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!