4
Wave Forces
on Structures
James F. Wilson
One approach used to estimate the highest expected wave forces on an offshore
structure is based on a single design wave. For a particular wave theory, with a
wave height and wave period chosen according to the location of the structure,
the corresponding pressure field and horizontal components of wave particle velocity and accélération are then determined. With this flow information, the
distributions of the two governing flow parameters Re and Kc (the Reynolds
and Keulegan-Carpenter numbers) are found for the structural components;
the flow régime is determined; and the appropriate fluid force coefficients for
drag, inertia, and diffraction (wave scattering) are chosen from a database. The
structural loading is then computed using these latter coefficients, together with
the expressions for wave velocity and accélération applied to either Morison’s
loading model, or a modified version thereof, or to a diffraction model. This
approach is now illustrated for cases where the fluid and structural motion are
liinited to the x, z-plane, and where the flows are normal to longitudinal axes
of the structural éléments, usually right circular cylinders, the basic element
of offshore structures. Identified are the flow régimes appropriate for the experimental coefficients Cd, Cm, and the diffraction coefficients, with a brief
summary of the uncertainties in these coefficients. Also defined are transfer
functions, or functions that relate the wave velocities and accélérations to the
structural forces. These transfer functions are employed in later chapters to
calculate the responses of linearly - behaving structures to actual sea States.
4.1
WAVE LOADING OF FLEXIBLE CYLINDERS
Suppose that a cylinder in a wave field has sufficient flexibility such that its
horizontal velocity v and horizontal accélération v are often significantly higher
than the corresponding quantities u and ù for the water wave. In this case,
Berge and Penzien (1974) suggested a modification of Morison’s équation (2.14)
in which u is replaced by the relative velocity (u — û), and û is replaced by the
relative accélération (û — ü). Recall Example Problem 2.3. A load model that
84
Wave Forces
on Structures
James F. Wilson
One approach used to estimate the highest expected wave forces on an offshore
structure is based on a single design wave. For a particular wave theory, with a
wave height and wave period chosen according to the location of the structure,
the corresponding pressure field and horizontal components of wave particle velocity and accélération are then determined. With this flow information, the
distributions of the two governing flow parameters Re and Kc (the Reynolds
and Keulegan-Carpenter numbers) are found for the structural components;
the flow régime is determined; and the appropriate fluid force coefficients for
drag, inertia, and diffraction (wave scattering) are chosen from a database. The
structural loading is then computed using these latter coefficients, together with
the expressions for wave velocity and accélération applied to either Morison’s
loading model, or a modified version thereof, or to a diffraction model. This
approach is now illustrated for cases where the fluid and structural motion are
liinited to the x, z-plane, and where the flows are normal to longitudinal axes
of the structural éléments, usually right circular cylinders, the basic element
of offshore structures. Identified are the flow régimes appropriate for the experimental coefficients Cd, Cm, and the diffraction coefficients, with a brief
summary of the uncertainties in these coefficients. Also defined are transfer
functions, or functions that relate the wave velocities and accélérations to the
structural forces. These transfer functions are employed in later chapters to
calculate the responses of linearly - behaving structures to actual sea States.
4.1
WAVE LOADING OF FLEXIBLE CYLINDERS
Suppose that a cylinder in a wave field has sufficient flexibility such that its
horizontal velocity v and horizontal accélération v are often significantly higher
than the corresponding quantities u and ù for the water wave. In this case,
Berge and Penzien (1974) suggested a modification of Morison’s équation (2.14)
in which u is replaced by the relative velocity (u — û), and û is replaced by the
relative accélération (û — ü). Recall Example Problem 2.3. A load model that
84