We present numerical computations of a new wind-wave coupling theory that is governed by a system of nonlinear advance-delay differential equations (NLADDE). NLADDE are functional differential equations for which the ...We present numerical computations of a new wind-wave coupling theory that is governed by a system of nonlinear advance-delay differential equations (NLADDE). NLADDE are functional differential equations for which the derivative of an unknown function depends nonlinearly on the past (delayed), present, and future (advanced) values of the unknown function (if time is the independent variable). A practical numerical method for solving NLADDE is implemented, based on a collocation method. The method is tested for two problems with known analytic solutions and is shown to be numerically convergent. Numerical solutions to the coupled wind and wave problem reveal estimates of the wave height spectrum, the distribution of breaking waves (both depend on wave scale), as well as the vertical air-side profiles of turbulent stress and wind speed.展开更多
基金supported by the U.S. National Science Foundation (Grant OCE- 0526177)the U.S. Office of Naval Research (Grant N00014-06-10729)supported by a WHOI/NOAA Cooperative Institute for Climate and Ocean Research Postdoctoral Scholarship
文摘We present numerical computations of a new wind-wave coupling theory that is governed by a system of nonlinear advance-delay differential equations (NLADDE). NLADDE are functional differential equations for which the derivative of an unknown function depends nonlinearly on the past (delayed), present, and future (advanced) values of the unknown function (if time is the independent variable). A practical numerical method for solving NLADDE is implemented, based on a collocation method. The method is tested for two problems with known analytic solutions and is shown to be numerically convergent. Numerical solutions to the coupled wind and wave problem reveal estimates of the wave height spectrum, the distribution of breaking waves (both depend on wave scale), as well as the vertical air-side profiles of turbulent stress and wind speed.
