USER MANUAL SWAN Cycle III version 40.72A

Definitions of variables 91
RPER
command. If p = 1 (the default value) PER is identical to TM01 and
if p = 0, PER = TMM10.
Average relative period (in s), defined as
∫ ∫ σ
RT m,p−1,p = 2π
p−1 E(σ,θ)dσdθ
∫ ∫ σ p E(σ,θ)dσdθ
FSPR
Here, if p = 1, RPER=RTM01 and if p = 0, RPER=RTMM10.
The normalized frequency width of the spectrum (frequency spreading),
as defined by Battjes and Van Vledder (1984):
FSPR = |∫ ∞
E(ω)e iωτ dω|
0
E tot
, for τ = T m02
DSPR
The one-sided directional width of the spectrum (directional spreading
or directional standard deviation,in o ), defined as
DSPR 2 = ( 180
π
) 2 ∫ 2π
0 (2 sin(θ−θ
2 ))2 D(θ)dθ
and computed as conventionally for pitch-and-roll buoy data
(Kuik et al. (1988); this is the standard definition for WAVEC buoys
integrated over all frequencies):
⎛
(∫ )
(DSPR π
√
2 (∫ ) ]
180 )2 = 2 ⎝1 − √[ ⎞ 2 sin
∫ θE(σ,θ)dσdθ cos θE(σ,θ)dσdθ
E(σ)dσ
+ ∫ ⎠
E(σ)dσ
QP
The peakedness of the wave spectrum, defined as
∫ ∫ σE
Q p = 2 ∫ ∫ 2 (σ,θ)dσdθ
( E(σ,θ)dσdθ) 2
MS
This quantity represents the degree of randomness of the waves.
A smaller value of Q p indicates a wider spectrum and thus
increased the degree of randomness (e.g., shorter wave groups),
whereas a larger value indicates a narrower spectrum and a more
organised wave field (e.g., longer wave groups).
As input to SWAN with the commands BOUNDPAR and BOUNDSPEC,
the directional distribution of incident wave energy is given by
D(θ) = A(cos θ) m for all frequencies. The parameter m
is indicated as MS in SWAN and is not necessarily an integer number.
This number is related to the one-sided directional spread of the waves
(DSPR) as follows: