
subcritical.
Backwater effect: downstream obstruction or
roughness (e.g. dams, vegetation) affects
upstream flow. Upstream distance over which
water depth is affected is called adaptation length.
This has a very large effect.
- Hydraulic jump: Fr=1
- Supercritical flow: fast, Fr>1, no downstream control. E.g. dams.
,Turbulence: self-formed friction in a flow.
(𝑢ℎ)
Reynolds number: 𝑅𝑒 = 𝑣
.
Laminar < 500. Turbulent > 2000. The transition is
somewhere around 1000. Particles do not travel a
simple path; they go all over the place. In practice, all
river flow is turbulent. This changes in tidal places
where flow can reach a standstill and will temporarily
be laminar. The whole velocity profile is affected by
the friction at the bottom.
𝑢∗ 𝑧
𝑢𝑧 = 𝐾
∗ ln (𝑧 )
0
𝜏
with shear velocity 𝑢∗ = √ 𝜌𝑜
𝑎𝑛𝑑 𝜏𝑜 = 𝜌𝑔ℎ𝑆. K =Karman constant=0.38-0.40
Turbulence is very complicated and far from solved, so use semi-empirical equations (and start to
include friction). Friction scales with R and roughness 𝑘𝑠 . Roughness of the surface compared to the
water depth. This gives the final formula of C.
, Sediment transport and bedforms
Sediment transport results from water flow. We need sediments. We can have bedload
sediment transport, suspended sediment transport (whirled up and thrown down) and
washload (stays suspended). The larger the particle the more difficult to whirl up by
turbulence, so washload is the smallest (dust) and bedload the largest.
Particle-size distribution: logarithmic, can be done by
sieving, settling tubes and lasers. This gives an average
particle size. D50 is the median size, and D90 is the
roughness height. Depends on the application.
Logarithmic scale. Another way is the Shields curve
(1936). Threshold for the beginning of motion. This is
a universal curve. The shield number is the flow shear
stress the driver of the mobility of the sediment, the
driver of sediment transport. Ratio of drive forces and
stop forces. Typical critical shields number 0.4-0.5.
Shield velocity (velocity near to the bed.
Flow energy drives sediment transport. The total shear stress is the sum of the skin and form friction.
We use several factors: 𝑘𝑠 ′= grain related roughness (skin friction), C’= grain related Chezy, τ = grain
related shear stress, θ’ = grain related shield function
1 1 1
Total friction = skin friction + form friction: 𝐶 2 = (𝐶 ′ )2
+ (𝐶")2
- Skin friction: grains, This applies to bedload sediment transport: moves sediments
- Form friction: bedforms, vegetation and engineering structures. This applies to total bed
material load transport = bedload + suspended bed material loads.
Sediment transport is calculated with a singular function with a whole range of different particles
because it is dimensionless. We have two reasons for the non-linear function because it is a function
of ^3/2 and asymptote. It can be used for many different sediments. There are many different forms.
There are no calculations for washload because there is (almost) no interactions with the bed and no
exchange between bed and suspended sediment. It is limited by the amount of upstream supply.
The nonlinearity of the water explains the river patterns. Rain pours down on a slope and sheetwash
starts to occur and forms a slight depression. At one point the sediment starts to move, and a channel
forms. Above that point nothing happens, so there is no sediment getting in but only getting out, so
erosion happens. A new channel starts to flow, and it attracts more water, and more and more
erosion happens and the channel grows bigger. It is a positive feedback loop with leads to channel
incision. Negative feedback: the amount of water is limiting, and the banks starts to collapse because
of gravity, so the channel fills up with sand again. Therefore, the channels become very wide.
