Elements of Physical Oceanography 2.8 Ocean Surface Tides 41
Part A | 2.8
Table 2.7 The six basic astronomical tide-producing force
frequencies are given in radians per unit time and degrees
per solar day
Source
Angular frequency
Earth rotation
! D
2
lunar day
D 360 ı 12:2 ı =d
Lunar revolution
! s D
2
sidereal month
D 13:176 ı =d
Solar declination ! h D
2
solar year
D 0:985=d
Revolution of
lunar perigee
! p D
2
8:87 years
D 0:111 ı =d
Precession of
lunar node
! N D
2
18:6 years
D 0:0529 ı =d
Revolution of
solar perigee
! p1 D
2
20 000 years
D 0:00005 ı =d
days the range of the tidal sea level excursions and associated currents cycle through a maximum called spring
tides and a minimum called neap tides (Fig. 2.41). This
phenomenon occurs because the tide-producing forces
associated with the moon and the sun reinforce (times
of full and new moon) and oppose (times of half moons)
each other twice a month.
As it turns out, there are five basic frequencies (Table 2.7) associated with astronomical tide- producing
Table 2.8 List of the identities, periods, and relative equilibrium tidal amplitudes of the 19 of the most important partial
tides (out of the 400)
Name of partial tides
Symbol
Speed (degrees per
mean solar hour)
Period (solar
hours)
Coefficient ratio
M 2 D 100
Semidiurnal components
Principal lunar
M 2
28.98410
12.42
100.0
Principal solar
S 2
30.00000
12.00
46.6
Larger lunar elliptic
N 2
28.43973
12.66
19.2
Luni-solar semidiurnal
K 2
30.08214
11.97
12.7
Larger solar elliptic
T 2
29.95893
12.01
2.7
Smaller lunar elliptic
L 2
29.52848
12.19
2.8
Lunar elliptic second order
2N 2
27.89535
12.91
2.5
Larger lunar evectional
Á 2
28.51258
12.63
3.6
Smaller lunar evectional
2
29.45563
12.22
0.7
Variational
2
27.96821
12.87
3.1
Diurnal components
Luni-solar diurnal
K 1
15.04107
23.93
58.4
Principal lunar diurnal
O 1
13.94304
25.82
41.5
Principal solar diurnal
P 1
14.95893
24.07
19.4
Larger lunar elliptic
Q 1
13.39866
26.87
7.9
Smaller lunar elliptic
M 1
14.49205
24.86
3.3
Small lunar elliptic
J 1
15.58544
23.10
3.3
Long-period components
Lunar fortnightly
M 1
1.09803
327.86
17.2
Lunar monthly
M m
0.54437
661.30
9.1
Solar semiannual
S sa
0.08214
2191.43
8.0
forces. Because the interaction of the astronomical tidal
forcing and the oceanic response is highly nonlinear, the
observed ocean tide anywhere on the earth can be decomposed into 400 partial tides (or tidal species). Each
partial tides has a unique frequency ! i that is determined by a set of integer weights a j (for j D 1; 2; 3; 4; 5,
and 6) that multiply these six basic frequencies according to
! i D a 1 ! C a 2 ! s C a 3 ! h C a 4 ! p C a 5 ! N C a 6 ! pl :
Doodson [2.17] developed a shorthand notation for
the weights called the Doodson number to define the
different partial tides. (For example, the interaction of
lunar declination changes and earth rotation leads to
a pair of frequencies ! C 4! s and ! 4! s ; which
have Doodson number specifications (1 4 0 0 0 0) and
(1 4 0 0 0 0), respectively). The short list of the most
important partial tides in Table 2.8 show equilibrium
tidal forcing amplitude ratios relative to that of the M 2
tidal constituent – at many sites the most important constituent.
For practical purposes, the astronomical tideproducing forcing is fixed for all time. So the tidal
response of the world’s oceans, while it is complex
spatially, is also fixed for all time. Thus to uniquely determine the tide at a particular location – say sea level
SL.t/ – the task is to determine the amplitude (H i ) and
Part A | 2.8
Table 2.7 The six basic astronomical tide-producing force
frequencies are given in radians per unit time and degrees
per solar day
Source
Angular frequency
Earth rotation
! D
2
lunar day
D 360 ı 12:2 ı =d
Lunar revolution
! s D
2
sidereal month
D 13:176 ı =d
Solar declination ! h D
2
solar year
D 0:985=d
Revolution of
lunar perigee
! p D
2
8:87 years
D 0:111 ı =d
Precession of
lunar node
! N D
2
18:6 years
D 0:0529 ı =d
Revolution of
solar perigee
! p1 D
2
20 000 years
D 0:00005 ı =d
days the range of the tidal sea level excursions and associated currents cycle through a maximum called spring
tides and a minimum called neap tides (Fig. 2.41). This
phenomenon occurs because the tide-producing forces
associated with the moon and the sun reinforce (times
of full and new moon) and oppose (times of half moons)
each other twice a month.
As it turns out, there are five basic frequencies (Table 2.7) associated with astronomical tide- producing
Table 2.8 List of the identities, periods, and relative equilibrium tidal amplitudes of the 19 of the most important partial
tides (out of the 400)
Name of partial tides
Symbol
Speed (degrees per
mean solar hour)
Period (solar
hours)
Coefficient ratio
M 2 D 100
Semidiurnal components
Principal lunar
M 2
28.98410
12.42
100.0
Principal solar
S 2
30.00000
12.00
46.6
Larger lunar elliptic
N 2
28.43973
12.66
19.2
Luni-solar semidiurnal
K 2
30.08214
11.97
12.7
Larger solar elliptic
T 2
29.95893
12.01
2.7
Smaller lunar elliptic
L 2
29.52848
12.19
2.8
Lunar elliptic second order
2N 2
27.89535
12.91
2.5
Larger lunar evectional
Á 2
28.51258
12.63
3.6
Smaller lunar evectional
2
29.45563
12.22
0.7
Variational
2
27.96821
12.87
3.1
Diurnal components
Luni-solar diurnal
K 1
15.04107
23.93
58.4
Principal lunar diurnal
O 1
13.94304
25.82
41.5
Principal solar diurnal
P 1
14.95893
24.07
19.4
Larger lunar elliptic
Q 1
13.39866
26.87
7.9
Smaller lunar elliptic
M 1
14.49205
24.86
3.3
Small lunar elliptic
J 1
15.58544
23.10
3.3
Long-period components
Lunar fortnightly
M 1
1.09803
327.86
17.2
Lunar monthly
M m
0.54437
661.30
9.1
Solar semiannual
S sa
0.08214
2191.43
8.0
forces. Because the interaction of the astronomical tidal
forcing and the oceanic response is highly nonlinear, the
observed ocean tide anywhere on the earth can be decomposed into 400 partial tides (or tidal species). Each
partial tides has a unique frequency ! i that is determined by a set of integer weights a j (for j D 1; 2; 3; 4; 5,
and 6) that multiply these six basic frequencies according to
! i D a 1 ! C a 2 ! s C a 3 ! h C a 4 ! p C a 5 ! N C a 6 ! pl :
Doodson [2.17] developed a shorthand notation for
the weights called the Doodson number to define the
different partial tides. (For example, the interaction of
lunar declination changes and earth rotation leads to
a pair of frequencies ! C 4! s and ! 4! s ; which
have Doodson number specifications (1 4 0 0 0 0) and
(1 4 0 0 0 0), respectively). The short list of the most
important partial tides in Table 2.8 show equilibrium
tidal forcing amplitude ratios relative to that of the M 2
tidal constituent – at many sites the most important constituent.
For practical purposes, the astronomical tideproducing forcing is fixed for all time. So the tidal
response of the world’s oceans, while it is complex
spatially, is also fixed for all time. Thus to uniquely determine the tide at a particular location – say sea level
SL.t/ – the task is to determine the amplitude (H i ) and