Two-Chamber Wave Tank Resonance

What is modelled

A 12 m by 6 m tank holds shallow water. A paddle on one end drives the water at a chosen frequency; the other walls are closed, and a baffle across the middle leaves an opening of adjustable width. A closed rectangular tank has standing-wave modes at f = (c/2) √((m/L_x)² + (n/L_y)²). A narrow opening splits the tank into two weakly coupled chambers whose modes move toward those of a single chamber of half the length.

Equations

• Linear shallow water: ∂η/∂t + h∇·u = 0, ∂u/∂t = −g∇η − γ u; speed c = √(g h).
• Longitudinal modes fm = m c / (2 L); chamber modes c / L when the baffle is nearly closed.
• Free ringing decays as e−γt/2.
• The impulse spectrum is the discrete Fourier transform of a 1D width-varying model driven by a short paddle stroke.

Checks run in the page

• First longitudinal mode period against 2L/c.
• 2D (1,1) mode period of the closed rectangle.
• Open and nearly closed baffle against c/(2L) and c/L.
• Decay rate of free ringing against γ/2.

Honest simplifications

The equations are linear and non-dispersive and the paddle is a plain moving wall, so there is no breaking, no nonlinear steepening and no edge effects at the baffle tip. The spectrum comes from a one-dimensional reduction that treats the opening only by its area ratio, so it misses transverse modes. This is a teaching-scale model, not a CFD solver.

• Press Longitudinal mode: the response at the probe grows over many periods to a large standing wave.
• Press Split basin and see the baffle change the resonance, then compare the third graph.
• Raise the drag and watch the resonance peak in the spectrum flatten.