flow 1.0 m/s  •  Re 1200
LAMINAR

ағын · fluid-mechanics lab

Agynhow rivers move

A living river, built from real physics. Ағын is the Kazakh word for a current — the flow of water. Scroll to read the water, or reach in and stir it.

Enter the current
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the lab

Stir the river

The whole background is a live flow simulation — thousands of tracer particles carried by a velocity field, solved fresh every frame. Change the current, thicken the water, pinch the channel, or drop in a rock.

Tap the water anywhere to place a rock — drag it to move it. Raise viscosity and the flow calms; lower it (or speed up) and it tears into turbulence.

Velocity1.0 m/s
Reynolds Re1200
RegimeLAMINAR
Constriction0% · ×1.00

01 · continuity

Squeeze the channel, speed up the water

A₁·v₁ = A₂·v₂

Water is very nearly incompressible, so the same volume must pass every cross-section each second. Watch the banks pinch into a throat above — the streamlines crowd together and the flow accelerates exactly where the channel narrows. Try the channel width slider in the lab: pull it up and watch the throat close while the current races through. Same discharge, smaller area, faster water.

wide reach ≈ 1.0 m/s  →  throat ≈ 1.8 m/s  (v scales with 1/width)

02 · bernoulli

Faster flow, lower pressure

P + ½ρv² + ρgh = constant (along a streamline)

Along a streamline the total energy is shared between pressure, motion and height. Where the water speeds through the throat, the ½ρv² term grows — so the pressure P must fall. That low-pressure throat is why a fast current can pull floating debris inward. Real rivers also bleed energy to friction, so it's never perfectly conserved.

throat: v  ⇒  P  •  dynamic pressure ½ρv² ≈ 0.5 kPa

03 · two kinds of flow

Smooth sheets, or chaotic eddies

Slow, thick flow glides in smooth parallel sheets — laminar. Push the same water faster, or thin it out, and it shatters into swirling, unpredictable eddies — turbulent. Real rivers snap between the two; there's no lingering in between. Try the switch:

laminar: thick, slow water — the sheets above stay parallel and calm.

04 · reynolds number

The ratio that decides

Re = ρvL / μ = vL / ν

The Reynolds number weighs inertia against viscosity. Low Re: viscosity wins and the flow is orderly and laminar. Push it past roughly Re ≈ 2000–4000 and inertia takes over — the stream breaks into swirling, chaotic turbulence. Flip the switch in the section above and watch this number leap across the threshold.

Re now = 1200  ·  LAMINAR

05 · boundary layer

The banks hold the water back

u(bank) = 0  ·  u peaks mid-channel

Water sticks to a solid surface — the no-slip condition. Velocity is exactly zero at each bank and climbs to a maximum in the middle, giving the curved velocity profile now drawn across the stream. That thin sheared skin next to each bank — the ripple texture behind this card is a close-up of it — is the boundary layer. Thicker, more viscous water spreads that drag further into the channel.

profile: parabolic when laminar → flattens toward a plug as it turns turbulent

06 · vortices & wake

The rock leaves a trail of spinning water

ω = ∇ × v  ·  St = f·D / v ≈ 0.2

Flow can't cleanly rejoin behind a blunt obstacle. Instead it sheds spinning parcels — vorticity — alternately from each side, forming a von Kármán vortex street in the wake. This is what it looks like in the wild: the same alternating shedding tears a mountain rapid to foam. The shedding frequency follows the Strouhal relation; it's the same effect that makes wires hum and flags flutter.

shedding ≈ 0.6 Hz  ·  alternating ± vortices behind the rock

07 · meanders · erosion & deposition

Bends write themselves into the land

A river almost never runs straight for long. The instant it bends, the fastest current — the thalweg — is flung toward the outer bank, undercutting and collapsing it into a steepening cut bank. On the inside of the bend the current slackens, dropping the sediment it carried to build a gently sloping point bar. Erosion here, deposition there — the bend migrates sideways and downstream, and the meander grows.

outer-bank current ≈ 1.4× faster than the inner bank through this bend

live schematic — flow accelerates outward through the bend, sediment settles inward

test the current

Four questions on the river

Everything above, distilled. Pick an answer — you'll get the explanation either way.

Score: 0 / 4