Waves in Fluids

Surface Gravity Waves

Surface Gravity Waves Dispersion Relation

For a flow of depth , the dispersion relation of surface gravity waves isIn shallow water (), it is non-dispersive, we have

Interfacial Waves

Thrm Interfacial Waves Dispersion Relation The dispersion relation for waves on an interface between two fluids of density (top fluid) and density (bottom fluid), with a surface tension (N/m) at the interface, and a uniform flow in the upper layer of (m/s) is given by

Hydrodynamic Instabilities

Def Instability A system such that any small initial perturbation will be exponentially amplified with time is called an unstable system.

Rayleigh-Taylor Instability

Def Rayleigh-Taylor Instability The Rayleigh-Taylor instability happens when the uniform flow in the upper layer of doesn’t move(i.e. ). And we have the dispersion relation:

Kelvin Helmholtz Instability

Def Kelvin Helmholtz Instability Kelvin Helmholtz instability happens when and :