Seiche

A seiche is a standing oscillation of water in an enclosed or partly enclosed basin. A disturbance can displace water toward one end; restoring gravity and reflection at boundaries then support repeated oscillation. Wind and atmospheric-pressure changes can excite such motion in natural basins.^[ref]

For an ideal straight basin of length $L$, uniform shallow depth $h$ and two closed ends, no normal flow at the walls gives surface-displacement modes proportional to $\cos (m\pi x/L)$. The shallow-water dispersion relation then gives ${\omega }_m=m\pi \sqrt{gh}/L$ for $m=1,2,\dots$. The fundamental period is $T_1=2L/\sqrt{gh}$.

An illustrative model with $L=2\mathrm{m}$, $h=0.10\mathrm{m}$ and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$ gives $T_1\simeq 4.04\mathrm{s}$. A gently disturbed tank can test the period. Variable depth, open connections, friction and finite wave amplitude modify this ideal prediction.

An ideal uniform shallow basin, closed at one end and held at zero displacement at its open end, has its lowest standing wave with a displacement node at the opening and an antinode at the closed end. Its wavelength is four times its length. Real mouths need not satisfy this perfectly reflecting idealization.