Everything about The Theory Of Tides totally explained
The
theory of tides is the application of
continuum mechanics to interpret and predict the
tidal deformations of planetary and satellite bodies and their atmospheres and oceans, under the gravitational loading of another astronomical body or bodies. It commonly refers to the fluid dynamic motions for the
Earth's
oceans.
Tidal physics
Tidal forcing
The forces discussed here apply to body (Earth tides), oceanic and atmospheric tides. Atmospheric tides on Earth, however, tend to be dominated by forcing due to solar heating.
On the planet (or satellite) experiencing tidal motion consider a point at latitude
and longitude
at distance
from the center of mass, then point can written in cartesian coordinates as
where
Ω is the
angular frequency of the planet's rotation,
g is the planet's gravitational acceleration at the mean ocean surface, and
U is the external gravitational tidal-forcing
potential.
William Thomson (Lord Kelvin) rewrote Laplace's momentum terms using the
curl to find an equation for
vorticity. Under certain conditions this can be further rewritten as a conservation of vorticity.
Tidal analysis and prediction
Harmonic analysis
There are about 62 constituents that could be used, but many less are needed to predict tides accurately.
Tidal constituents
Amplitudes are given for the following example locations:
» ME Eastport,
MS Biloxi,
» PR San Juan,
AK Kodiak,
» CA San Francisco, and
HI Hilo.
Higher harmonics
|
Darwin
|
Period
|
Phase
|
Doodson coefs
|
Doodson
|
Amplitude at example location (cm)
|
NOAA
|
| Species
|
Symbol
|
(hr)
|
rate(°/hr)
|
n1 (L) |
n2 (m) |
n3 (y) |
n4 (mp) |
number
|
ME
|
MS
|
PR
|
AK
|
CA
|
HI
|
order
|
| Shallow water overtides of principal lunar |
M4 |
6.210300601 |
57.9682084 |
4 |
|
|
|
455.555 |
6.0 |
0.6 |
|
0.9 |
2.3 |
|
5 |
| Shallow water overtides of principal lunar |
M6 |
4.140200401 |
86.9523127 |
6 |
|
|
|
655.555 |
5.1 |
0.1 |
|
1.0 |
|
|
7 |
| Shallow water terdiurnal |
MK3 |
8.177140247 |
44.0251729 |
3 |
1 |
|
|
365.555 |
|
|
|
0.5 |
1.9 |
|
8 |
| Shallow water overtides of principal solar |
S4 |
6 |
60 |
4 |
4 |
-4 |
|
491.555 |
|
0.1 |
|
|
|
|
9 |
| Shallow water quarter diurnal |
MN4 |
6.269173724 |
57.4238337 |
4 |
-1 |
|
1 |
445.655 |
2.3 |
|
|
0.3 |
0.9 |
|
10 |
| Shallow water overtides of principal solar |
S6 |
4 |
90 |
6 |
6 |
-6 |
|
* |
|
0.1 |
|
|
|
|
12 |
| Lunar terdiurnal |
M3 |
8.280400802 |
43.4761563 |
3 |
|
|
|
355.555 |
|
|
|
|
0.5 |
|
32 |
| Shallow water terdiurnal |
2"MK3 |
8.38630265 |
42.9271398 |
3 |
-1 |
|
|
345.555 |
0.5 |
|
|
0.5 |
1.4 |
|
34 |
| Shallow water eighth diurnal |
M8 |
3.105150301 |
115.9364166 |
8 |
|
|
|
855.555 |
0.5 |
0.1 |
|
|
|
|
36 |
| Shallow water quarter diurnal |
MS4 |
6.103339275 |
58.9841042 |
4 |
2 |
-2 |
|
473.555 |
1.8 |
|
|
0.6 |
1.0 |
|
37 |
Semi-diurnal
|
Darwin
|
Period
|
Phase
|
Doodson coefs
|
Doodson
|
Amplitude at example location (cm)
|
NOAA
|
| Species |
Symbol
|
(hr)
|
(°/hr)
|
n1 (L) |
n2 (m) |
n3 (y) |
n4 (mp) |
number
|
ME
|
MS
|
PR
|
AK
|
CA
|
HI
|
order
|
| Principal lunar semidiurnal |
M2 |
12.4206012 |
28.9841042 |
2 |
|
|
|
255.555 |
268.7 |
3.9 |
15.9 |
97.3 |
58.0 |
23.0 |
1 |
| Principal solar semidiurnal |
S2 |
12 |
30 |
2 |
2 |
-2 |
|
273.555 |
42.0 |
3.3 |
2.1 |
32.5 |
13.7 |
9.2 |
2 |
| Larger lunar elliptic semidiurnal |
N2 |
12.65834751 |
28.4397295 |
2 |
-1 |
|
1 |
245.655 |
54.3 |
1.1 |
3.7 |
20.1 |
12.3 |
4.4 |
3 |
| Larger lunar evectional |
ν2 |
12.62600509 |
28.5125831 |
2 |
-1 |
2 |
-1 |
247.455 |
12.6 |
0.2 |
0.8 |
3.9 |
2.6 |
0.9 |
11 |
| Variational |
MU2 |
12.8717576 |
27.9682084 |
2 |
-2 |
2 |
|
237.555 |
2.0 |
0.1 |
0.5 |
2.2 |
0.7 |
0.8 |
13 |
| Lunar elliptical semidiurnal second-order |
2"N2 |
12.90537297 |
27.8953548 |
2 |
-2 |
|
2 |
235.755 |
6.5 |
0.1 |
0.5 |
2.4 |
1.4 |
0.6 |
14 |
| Smaller lunar evectional |
λ2 |
12.22177348 |
29.4556253 |
2 |
1 |
-2 |
1 |
263.655 |
5.3 |
|
0.1 |
0.7 |
0.6 |
0.2 |
16 |
| Larger solar elliptic |
T2 |
12.01644934 |
29.9589333 |
2 |
2 |
-3 |
|
272.555 |
3.7 |
0.2 |
0.1 |
1.9 |
0.9 |
0.6 |
27 |
| Smaller solar elliptic |
R2 |
11.98359564 |
30.0410667 |
2 |
2 |
-1 |
|
274.555 |
0.9 |
|
|
0.2 |
0.1 |
0.1 |
28 |
| Shallow water semidiurnal |
2SM2 |
11.60695157 |
31.0158958 |
2 |
4 |
-4 |
|
291.555 |
0.5 |
|
|
|
|
|
31 |
| Smaller lunar elliptic semidiurnal |
L2 |
12.19162085 |
29.5284789 |
2 |
1 |
|
-1 |
265.455 |
13.5 |
0.1 |
0.5 |
2.4 |
1.6 |
0.5 |
33 |
| Lunisolar semidiurnal |
K2 |
11.96723606 |
30.0821373 |
2 |
2 |
|
|
275.555 |
11.6 |
0.9 |
0.6 |
9.0 |
4.0 |
2.8 |
35 |
Diurnal
|
Darwin
|
Period
|
Phase
|
Doodson coefs
|
Doodson
|
Amplitude at example location (cm)
|
NOAA
|
| Species |
Symbol
|
(hr)
|
(°/hr)
|
n1 (L) |
n2 (m) |
n3 (y) |
n4 (mp) |
number
|
ME
|
MS
|
PR
|
AK
|
CA
|
HI
|
order
|
| Lunar diurnal |
K1 |
23.93447213 |
15.0410686 |
1 |
1 |
|
|
165.555 |
15.6 |
16.2 |
9.0 |
39.8 |
36.8 |
16.7 |
'4 |
| Lunar diurnal |
O1 |
25.81933871 |
13.9430356 |
1 |
-1 |
|
|
145.555 |
11.9 |
16.9 |
7.7 |
25.9 |
23.0 |
9.2 |
6 |
| Lunar diurnal |
OO1 |
22.30608083 |
16.1391017 |
1 |
3 |
|
|
185.555 |
0.5 |
0.7 |
0.4 |
1.2 |
1.1 |
0.7 |
15 |
| Solar diurnal |
S1 |
24 |
15 |
1 |
1 |
-1 |
|
164.555 |
1.0 |
|
0.5 |
1.2 |
0.7 |
0.3 |
17 |
| Smaller lunar elliptic diurnal |
M1 |
24.84120241 |
14.4920521 |
1 |
|
|
|
155.555 |
0.6 |
1.2 |
0.5 |
1.4 |
1.1 |
0.5 |
18 |
| Smaller lunar elliptic diurnal |
J1 |
23.09848146 |
15.5854433 |
1 |
2 |
|
-1 |
175.455 |
0.9 |
1.3 |
0.6 |
2.3 |
1.9 |
1.1 |
19 |
| Larger lunar evectional diurnal |
ρ |
26.72305326 |
13.4715145 |
1 |
-2 |
2 |
-1 |
137.455 |
0.3 |
0.6 |
0.3 |
0.9 |
0.9 |
0.3 |
25 |
| Larger lunar elliptic diurnal |
Q1 |
26.868350 |
13.3986609 |
1 |
-2 |
|
1 |
135.655 |
2.0 |
3.3 |
1.4 |
4.7 |
4.0 |
1.6 |
26 |
| Larger elliptic diurnal |
2Q1 |
28.00621204 |
12.8542862 |
1 |
-3 |
|
2 |
125.755 |
0.3 |
0.4 |
0.2 |
0.7 |
0.4 |
0.2 |
29 |
| Solar diurnal |
P1 |
24.06588766 |
14.9589314 |
1 |
1 |
-2 |
|
163.555 |
5.2 |
5.4 |
2.9 |
12.6 |
11.6 |
5.1 |
30 |
Long period
|
Darwin
|
Period
|
Phase
|
Doodson coefs
|
Doodson
|
Amplitude at example location (cm)
|
NOAA
|
| Species |
Symbol
|
(hr)
|
(°/hr)
|
n1 (L) |
n2 (m) |
n3 (y) |
n4 (mp) |
number
|
ME
|
MS
|
PR
|
AK
|
CA
|
HI
|
order
|
| Lunar monthly |
Mm |
661.3111655 |
0.5443747 |
0 |
1 |
|
-1 |
65.455 |
|
|
0.7 |
1.9 |
|
|
20 |
| Solar semiannual |
Ssa |
4383.076325 |
0.0821373 |
0 |
|
2 |
|
57.555 |
1.6 |
|
2.1 |
1.5 |
3.9 |
|
21 |
| Solar annual |
Sa |
8766.15265 |
0.0410686 |
0 |
|
1 |
|
56.555 |
|
|
5.5 |
7.8 |
3.8 |
4.3 |
22 |
| Lunisolar synodic fortnightly |
Msf |
354.3670666 |
1.0158958 |
0 |
2 |
-2 |
|
73.555 |
|
|
|
1.5 |
|
|
23 |
| Lunisolar fortnightly |
Mf |
327.8599387 |
1.0980331 |
0 |
2 |
|
|
75.555 |
|
|
1.4 |
2.0 |
|
0.7 |
24 |
Further Information
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