Nomenclature

a

variable in spectrum definition

variable in spectrum definition, non-dimensional damping factor

g

peak enhancement factor

e

phase

z

wave elevation

z0

wave amplitude

z1/3

significant wave amplitude

q

angular motion

l

wave length

m

wave heading relative to vessel

r

water density

 

displaced volume of vessel

s

spectral width parameter

s0

standard deviation of wave spectrum (RMS)

w

wave frequency

we

encounter frequency

A

variable in spectrum definition

a

added mass, linear acceleration

B

vessel beam, variable in spectrum definition

b

Damping

c

wave speed, restoring force (stiffness)

Caw

added resistance coefficient in regular waves

E

Energy

F

excitation force

g

acceleration due to gravity

H

wave height

H1/3

significant wave height

Hchar

Characteristic wave height

kxx

roll radius of gyration

kyy

pitch radius of gyration

I

Inertia

L

length of vessel

m

Mass

m0

variance of wave spectrum, zeroth spectral moment

mn

nth spectral moment

p

Probability

q

Probability

Raw

added resistance in regular waves

 

total added resistance in irregular waves

RAO

response amplitude operator

S

spectral energy

T

wave period

T0

modal wave period

Tave

average wave period

Tz

zero-crossing wave period

t

Time

tf

transfer function (RAO)

Uwind

wind speed

U

ship speed

u*

threshold velocity

z

linear motion