Seiche - Period of underwater internal waves

Description

A seiche (/ˈseɪʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbours and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.

The term was promoted by the Swiss hydrologist François-Alphonse Forel in 1890, who was the first to make scientific observations of the effect in Lake Geneva, Switzerland. The word originates in a Swiss French dialect word that means “to sway back and forth”, which had apparently long been used in the region to describe oscillations in alpine lakes.

Seiches in harbours can be caused by long period or infragravity waves, which are due to subharmonic nonlinear wave interaction with the wind waves, having periods longer than the accompanying wind-generated waves.

Causes and nature of seiches

Seiches are often imperceptible to the naked eye, and observers in boats on the surface may not notice that a seiche is occurring due to the extremely long wavelengths.

The effect is caused by resonances in a body of water that has been disturbed by one or more factors, most often meteorological effects (wind and atmospheric pressure variations), seismic activity, or tsunamis. Gravity always seeks to restore the horizontal surface of a body of liquid water, as this represents the configuration in which the water is in hydrostatic equilibrium.

Vertical harmonic motion results, producing an impulse that travels the length of the basin at a velocity that depends on the depth of the water. The impulse is reflected back from the end of the basin, generating interference. Repeated reflections produce standing waves with one or more nodes, or points, that experience no vertical motion. The frequency of the oscillation is determined by the size of the basin, its depth and contours, and the water temperature.

The longest natural period of a seiche is the period associated with the fundamental resonance for the body of water—corresponding to the longest standing wave. For a surface seiche in an enclosed rectangular body of water this can be estimated using Merian’s formula.

Underwater (internal) waves

Although the bulk of the technical literature addresses surface seiches, which are readily observed, seiches are also observed beneath the lake surface acting along the thermocline in constrained bodies of water.

In analogy with the Merian formula, the expected period of the internal wave can be expressed as shown here.

Related formulas

Variables

Tperiod of underwater internal waves (1/hz)
Llength (m)
cfactor related to the the average thicknesses of the two layers separated by stratification (e.g. epilimnion and hypolimnion) and the densities of these two same layers (m/s)