The Hjulström Curve: Erosion, Transport and Deposition
Why clay needs a higher velocity to erode than sand, competence against capacity, the four modes of load transport, hydraulic geometry and why rivers speed up downstream, and what a graded stream actually means.
The Hjulström curve plots stream velocity against particle size and marks out three fields: erosion, transport and deposition. It is worth learning because its central result is counter-intuitive and explains a great deal about river behaviour that the landform vocabulary alone does not. Fine clay requires a higher velocity to erode than sand does.
Reading the Curve
Two curves cross the diagram. The upper one is the critical erosion velocity, the speed at which a particle of a given size is picked up. The lower one is the settling or deposition velocity, the speed below which it drops out of the flow.
- Above the upper curve, material of that size is being eroded.
- Between the two curves it is being transported, already in motion but not being newly entrained.
- Below the lower curve it is being deposited.
The Counter-Intuitive Result
Sand of roughly 0.2 to 0.5 millimetres is entrained at the lowest velocity of any grain size. Move away from that size in either direction and the required velocity rises, but for two entirely different reasons.
- Coarser material needs a higher velocity because it is heavier. That is expected, and it is simply a question of the force needed to lift a larger mass.
- Finer material also needs a higher velocity, because of cohesion. Silt and especially clay are platy particles with large surface areas and electrostatic attraction between them. They stick together, and the flow must prise them apart rather than merely lift them.
So the erosion curve is J-shaped rather than a simple rising line, with its minimum in the sand range.
Two Consequences That Explain Real Rivers
- Once fine clay is deposited it is very hard to re-erode. This is why cohesive mud banks are stable while sand bars shift with every flood, why the outer bank of a meander cut in clay retreats slowly, and why a clay-lined channel holds its form.
- The deposition threshold lies well below the erosion threshold. A stream carries its load at velocities far lower than it needed to pick that load up. This is why suspended sediment travels enormous distances, and why a river deposits only when it slows substantially rather than as soon as it slows at all.
A river picks up sand easily and clay with difficulty, then carries both a long way and puts the clay down last.
Competence and Capacity
Two related quantities are often confused, and keeping them apart is worth doing.
- Competence is the largest particle a stream can move. It rises very steeply with velocity, approximately with its sixth power, which is why a flood that doubles in speed can move boulders it could not previously shift at all.
- Capacity is the total quantity of load a stream can carry. It rises with discharge as well as velocity.
The sixth-power relationship is the reason nearly all geomorphic work in a river channel is done during a small number of high-flow events, and almost none during the long periods of ordinary flow.
How a Stream Carries Its Load
| Mode | What moves | How |
|---|---|---|
| Traction | Largest particles | Rolled or dragged along the bed |
| Saltation | Sand-sized particles | Bounced along the bed in short hops |
| Suspension | Silt and clay | Held up within the body of the flow by turbulence |
| Solution | Dissolved minerals | Carried chemically, independent of velocity |
Solution load is the one that behaves differently from all the others: it does not settle out when the stream slows, so it travels all the way to the sea. That is why river water is not pure even where the water runs clear.
Hydraulic Geometry
The Hjulström curve describes single particles. Hydraulic geometry, from Leopold and Maddock in 1953, describes the channel as a whole, through power-law relationships between discharge and the channel’s width, depth and velocity.
- At-a-station hydraulic geometry describes how one cross-section changes as discharge rises and falls through a flood. Depth and velocity increase sharply; width increases less.
- Downstream hydraulic geometry describes how the channel changes along the river as discharge grows. Width and depth both increase, and, contrary to intuition, velocity also increases slightly downstream.
That last point is the standard misconception. A mountain torrent looks faster than a lowland river because it is turbulent and shallow over a rough bed, but the mean velocity of the lowland channel is usually higher, because the great reduction in bed roughness and the increase in hydraulic radius more than offset the gentler gradient.
Grade
A stream is described as graded when slope, discharge, channel form and sediment load are mutually adjusted so that it transports its load with neither net erosion nor net deposition over a period of years.
Grade is a dynamic equilibrium rather than a fixed state. A graded stream still erodes in one place and deposits in another; what is constant is the balance across the system. Disturb any variable, by damming, by land-use change upstream, or by a fall in base level, and the channel adjusts its slope and form until a new balance is reached. That adjustment is why a dam causes scour downstream and aggradation upstream for decades after it is built.
Practice Questions
Prelims
1. According to the Hjulström curve, the particle size entrained at the lowest velocity is
- (a) clay
- (b) fine silt
- (c) sand of about 0.2 to 0.5 mm
- (d) fine gravel
Answer: (c)
2. Clay requires a high velocity for erosion mainly because of
- (a) its mass
- (b) cohesion between particles
- (c) its density
- (d) its angularity
Answer: (b)
3. The competence of a stream varies approximately with velocity raised to the power
- (a) two
- (b) three
- (c) six
- (d) one
Answer: (c)
4. Material carried in solution differs from other load in that it
- (a) settles first
- (b) does not settle out when the stream slows
- (c) moves by saltation
- (d) is confined to the bed
Answer: (b)
5. Downstream hydraulic geometry shows that mean velocity generally
- (a) decreases downstream
- (b) increases slightly downstream
- (c) remains constant
- (d) fluctuates randomly
Answer: (b)
Mains
- Explain the Hjulström curve and account for its J-shaped erosion threshold. (10 marks)
- Distinguish between competence and capacity, and explain why most geomorphic work occurs during floods. (10 marks)
- Describe the four modes of stream load transport and state which is independent of velocity. (10 marks)
- “Mean velocity increases downstream.” Examine this statement with reference to hydraulic geometry. (15 marks)
- What is a graded stream? Discuss how a river adjusts to the construction of a dam. (20 marks)