3. Radiation and Diffraction Flashcards
Rayleigh distribution is considered a good approximation for the probability density function of the maxima of the wave elevation if
If a gaussian distribution is a good approximation for the instantaneous wave elevation and the wave-spectrum is narrow banded
The probability associated with a certain sea condition is given by
It’s occurrence divided by the sum of all possible occurrences
Short-crested waves mean
The wave spectrum varies with the direction theta
Linear hydrodynamic loads are split into
Diffraction and radiation
Contributions to the diffraction problem
Excitation loads
- Froude-Kriloff loads
- Diffraction loads
Froude-Kriloff principle
The flow penetrates the body with a normal velocity like the body was not there. This causes hydrodynamic loads on the body called FK loads
Diffraction loads principle
To recover the body impermeability, the body presence causes a flow (and so waves)
The wave excitation loads are obtained by
Integrating the incident wave dynamic pressure and the diffraction dynamic pressure along the mean wetted hull surface
Radiation problem HP
The body is forced to oscillate in its six degrees of freedom
(Radiation) hydrodynamic loads identifies as
Added mass
Damping
Restoring terms
Added mass is in phase with ____
Damping is in phase with ____
Acceleration
Velocity
The vertical FK force component is given by
The incident wave vertical acceleration at the geometrical center of the 2D body multiplied by the mass of water displaced by the body
Strip theory for radiation problem
Justified for zero speed when the frequencies correspond to a wavelength in the order of the cross-sectional dimension in y,z plane.
—> 3D problems sum of 2D problems
Strip theory for diffraction problem
Considers wavelengths large compared to cross section in z,y plane by adding FK forces
—> 3D problem by sum of 2D + FK loads
Does the body move in the diffraction problem
The body does not move: incident-waves plus diffraction flow give zero normal velocity at the fixed-body surface
Consequence of long-wave approximation for excitation forces:
Waves generated by the wave-body interaction are small —> the damping contribution to the forces are small relative to the terms proportional to the acceleration and can be neglected
What happens to B33 when omega goes to infinity or zero
It is zero as it is connected with the square power of the amplitude if the radiated waves
A33 for a half circle in omega—> infinity
Equals the mass of the water displaced by the half circle
can Ajj and Bjj be negative?
Wave radiation damping Bjj can not be negative.
Added mass Ajj can be negative for certain frequencies and body shapes. E.g., catamaran
Added mass and damping coefficients depend on
Frequency
Body shape
Forward speed U
