Archive image from page 31 of Directional irregular wave kinematics (1998) Directional irregular wave kinematics directionalirreg00bark Year: 1998 24 Elevations of water surface I nodes are sought Bernoulli equation appHed at known elevation, zp at Figure : Schematic of system of equations in a window jf and wl terms in Eq. ). There is also a significant nonlinearity introduced by the application of the boundary conditions at the unknown and varying free surface. Observational Equations The given form for the potential function could repre- sent any periodic flow, subject to the bot
Archive image from page 31 of Directional irregular wave kinematics (1998) Directional irregular wave kinematics directionalirreg00bark Year: 1998 24 Elevations of water surface I nodes are sought Bernoulli equation appHed at known elevation, zp at Figure : Schematic of system of equations in a window jf and wl terms in Eq. ). There is also a significant nonlinearity introduced by the application of the boundary conditions at the unknown and varying free surface. Observational Equations The given form for the potential function could repre- sent any periodic flow, subject to the bottom boundary condition. The FSBCs define the flow as a gravity-constrained, free surface flow. The observational equations are the equations in the system that force the solution to fit the given record. For a subsurface pressure record, this is the Bernoulli equation, applied at the location of the pressure measurement. The required number of independent equations are es- tablished by applying the Bernoulli equation at a number of times throughout the window considered. The error in the Bernoulli equation is the difference between the measured dynamic pressure and that computed from the kinematics defined by the potential function. The solution is the set of parameters in the potential function and the set of water surface nodes that produces a predicted dynamic pressure that matches the measured record, while simultaneously satisfying the FSBCs. A system of equations is specified if there are as many independent equations as unknown parameters in the system. If there are more equations than unknowns, the solution can be defined as that which results in the smallest squared errors in the equations. This least squares formulation is also appropriate for a uniquely defined
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