THE DIFFRACTION OF SECOND-ORDER BICHROMATIC WAVES BY A SEMI-IMMERSED HORIZONTAL RECTANGULAR CYLINDER |
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| Institution: | 1. Dipartimento di Sicurezza e Bioetica, Università Cattolica del Sacro Cuore, Rome, Italy;2. Dipartimento di Scienze di Laboratorio e Infettivologiche, Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Rome, Italy;3. Dipartimento di Scienze della Salute della Donna e del Bambino e di Sanità Pubblica, Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Rome, Italy;4. Dipartimento di Scienze dell’Emergenza, Anestesiologiche e della Rianimazione, Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Rome, Italy;5. Dipartimento di Scienze Cliniche e Medicina Translazionale, Università degli Studi di Roma Tor Vergata, Rome, Italy |
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| Abstract: | The diffraction of second-order bichromatic Stokes waves by a semi-immersed horizontal rectangular cylinder (prism) is investigated theoretically. The problem is assumed two-dimensional and the fluid domain is divided into three regions: upwave, beneath and downwave of the structure. Analytical expressions for the velocity potentials in each region at both first- and second-order are obtained by an eigenfunction expansion approach. The solutions in each fluid region are linked through matching conditions on the imaginary fluid interfaces between them. Semi-analytical expressions are derived for the sum-and difference-frequency hydrodynamic loads and the free-surface elevations upwave and downwave of the structure to second-order. Numerical results are presented which illustrate the influence of the different wave and structural parameters on these quantities at both first- and second-order. |
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