MAR555 Lec 19 - University of Massachusetts Dartmouth
Transcript of MAR555 Lec 19 - University of Massachusetts Dartmouth
Tides
C. Chen
General Physical OceanographyMAR 555
School for Marine Sciences and TechnologyUmass-Dartmouth
MAR 555 Lecture 21: Tides
The tide is the name given to the periodic rise and fall of sea level. Thisis one of the earliest scientific venture of the oceanic exploration.
Causes of Tides (for the global scale): Gravitational pull of the moon andsun and the inertial centrifugal force
DE
Earth
Moon
0.25DE
30DE
North PoleΩ
Equator
Common center of the earth and moon
The earth and moon pair rotates counterclockwise about the central mass pointof the earth and moon
Point A
Center of mass
Center of Earth
Earth
Moon
The earth and moon rotates counterclockwise about their common centerof mass with a radius equal the distance between the center of the earthmass and the center of two bodies’ masses.
Inertial Centrifugal Force ( )
�
!
F c
The inertial centrifugal force is the same everywhere on the earth,because all parcels rotates with the same radius and angular velocity
Earth
Moon
Bulge of water
�
!
F g = µM1M2
r2(
! r
r)
Earth
Moon
M1 M2
r
�
r3
Gravitational Force ( ):
�
!
F g
The gravitational force larger on the side of close to the moonand smaller on the back side of the earth
�
!
F c =
!
F g
At the center of the earth:
On the side facing to the moon:
�
!
F c <
!
F g
On the back side to the moon:
�
!
F c >
!
F g
Sum of gravitational and centrifugal forces
X’ X
x and x’ indicate the change in position of a point onEarth’s surface after half a lunar day (12 hours 25minutes), which have two equal tides per 24 hours and50 minutes at these two positions.
Semidiurnal tide: period-12.42 hours
x
Moon
Moon
Today
Tomorrow
Equator
Top view from the north pole
Earth
North pole
The moon’s location relative to the earth varies with time. The one-daymovement of the moon cause the delay of high water or low watertiming by apprimately 50 minutes.
The moon moves at various angles to the north and south of the equator up toa maximum angle of 35o (depending on the season and also the time of thelunar month. Then observer at the location of “x” will notice two high tideswith unequal height per lunar day. It is called “diurnal inequality”.
X’ X
Earth
South Pole
North Pole
Moon
θ
Spring and Neap tides [fortnightly (14-days) variation]
Moon
Spring TideNew Moon
Lunar tideSolar tide
SunEarth
Earth
Moon
Neap Tide
Top view from the north pole
First quarter Moon
EarthMoon
Spring Tide Full Moon
Sun
Sun
Earth
Moon
Sun
Third quarter Moon
Amphidromic System
Tidal Terminology
The tide at first and third quarter moonsNeap tide:
the tides at full and new moonsSpring tide:
the difference between two successive low orhigh tides
Daily inequality:
the difference between high and low watersTidal range:
the mean water level relative to a referencepoint over a long-term average
Mean tidal level:
the minimum water level during a tidal periodLow water(or low tide):
the maximum water level during a tidal periodHigh water(or high tide):
12.66 hours-larger lunar elliptic induced tide.N2 tide
24 hours-diurnal solar tide produced by the sunK1 tide
24 h 50 min-diurnal lunar tide produced by the moonO1 tide
12 hours (1/2 solar day)-semidiurnal solar tideproduced by the sun
S2 tide
12 h 25 min (1/2 lunar day)-semidiurnal lunar tideproduced by the moon
M2 tide
Major Tidal Constituents
The tides observed in the ocean is the sum of more than hundred harmonicperiodic oscillations. In most situations, the tide is dominated by five majortidal constituents given below.
Tidal ClassificationIn most regions, the change of the tidal elevation and currents aredominated by either semidiurnal tides or diurnal tides. A moresystematic classification of tidal types is defined by the so-called“Form Ratio” given as
�
F =K1
+O1
M2
+ S2
Diurnal tides: generally only one high waterper day. The mean spring tide range = 2 (K1+O1)
> 3.0
Mixed tides with mainly diurnal tides:frequently only one high water per day. hemean spring tide range = 2 (K1 +O1)
1.5-3.0
Mixed tides with mainly semidiurnal tides:large inequalities in tidal range and timebetween highs and lows each day. The meanspring tide range = 2 (M2 +S2)
>0.25 and<1.5
Semidiurnal tides: two high waters and lowwaters with about the same height each day.The mean spring tide range = 2 (M2 +S2)
0-0.25
Tidal Currents
In the global and regional oceans, the tidal currents rotate with time over a tidalcycle.
Semi-diurnal equal tide Semi-diurnal unequal tide
QS. 1: Is the equilibrium tidal theory described in this lecture used toexplain the tidal features observed in the coastal region?
QS. 2: Is the tide in the coastal region produced by the resultingforcing of gravitational and inertial centrifugal forces?
Or
If yes, what tidal features do you expect to see?
Or not, what is the key process to drive the tides in the coastal areaand estuaries?
We will discuss it in the next lecture!