3. Radiation and Diffraction

Question 1

Rayleigh distribution is considered a good approximation for the probability density function of the maxima of the wave elevation if

Answer 1

If a gaussian distribution is a good approximation for the instantaneous wave elevation and the wave-spectrum is narrow banded

Question 2

The probability associated with a certain sea condition is given by

Answer 2

It’s occurrence divided by the sum of all possible occurrences

Question 3

Short-crested waves mean

Answer 3

The wave spectrum varies with the direction theta

Question 4

Linear hydrodynamic loads are split into

Answer 4

Diffraction and radiation

Question 5

Contributions to the diffraction problem

Answer 5

Excitation loads

• Froude-Kriloff loads
• Diffraction loads

Question 6

Froude-Kriloff principle

Answer 6

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

Question 7

Diffraction loads principle

Answer 7

To recover the body impermeability, the body presence causes a flow (and so waves)

Question 8

The wave excitation loads are obtained by

Answer 8

Integrating the incident wave dynamic pressure and the diffraction dynamic pressure along the mean wetted hull surface

Question 9

Radiation problem HP

Answer 9

The body is forced to oscillate in its six degrees of freedom

Question 10

(Radiation) hydrodynamic loads identifies as

Answer 10

Added mass
Damping
Restoring terms

Question 11

Added mass is in phase with ____

Damping is in phase with ____

Answer 11

Acceleration

Velocity

Question 12

The vertical FK force component is given by

Answer 12

The incident wave vertical acceleration at the geometrical center of the 2D body multiplied by the mass of water displaced by the body

Question 13

Strip theory for radiation problem

Answer 13

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

Question 14

Strip theory for diffraction problem

Answer 14

Considers wavelengths large compared to cross section in z,y plane by adding FK forces

—> 3D problem by sum of 2D + FK loads

Question 15

Does the body move in the diffraction problem

Answer 15

The body does not move: incident-waves plus diffraction flow give zero normal velocity at the fixed-body surface

Question 16

Consequence of long-wave approximation for excitation forces:

Answer 16

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

Question 17

What happens to B33 when omega goes to infinity or zero

Answer 17

It is zero as it is connected with the square power of the amplitude if the radiated waves

Question 18

A33 for a half circle in omega—> infinity

Answer 18

Equals the mass of the water displaced by the half circle

Question 19

can Ajj and Bjj be negative?

Answer 19

Wave radiation damping Bjj can not be negative.

Added mass Ajj can be negative for certain frequencies and body shapes. E.g., catamaran

Question 20

Added mass and damping coefficients depend on

Answer 20

Frequency
Body shape
Forward speed U