As a consequence, there is some freedom in choosing the phase speed ( celerity ) of the wave . identified two logical definitions of phase speed, known as Stokes'first and second definition of wave celerity:
42.
As a consequence, there is some freedom in choosing the phase speed ( celerity ) of the wave . identified two logical definitions of phase speed, known as Stokes'first and second definition of wave celerity:
43.
For very short waves ( as the zonal wavenumber increases ), the group velocity ( energy packet ) is eastward and opposite to the phase speed, both of which are given by the following relations:
44.
Since \ scriptstyle c = \ omega / k is the phase speed in terms of the angular frequency \ scriptstyle \ omega and the wavenumber, the gravity wave angular frequency can be expressed as
45.
For given ( real-valued ) wavenumber k and mean flow velocity U ( z ), the eigenvalues are the phase speeds c, and the eigenfunctions are the associated streamfunction amplitudes \ varphi ( z ).
46.
Which is independent of the wave nonlinearity ( i . e . does not depend on the wave height H ), and this phase speed c the same as for Airy's linear waves in deep water.
47.
The solution to these equations yields the following phase speed : " c " 2 = " gH ", which is the same speed as for shallow-water gravity waves without the effect of Earth s rotation.
48.
The strong growth of frequency \ omega _ \ mathrm { KdV } and phase speed with wavenumber k posed problems in the numerical solution of the KdV equation, while the BBM equation does not have these shortcomings.
49.
In a frame of reference moving with the phase speed, in which reference frame the flow becomes a steady flow, the cnoidal wave solutions can directly be related to the mass flux, momentum flux and energy head of the flow.
50.
They showed that the QBO could be driven by vertically propagating gravity waves with phase speeds in both westward and eastward directions and that the oscillation arose through a mechanism involving a two-way feedback between the waves and the mean flow.
