How fast can a hidden wave travel?

Change the layer depths or their small density difference. This idealized model compares a long internal wave with a surface gravity wave in the same total depth.

Upper layer depth (metres)Lower layer depth (metres)Density difference (kg/m³)

Default example: internal speed ≈1.24 m/s; surface speed ≈70.0 m/s; 10 km internal-wave travel time ≈2.24 hours.

Formula, assumptions and limits

Reduced gravity g′ = 9.81 Δρ/1025. Internal speed c = √[g′ h₁h₂/(h₁+h₂)]. Surface speed cₛ = √[9.81(h₁+h₂)]. Inputs use SI units. The reference density is fixed at 1025 kg/m³.

The internal calculation assumes two uniform, stable layers with a small density difference, a nearly rigid upper boundary, waves much longer than the depths, small amplitude, and no rotation, currents or mixing. It cannot calculate real wave height, breaking or coastal risk.

Background: University of Washington geophysical-fluid-dynamics notes. These inputs are an illustrative scenario, not observations. No information is sent from this page.