Disturbed critical surface waves in a channel of arbitrary cross section
نویسنده
چکیده
Long waves in a current of an inviscid fluid of constant density flowing through a channel ofarbitrary cross section under disturbances of pressure distribution on free surface and obstructors on thewall of the channel are considered. The first order asymptotic approximation of the elevation of the freesurface satisfies a forced Korteweg-de Vries equation when the current is near its critical state. Todetermine the coefficients of the forced Korteweg-de Vries equation, we need to solve a linear Neumannproblem of an elliptic partial differential equation, of which analytical solutions are found for constantcurrent and rectangular or triangular cross section of the channel. It is proved that the forcedKorteweg-de Vries equation has at least two solutions when the current is supercritical and the parameter2 is greater than a critical value 2 c > 0. It is also proved that there do not exist solitary waves in a currentexactly at its critical state. Numerical solutions of steady state are obtained for both supercritical andsubcritical currents.(Received: March 18, 1988, revised: August 24, 1988)
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