River Processes and Landforms

Spec mapping: AQA 7037, Paper 1 (Physical), §3.1.1 — although the Water and Carbon core foregrounds the basin hydrological cycle, the fluvial processes and landforms developed here support the systems-and-equilibrium framework that runs through the whole unit, and they are directly examinable where the specification asks about the operation of the drainage basin and channel system over time. (They also strongly underpin §3.1.3 Coastal systems and §3.1.5 Hazards through shared process and equilibrium concepts.) This depth lesson goes well beyond an introductory treatment, using the Hjulström curve, competence/capacity, hydraulic geometry and the graded profile to reason quantitatively about channel form. AOs exercised: AO1 (erosion/transport/deposition processes; landform formation), AO2 (applying energy and equilibrium concepts to explain landform assemblages), AO3 (reading the Hjulström curve, calculating hydraulic radius and downstream change).

A river channel is a dynamic geomorphological system in which the available energy (a function of discharge and slope) is expended against friction and the sediment load. Landforms are the expression of how that energy is partitioned between erosion, transport and deposition — and explaining them in those terms, with numbers, is what lifts a response into the top band.

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Energy in the Channel System

The power available to a river — its stream power — can be expressed as:

$\Omega = \rho\, g\, Q\, S$Ω=ρgQS

where $\rho$ρ is water density (~1000 kg/m³), $g$g is gravitational acceleration (9.81 m/s²), $Q$Q is discharge (m³/s) and $S$S is channel slope. Stream power rises with both discharge and gradient, so although gradient falls downstream, the large increase in $Q$Q means total stream power generally increases towards the mouth. How that power is used — eroding the bed and banks, transporting load, or being dissipated as heat against friction — depends on the sediment supply and the channel's efficiency. This single relationship organises everything that follows.

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The Hjulström Curve

The Hjulström curve (Filip Hjulström, 1935) relates mean flow velocity to sediment particle size, defining the thresholds of erosion, transport and deposition.

The two key curves

• The critical erosion (entrainment) velocity — the minimum velocity needed to lift a particle of a given size from the bed.
• The settling (fall) velocity — the velocity below which a moving particle is deposited.

The gap between them is the transport zone: a particle already in motion stays in motion at velocities below those needed to entrain it.

Reading the curve quantitatively

Particle size	Behaviour on the Hjulström curve
Clay/silt (< 0.06 mm)	Disproportionately high entrainment velocity because electrostatic cohesion binds fine particles; once suspended they stay up to near-zero velocities (so clay is deposited only in still water — estuaries, oxbows).
Sand (~0.06–2 mm)	The curve reaches its minimum near 0.2–0.5 mm: medium sand is the most easily entrained particle, needing only ~0.2 m/s.
Gravel/cobbles (> 2 mm)	Entrainment velocity rises steeply with size because of particle mass; transport and entrainment velocities nearly coincide.
Boulders (> 256 mm)	Move only in extreme floods (velocities of metres per second).

Exam significance: The curve explains why sandy beds are common (sand is mobilised at the lowest velocities), why clay banks resist erosion yet, once eroded, build mudflats and estuarine deposits, and why a falling flood deposits its coarsest load first and its finest last (graded bedding). The single most-missed AO3 reading is the high entrainment velocity for clay — students wrongly assume "small = easy to erode".

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Competence and Capacity

Two distinct measures of transport ability:

• Competence — the maximum particle diameter a river can entrain at a given velocity. Competence scales with roughly the sixth power of velocity: doubling velocity raises competence by $2^{6} = 64$26=64 times. This is why an otherwise tranquil river can shift boulders in flood.
• Capacity — the total load (mass or volume) a river can carry, which depends on discharge as well as velocity and generally increases downstream.

$\text{competence} \propto V^{6}, \qquad \text{capacity} \propto Q \ (\text{and } V).$competence∝V6,capacity∝Q (and V).

Key distinction: A large lowland river in spate has high capacity (vast suspended load) but may have only moderate competence (fine bed), whereas a small steep mountain torrent in flood has high competence (moves cobbles) but low capacity. The $V^{6}$V6 law is the most examinable single fact here, because it quantifies the geomorphic dominance of rare high-magnitude floods.

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Channel Efficiency and Hydraulic Geometry

Hydraulic radius

Channel efficiency is measured by the hydraulic radius:

$R = \frac{A}{P}$R=PA​

where $A$A is the cross-sectional area of flow (m²) and $P$P is the wetted perimeter (m). A larger $R$R means a smaller proportion of the flow is in frictional contact with the bed and banks, so less energy is lost and velocity is higher for a given slope (consistent with Manning's equation from the previous lesson). A semicircle is the theoretically most efficient shape; natural channels approximate a wide, shallow parabola.

Worked illustration. A near-rectangular channel 10 m wide and 2 m deep has $A = 20$A=20 m² and $P = 10 + 2 + 2 = 14$P=10+2+2=14 m, so $R = 20/14 = 1.43$R=20/14=1.43 m. A narrow, deep channel of the same area — 5 m wide, 4 m deep — has $P = 5 + 4 + 4 = 13$P=5+4+4=13 m and $R = 20/13 = 1.54$R=20/13=1.54 m, i.e. more efficient despite identical area, because relatively less perimeter is wetted. This is the geometric reason deep channels run faster than shallow ones of equal area.

Downstream changes (the Bradshaw model)

Variable	Downstream trend	Reason
Discharge	Increases	Tributary and groundwater inputs
Width	Increases	Bank erosion accommodates more water
Depth	Increases	Bed erosion deepens the channel
Hydraulic radius	Increases	Depth rises faster than wetted perimeter
Velocity	Generally increases	Rising $R$R more than offsets falling gradient
Bed sediment size	Decreases	Attrition and selective transport
Channel roughness	Decreases	Finer bed, fewer obstructions

Common misconception: That velocity falls downstream "because the gradient is gentler". Measured mean velocity usually rises downstream because the gain in hydraulic radius (efficiency) outweighs the loss of slope — a counter-intuitive but well-evidenced result first quantified by Leopold and Maddock (1953).

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Reynolds Number and Turbulence

The Reynolds number classifies flow:

$Re = \frac{V\, d\, \rho}{\mu}$Re=μVdρ​

where $V$V is velocity, $d$d depth, $\rho$ρ density and $\mu$μ dynamic viscosity (Pa·s).

• $Re < 500$Re<500: laminar flow — smooth parallel layers; essentially absent in natural rivers except in thin films.
• $Re > 2000$Re>2000: turbulent flow — eddies and vortices; the normal condition in rivers.

Turbulence matters because the upward components of turbulent eddies provide the lift and drag that entrain sediment; without turbulence a river would have almost no erosive or transporting power. The Reynolds number thus underpins the Hjulström thresholds physically.

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The Long Profile and Graded Equilibrium

The long profile plots channel altitude from source to mouth and is typically a smooth concave curve — steep in the upper course (high potential energy, small discharge), gentler downstream (lower slope, large discharge, high kinetic energy for lateral work).

A graded river (Mackin, 1948) is one whose slope is delicately adjusted so that, over a period of years, the available discharge and channel characteristics provide just the velocity needed to transport the supplied sediment load — a state of dynamic equilibrium. The graded profile is an ideal: real rivers approach but never perfectly attain it, because geology, sediment supply, base level and human activity keep perturbing it. When perturbed, the river adjusts (eroding to lower a steepened reach, depositing to build up a starved one) in a negative-feedback restoration of grade — a direct application of the equilibrium concept that unifies this entire unit.

flowchart LR
  PERT[Perturbation
e.g. base-level fall] --> STEEP[Reach steepens]
  STEEP --> ERODE[Increased erosion
+ knickpoint retreat]
  ERODE --> ADJUST[Slope reduced
towards grade]
  ADJUST --> EQ[Dynamic equilibrium
restored]
  EQ -. new perturbation .-> PERT

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Knickpoints and Rejuvenation

A knickpoint is a sharp break in the long profile, usually a waterfall or rapids. Causes include:

• Rejuvenation — a fall in base level (eustatic sea-level fall or isostatic/tectonic uplift) renews the river's potential energy; the knickpoint retreats upstream by headward erosion.
• Resistant rock bands — a hard outcrop crossing the channel (e.g. High Force on the Tees, where the Whin Sill dolerite caps softer Carboniferous limestone and sandstone, producing a ~21 m fall).
• Glacial overdeepening — hanging valleys where tributaries meet an overdeepened glacial trough.

Rejuvenation gives renewed vertical erosive energy, letting a river incise into its own floodplain. Diagnostic landforms include:

• River terraces — remnants of former floodplains left perched above the new one after incision. Paired terraces (equal height both sides) imply a single rapid incision; unpaired terraces imply lateral migration during incision.
• Incised meanders — meanders cut deep into bedrock: entrenched (symmetrical valley, rapid uplift) or ingrown (asymmetrical, slower uplift with continued lateral erosion).
• Migrating knickpoints working upstream.

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Meander Migration and Floodplain Development

Process

• Helicoidal flow — a corkscrew secondary circulation in bends. Surface flow is driven to the outer (concave) bank by momentum, concentrating erosion (hydraulic action, abrasion) and producing a steep cut bank / river cliff; the compensating near-bed return flow carries sediment to the inner (convex) bank, building a gently sloping point bar.
• Thalweg — the line of maximum velocity, which swings from mid-channel on straight reaches to hug the outer bank in bends, steering the erosion.

Feature	Location	Process	Form
Point bar	Inner (convex) bank	Deposition by slow inner flow	Gently sloping, sorted sand/gravel
Cut bank / river cliff	Outer (concave) bank	Lateral erosion, undercutting	Steep, actively eroding

Floodplain construction and oxbow lakes

Through repeated outer-bank erosion and inner-bank deposition, meanders migrate laterally and downstream, sweeping the channel across the valley floor and laying down a belt of alluvium — the floodplain, further built up by overbank deposition of fine silt during floods (which also raises natural levées along the banks). When a meander neck narrows and is breached in a flood, the loop is cut off and sealed by deposition to form an oxbow lake — a textbook landform recording former lateral migration.

flowchart TB
  A[Sinuous meander
neck narrowing] --> B[Flood breaches
the neck]
  B --> C[Flow takes
shorter path]
  C --> D[Old loop sealed
by deposition]
  D --> E[Oxbow lake
later infills to meander scar]

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AO3 skills exemplar: Hjulström + downstream change

A field group measures velocity and bed-material size at three sites:

Site	Mean velocity (m/s)	Median bed grain size $D_{50}$D50​ (mm)
Upper	0.45	64 (cobbles)
Middle	0.80	8 (gravel)
Lower	1.10	0.4 (medium sand)

Describe. Velocity rises downstream (0.45 → 1.10 m/s) while median grain size falls sharply (64 → 0.4 mm).

Manipulate / interpret with Hjulström. At the upper site, 0.45 m/s is below the entrainment velocity for 64 mm cobbles, so these are largely immobile in normal flow (they were emplaced by past floods). At the lower site, 1.10 m/s is far above the ~0.2 m/s needed to entrain 0.4 mm sand, so the bed is actively transported. Percentage change in velocity:

$\frac{1.10 - 0.45}{0.45} \times 100 = 144\%.$0.451.10−0.45​×100=144%.

Explain. Velocity rises because hydraulic radius and discharge increase downstream, outweighing the gentler gradient; grain size falls through attrition (particles round and shrink) and selective transport (finer material is carried furthest). The two trends are linked: the more efficient, higher-velocity lower channel can still only build a sandy bed because the coarse fraction has been comminuted and left upstream.

Evaluate. $D_{50}$D50​ at a single survey reflects the day's flow, not the formative flood; one set of point measurements cannot capture the $V^{6}$V6 competence spikes that actually emplace the coarse upper-course material. The data illustrate the average trend but understate the role of rare events.

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Case Study: The River Tees, Northern England

The Tees (~137 km, Cross Fell to the North Sea at Teesmouth) displays the full process–landform sequence:

• Upper course (Cross Fell – Middleton-in-Teesdale): steep gradient, V-shaped valley, High Force waterfall (~21 m over Whin Sill dolerite) and the rapids of Low Force, large angular boulders mobilised only in flood — high competence, low capacity.
• Middle course (Middleton – Yarm): gradient eases, sinuosity increases, meanders and a widening floodplain develop, with river terraces near Darlington recording earlier incision.
• Lower course (Yarm – Teesmouth): broad floodplain, prominent levées, and salt marsh and mudflats at the estuary (clay deposited at near-zero velocity, per Hjulström); the reach is heavily engineered for industry and flood control, illustrating human modification of an equilibrium system.

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Erosion, transport and deposition processes in detail

A depth treatment must name the specific processes, not merely list "erosion, transport, deposition".

Erosional processes:

• Hydraulic action — the sheer force of moving water (and, in cracks, the compression of trapped air) prising material from bed and banks; dominant in high-energy reaches and at waterfalls.
• Abrasion (corrasion) — the river's sediment load grinding against the bed and banks, the principal agent of vertical and lateral bedrock erosion (and the maker of potholes).
• Attrition — load particles colliding and wearing each other down, reducing grain size downstream (the cause of the downstream fining in the Bradshaw model) — strictly a modification of the load rather than channel erosion.
• Solution (corrosion) — chemical dissolution of soluble rock (limestone, chalk) by slightly acidic water; significant in carbonate catchments.