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Water wave propagation can be attenuated by various physical mechanisms. Oneof the main sources of wave energy dissipation lies in boundary layers. Thepresent work is entirely devoted to thorough analysis of the dispersionrelation of the novel visco-potential formulation. Namely, in this study werelax all assumptions of the weak dependence of the wave frequency on time. Asa result, we have to deal with complex integro-differential equations thatdescribe transient behaviour of the phase and group velocities. Using numericalcomputations, we show several snapshots of these important quantities atdifferent times as functions of the wave number. Good qualitative agreementwith previous study [Dutykh2009] is obtained. Thus, we validate in some senseapproximations made anteriorly. There is an unexpected conclusion of thisstudy. According to our computations, the bottom boundary layer createsdisintegrating modes in the group velocity. In the same time, the imaginarypart of the phase velocity remains negative for all times. This result can beinterpreted as a new kind of instability which is induced by the bottomboundary layer effect.

Group and phase velocities in the free-surface visco-potential flow: new kind of boundary layer induced instability