metocean2_ tide.pdf

7/27/2019 Metocean2_ Tide.pdf

http://slidepdf.com/reader/full/metocean2-tidepdf 1/10

_____________________________________________________________________________________________________________________

- 1 - Metocean

Tides



_____________________________________________________________________________________________________________________

- 2 - Metocean

Main visible results of tides is the local rise and fall of the sea level, as a result of gravitational forces exerted on the oceans, mostly bythe Moon and the Sun and combined with the rotation of the Earth.

The rotation of the moon (mass M) around the earth induces a

potential V M at each point P of the earth’s surface :

d

M V M

where is the gravitational constant

Since cos2222

rR Rr d

2/12/1

cos21

R

r

R

r

R

M

V M

which can be expanded in powers of r/R (r/R >>1/60)

...1cos3

21cos1 22

Rr

Rr

R M

V M

Tidal forces are derived from the spatial gradient of the tidal

potential V M

When deriving forces, the first term of the potential cancels, thesecond term yields a constant force parallel to the earth-moonaxis which keeps earth in orbit about the centre of mass of the

earth-moon system.The third term is then the tide generating potential from whichcan be derived a parallel and a perpendicular components of thetidal force (neglecting higher order terms).The tides are produced by the horizontal component (verticalcomponent being balanced by pressure on the sea bed)

2sin

231

3

RF Mr V

r H

This force is aligned with the earth-moon line and will producesymmetric bulges at zenith and nadir.

Earth

Moon

O

d

R

r

P

A

High tide

Low tide

Earth

Moon

ZenithNadir



_____________________________________________________________________________________________________________________

- 3 - Metocean

Tidal forces due to the sun can be derived exactly the same way. In spite of its huge mass and because of its distance to earth, the tidalforce induced by the sun is only 46% of the lunar component.

Tidal Period In most places around the world, one can observe two low tides and two high tides per day. This Semidiurnal tidal regime is due to therotation of the earth.

Actually, since the moon also rotates around the earth (1/28 of a revolution per day) the time at which the moon passes again above thesame point is 24h50’28” so that the semidiurnal period is 12h25’14”.

MOON

EARTH



_____________________________________________________________________________________________________________________

- 4 - Metocean

As the earth spins around its polar axis it also follows an elliptical orbit around the sun. Earth's axis of rotation is inclined 23.45° withrespect to the plane of Earth's orbit about the sun (defining the ecliptic). The orientation of the ellipse in the ecliptic plane changes slowlywith time, causing the distance between earth and sun to vary with a long period (~21000 years). Additionally the sun declination varies

with a one solar year period.The moon’s elliptical orbit is also modified by various periodic interactions so that tidal forces resulting from all these components areactually modulated.

In order to describe this pseudoperiodic modulated tide, it is possible to decompose it in series of harmonics.These harmonics can be classified in various categories, related to their period range.In order to predict the tide, a minimum of 105 harmonics are used.

Tidal constituent Name Period (hours)

Semidiurnal Principal lunar M2 12.4206 Principal solar S2 12.0000 Lunar elliptic N2 12.6584 Lunisolar K 2 11.9673

Diurnal Lunisolar K 1 0.141565 Principal lunar O1 0.100514 Principal solar P1 0.046843 Elliptic lunar >Q1 0.019256

Long Period Fortnightly Mf 0.041742 Monthly Mm 0.022026 Semiannual Ssa 0.019446

Main tidal constituents



_____________________________________________________________________________________________________________________

- 5 - Metocean

Amplitudes of the main harmonics in the port of Brest

Principal lunar Principal Lunar (M2)

Principal Solar (M2)

Principal Lunar diurnal (O1)

Tide

Recomposition of tides from harmonics



_____________________________________________________________________________________________________________________

- 6 - Metocean

Diurnal tides : Since the moon is generally not in the Equatorial

plane, the two bulges are not symetrical. The bulge at nadir issmaller than the one at Zenith so that tides are alternatively largeand small.In locations like the channel for instance where this component issmall, there is very little difference between the morning andevening high tides. In other places like Gulf of mexico tides aremostly diurnal.

The periodicity of the tide actually depends on the relativeamplitude of the diurnal and semidiurnal components.

Classification is made according to the coefficient

ratio between diurnal and semidiurnal amplitudes

Semidiurnal 0<F<0.25 Mixed 0.25<F<3 Diurnal F>3

Larger Hightide

Smaller hightide

Moon

N



_____________________________________________________________________________________________________________________

- 7 - Metocean

Semidiurnal

Semidiurnal with diurnal influence

Diurnal

Mixed



_____________________________________________________________________________________________________________________

- 8 - Metocean

Neap Tides and Spring tides

It is observed that the amplitude of the semidiurnal tides varies over a cycle of about two weeks. This is the result of the superimposition of the lunar and solar influences. The lunar component is modulated by the solar one.

When the Sun and the moon are aligned (new and full moon), the lunar component is reinforced by the solar force and the tidal amplitudeis larger . This is called “spring tide”.

When the Sun and the moon are at 90° (first and last quarter), solar and lunar components are opposite and tend to cancel. The tidalamplitude is then smaller . This is called “neap tide”.

Moon Sun

Earth

New Moon – Spring Tide

First Quarter – Neap Tide

Last Quarter – Neap Tide

Full Moon – Spring Tide



_____________________________________________________________________________________________________________________

- 9 - Metocean

As a matter of fact, the tide does not behave as a bulgepropagating around the earth. This for various reasons :

Even though oceans occupy more than 70% of the surface of theearth, continents a large and spread enough to prevent the tide topropagate as a travelling wave around the globe

Shallower areas, continental shelves and coastal areas have aninfluence on the velocity of the tide wave

The coriolis force also has an influence, forcing the propagationof the wave counter clockwise in the northern hemisphere.

So that the tide globally behaves like a stationary wave turningaround fixed points. Such points where the amplitude of the tideis zero are called amphidromic points.

Map of tides evolution along the channel

Blue lines : iso-amplitude linesRed lines : cotidal lines connecting points being at high tide atthe same time



_____________________________________________________________________________________________________________________

- 10 - Metocean

Tides are to be taken into account for the design of marinestructures. Actually it is tides main effects, rise and fall of the sealevel and currents which are to be investigated in many designstudies.

Periodic change of the sea level :

Design of fixed coastal structures,Design of mooring lines for floating structures, Air-gap of TLP,Marine operations, Alteration of the waves characteristics in coastal areas…

Wave-current interaction

Currents :

Tidal currents can be really strong (~5m/s) in coastal areas wherethey can represent an interesting and renewable resource of marine energy.But these tidal currents can be felt even far from shore andbeyond the continental shelf. Their main characteristic is that theyare periodic in amplitude and direction hence should be taken into

account for the :

Design of fixed or floating structures,Design of mooring lines for floating structures,Marine operations,Fatigue of structures and moorings,

Alteration of the waves characteristics …

TLP offset + Setdown

Vortex Induced Vibrations

metocean2_ tide.pdf

Documents