This pattern follows from the dispersion relation of deep water waves, which is often written as,
where
:  = the strength of the gravity field
:  is the angular frequency in radians per second
:  = angular wavenumber in radians per metre
"Deep" means that the depth is greater than half of the wavelength.
This formula  implies that  the group velocity of a deep water wave is half of its phase velocity, which, in turn, goes as the square root of the wavelength.
Two velocity parameters of importance for the wake pattern are:
:  is the relative velocity of the water and the surface object that causes the wake.
:  is the phase velocity of a wave, varying with wave frequency.