Bài giảng hải dương học chương 4

Chapter 4

Tide and tidal currents

Ni dung
1. Thuật ng
ngữ
ữ thiên văn và thuỷ văn

2. Lực tạo triều
3. Phân tích thuỷ triều
4. Dự báo triều
5. Thuỷ triều Biển đô
đông
ng
6. Cửa sông và thuỷ triều vùng cửa sông
7. Bài tập


Thuật ng
ngữ
ữ thiên văn

Thiên cầu hay mặt cầu bầu trời
Trục vũ trụ
Thiên cực bắc và thiên cực nam
Thiên đỉnh và thiên đế
Mặt phẳng chân trời
Đ-ờng chân trời
trời,, xớch o tri
tri..
Thiên cầu bắc và thiên cầu nam
nam..
Kinh tuyến trời
trời..
Điểm bắc và điểm nam
nam,, điểm đô
đông
ng và điểm tây
tây..
Vòng giờ
giờ,, vòng nhật động
ộng.. Vòng hoàng đạo, bạch đạo.
đạo.
Xuân phân (21/III),
(21/III),thu
thu phân (23/IX),
(23/IX),hạ
hạ chí (22/VI), đô

đông
ng chí (22/XII).
Ngày sóc th-ợng huyền , ngày vọng hạ huyền .

Thuật ng
ngữ
ữ thuỷ văn
- Đỉnh triều
- Chân triều
- Chu kỳ triều
- Độ lớn thuỷ triều
- Biên độ triều

- Tr, Td
- Kỳ n-ớc c-ờng, kỳ n-ớc kém
- 0 lục địa , 0 độ sâu


Tidal Characteristics
single

waves - stretch across entire
ocean basins.
shallow
shallow--water waves
– wavelengths greatly exceed the depth of
the ocean.
complex

sun

interactions of moon and


Why Care About Tides?


Aquaculture


The Tides of the
Bay of Fundy


Origin of the Tides
Unlike

wind--driven surface waves
wind
and unlike tsunamis, tides are
caused by two principal factors:
– Gravitational attraction
– Centrifugal force


Gravitational Attraction
All

masses are drawn to each other.
The moon because of its closeness

to the Earth exerts a greater
gravitational effect on the Earth than
the Sun,
Sun, despite the fact that the Sun
is much more massive than the
Moon.

x=?



Gravitational Effect of Moon

Centrifugal Forces: Center of Rotation


2 Bulges from Gravitational Attraction
& Centrifugal Force


Gravitational forces

Tractive force
Fs  Fm  sin(   )  Fa  sin( )

Fs 

3gM
 sin 2
2K 3

Distribution of tractive forces over the Earth
surface.

Ratio of the tractive forces od the Moon and the Sun.
Symbol
M
K

Moon
0.0123
60.3

Sun
333,000
23,500

Dimension
(-)
(-)

3gM/(2K3)

0.82*10-6

0.38*10-6

(m/s2)

The equilibrium theory
assumed that the Earth is fully covered with water

The
plane
of the
moon
is in
the
plane
of the
equator


 why

not exactly 24 hours or 12 hours?
 Moon moves forward in it’s orbit each day.
– Takes 50 additional minutes for a spot on the
Earth’s surface to regain it’s position relative to
the Moon.
E = 15.041 o/h m = 0.549 o/h

2
360o
2T 

 24.84h
o

E  m  14.49 /h
T = 12.42 h = 12 h 25’


The
plane of
the
moon
makes
an angle
with the
plane of
the
equator


Joint effect of moon and sun on the tides
 Spring

tides occur when the Earth, Sun, and Moon are
aligned.
– New Moon and Full Moon phases
– Constructive interference
 Neap tides occur when the Sun and Moon are aligned
at right angles to one another.
– Quarter Moon phases
– Destructive interference


 Spring

tide:: phase when tidal range is maximal
tide
maximal..
 Neap tide:
tide: phase when tidal range is minimal
minimal..
 There are 2 spring and 2 neap tides each month

2
m  s 

360o
2T 
 708h
o
0.508 /h

T = 354 h = 14.8 days


Moving position of the perigeum

Elliptical orbit of the Earth


Relative motions of moon and sun in relation to the celestrial sphere

3gM
3gM

Fs 
sin
2


2K 3
2K 3

n


A

A
cos(

t


)

o
i
i
i


i 1



Ao = constant
Ai = amplitude of component i
i = angular speed of component i
= jE + k m +l s + m p
in which E m s p are the angular speeds of the
Earth, the Moon, the Sun, perigeum of the moon
i = phase of component i at t = 0.


Periods and angular speeds
Origin
Rotation Earth Rotation Earth
Moon around Earth
Earth around Sun

Perigeum Moon
Nodes lunar orbit

Angular speed in o/hour
15.041069
0.549016
0.041069

Period
0.997 days
27.32 days
365.24 days

0.004642

0.002206

8.85 years
18.60 years

The variation due to the revolution of the nodes is taken into account
by multiplying the amplitude with a factor fi and adding a phase shift
ui to the harmonic terms

The number of harmonic terms is large:
- The orbits are not in the plane of the equator, which
cause declination tides (mainly diurnal);
- The distance between the Earth and the moon and sun
are not constant, as their orbits are ellipses. The distances
vary and also the angular speed. That causes the elliptical
tides (both diurnal and semi-diurnal).


Main astronomic constituents of the tide
Gro
up

Sym
bol

Frequency

Period
(hours)

Angular Astronomi Type of constituent
speed
c
(o/hour) coefficients

I

M2
S2
K1
O1

2we-2wm
2we-2ws
we
we-2wm

12.42
12.00
23.94
25.80

28.9841
30.0000
15.0411
13.9430

II

P1

N2
K2

we-2ws
2we-wm+wp
2we

24.07
12.66
11.97

14.9589 0.176
28.4397 0.174
30.0821 0.115

0.908
0.423
0.531
0.377

semi-diurnal principle lunar tide
semi-diurnal principle solar tide
diurnal lunar-solar declination tide
diurnal lunar declination tide
diurnal solar declination tide
semi-diurnal lunar elliptic tide
semi-diurnal lunar-solar
declination tide

constituents of the tide (conts

(conts))
III

Q1
L2

e-3m+p
2e-m-p

26.87
12.19

13.3987
29.5285

0.072
0.026

diurnal lunar elliptic tide
semi diurnal lunar elliptic tide

IV

Mf
Mm
Ssa

2m
m-p
2s

328
661
4383

1.0980
0.5444
0.0821

0.156
0.083
0.026

long periodic lunar tide
long periodic lunar tide
long periodic solar tide

V

Sa
Msm
Msf
Mtm
M1
1
1
J1
001
2N2
m2

n2
l2
T2

s
m-2s+p
2m-2s
3m-p
e-m+p
e-3s
e+2s
e+m-p
e+2m
2e-4m+2p
2e-4m+2s
2e-3m+2sp
2e-m2s+p
2e-3s

8759
764
354
219
24.83
24.13
23.80
23.10
22.31
12.91
12.87

12.63
12.22
12.02

0.0411
0.4715
1.0159
1.6424
14.4967
14.9179
15.1232
15.5854
16.1391
27.8954
27.9682
28.5126
29.4556
29.9590

0.012
0.012
0.008
0.030
0.030
0.010
0.008
0.030
0.016
0.024
0.022

0.034
0.007
0.025

long periodic solar tide


Shallow water tidal
- Bottom friction;
- Variable propagation speed of the tidal wave.

- Variable propagation speed of the tidal wave.


Shallow water tides
Symbol Origin

Frequency

Period
(hrs)

Angular
speed
(deg./h)

MNS2
2MS2
2SM2
MK3

2MK3
SK3
SO3
M4
MS4
MN4
MK4
S4

2e-5m+2s+p
2e-4m+2s
2e+2m-4s
3e-2m
3e-4m
3e-2s
3e-2m-2s
4e-4m
4e-2m-2s
4e-5m+p
4e-2m
4e-4s

13.13
12.87
11.61
8.18
8.39
7.99
8.19
6.21

6.10
6.27
6.09
6.00

27.4238
27.9682
31.0159
44.0252
42.9271
45.0411
43.9430
57.9682
58.9841
57.4238
59.0662
60.0000

M2+N2-S2
2M2-S2
2S2-M2
M2+K1
2M2-K1
S2+K1
S2+O1
2M2
M2+S2
M2+N2
M2+K2
2S2

Remarks
semi-diurnal

terdiurnal

quarter diurnal


Shallow water tides
Symbol Origin

Period Angular
speed
(hrs)

Frequency

Remarks

(deg./h)

M6
2MS6
2MN6
2SM6
MSN6
S6
M8
3MS8

2(MS)8
2MSN8
S8

3M2
2M2+S2
2M2+N2
2S2+M2
M2+S2+N2
3S2
4M2
3M2+S2
2M2+2S2
2M2+S2+N2
4S2

6e-6m
6e-4m-2s
6e-7m+p
6e-2m-4s
6e-5m-2s+p
6e-6s
8e-8m
8e-6m-2s
8e-4m-4s
8e-7m-2s+p
8e-8s

4.14
4.09

4.17
4.05
4.12
4.00
3.11
3.08
3.05
3.07
3.00

86.9523 sixth diurnal
87.9682
86.4079
88.9841
87.4238
90.0000
115.9364 eighth diurnal
116.9523
117.9682
117.4079
120.0000

Phân loại thủy triều
KiÓu triÒu

H

TriÒu hçn hîp
B¸n nhËt
BN triÒu NhËt triÒu NhËt triÒu

triÒu
kh«ng ®Òu kh«ng ®Òu
®Òu

h K 1  hO1
0.0 < 0.5
hM 2

+
F = H K1 H 01
H M2 + H S2 < 0.25

0.5  2.0

2.0  4.0

0.25  1.5

1.5 3.

> 4.0

>3