Fluid dynamics · water-wave diffraction

Ripple Tank

Orbit the exaggerated height surface, then inspect the same field from above and sample its probe history. Compare one or two point sources, one or two slits, a disk obstacle, fixed-height reflection, rigid-wall reflection, and outgoing boundaries. Pause, step, or switch off the drive without erasing the waves.

Wave-equation energy proxy (not joules) $0\,\mathrm{m^4\,s^{-2}}$

Simulation time $0.0000\,\mathrm{s}$

Nominal wavelength

\lambda_0

$0.50\,\mathrm{m}$

Resolved slit ratio

a_h/\lambda_0

$1.04$

Grid opening

a_h

$0.522\,\mathrm{m}$

Probe height

\eta

$0.000\,\mathrm{mm}$

Field height RMS

\eta_{\mathrm{rms}}

$0.000\,\mathrm{mm}$

Probe position

(x_p,y_p)

$(3.94,\,1.52)\,\mathrm{m}$

Courant number

C

$0.102$

Controls

Shape the diffraction field

Drive the sourceSwitch off to observe existing waves without clearing the field.Probe historyA fixed eight-second window, sampled every solver step.Solver gridReveal the numerical mesh behind the field.Source: plane / single / double

\text{plane}

Geometry: single slit / double slit / open / disk

\text{single slit}

Wall: fixed height / rigid / outgoing

\text{outgoing}

Source amplitude

A

3\,\mathrm{mm}

Requested double-slit separation

d

1.20\,\mathrm{m}

Outgoing-boundary absorption

s

1

Source frequency

f

1.50\,\mathrm{Hz}

Wave speed

c

0.75\,\mathrm{m\,s^{-1}}

Damping

\beta

0.30\,\mathrm{s^{-1}}

Requested slit width

a

0.55\,\mathrm{m}

Double-slit openings are capped at 0.9 m each; separation is constrained to retain a solid divider and fit the tank. The opening readout reports one actual aperture. Zero absorption blends back to a reflecting copied-edge approximation. Energy is a wave-equation proxy, not a calibrated fluid energy.

Click the transmitted field or focus the canvas and use arrow keys to move the probe. Only its trace restarts; reset and presets preserve its position and playback state.

This Lab solves the damped, linear two-dimensional wave equation $\frac{\partial^2\eta}{\partial t^2}+2\beta\frac{\partial\eta}{\partial t}=c^2\nabla^2\eta$ . Dirichlet fixes height and Neumann fixes its normal gradient. Absorbing mode uses first-order Mur outgoing conditions and a sponge at the outer walls, with zero-normal-flux internal obstacles. Oblique incidence and corners still reflect. The 3D display exaggerates the same height by 25 times; no breaking, viscosity, dispersion, or three-dimensional free-surface dynamics are solved.

Start with the essentials

Focus question: Why does narrowing an opening make the transmitted wave spread through a wider angle?
One-sentence intuition: Spreading is controlled not by slit width $a$ alone, but by its ratio to wavelength $\lambda$ .

Core mathematical model

Damped wave equation

\frac{\partial^2\eta}{\partial t^2}+2\beta\frac{\partial\eta}{\partial t}=c^2\nabla^2\eta

Spatial curvature restores the surface toward equilibrium while damping reduces amplitude during propagation.

Frequency, speed, and wavelength

\lambda_0=\frac{c}{f}

The readout is the nominal wavelength of the undamped model; damping and the finite grid alter actual propagation. At fixed speed, higher frequency shortens this reference scale.

Grid-resolved opening

a_h=N_{\mathrm{open}}\Delta y,\qquad \Delta y=\frac{3}{69}\,\mathrm{m}

The opening changes in discrete nodes. Its drawing and readout share the solver mask; the width describes the intervals represented by open nodes, not a sub-grid wall location.

The physical probe clock

t_n=n\Delta t,\qquad \Delta t=\frac{1}{240}\,\mathrm{s}

Every solver step records a timestamped height in a fixed eight-second plot. Display frame rate does not change sampling. Per-frame advancement is capped during stalls, so simulation time need not follow wall-clock time.

Single-slit spreading scale

\sin\theta\sim\frac{\lambda}{a}

An opening comparable to one wavelength spreads strongly sideways. This is a scaling guide, not a replacement for the full field.

Common difficulties

Color is signed water height

Typical misconceptionThe brighter color always means more energy and the darker color means no wave.

Better mental modelThe two colors represent crests and troughs. Energy depends on squared amplitude and cannot be read directly from the sign of the color.

A narrow slit does not create energy

Typical misconceptionWider spreading means the slit amplified the transmitted wave.

Better mental modelThe barrier redistributes transmitted energy by angle and reflects part of the incident wave; wider spreading does not mean larger total energy.

Run the experiment

01
Begin with the wide opening
Choose Wide slit and wait for the wavefront to cross.
What to observe: The central transmitted front remains mostly plane, with strong bending confined near the two edges.
02
Shrink the opening toward one wavelength
Choose Narrow slit and compare the $a_h/\lambda_0$ readout.
What to observe: Nearly circular fronts emerge behind the opening, and probes far to the side begin recording an oscillation.
03
Measure while paused
Pause and advance half a second at a time until transmitted waves reach the probe. Move the probe, switch off Drive the source, and keep advancing.
What to observe: Moving starts a trace at the new location without clearing waves. After the drive stops, existing waves continue travelling and decaying. One step advances exactly one solver step.
04
Shorten only the wavelength
Keep the opening fixed and choose Short waves.
What to observe: The same opening becomes wider relative to wavelength, so sideways spreading weakens.

Conceptual inspiration: FluidMotion. Original simulations and graphics; the model limits are described above.