Tides - CCPOatkinson/OEAS405/OtherStuff/LecturePPTS/Lec_2… · Dynamic theory of tides: shallow-water waves driven by periodic forcing- amplified when basin in resonant with dominant

Tides

Tides:

longest waves

Tides

Simulated & observed tides, Cook Inlet, Alaska

• Definition: The rise and fall of sea level due to the

gravitational forces of the Moon and Sun and the

rotation of the Earth.

• Why tides are important?

- ship navigation in harbors

- coastal morphology (sediments motion)

- tidal currents impact ocean mixing

• How to predict tides?

- mechanical tide calculating machines

since 1880s, tidal charts and analysis

- computer models, tide gauges, satellite

altimetry, etc.

• Largest tides: 17m range: Bay of Fundy &

Ungava Bay (Canada); ~10m: Cook Inlet (Alaska)

Tidal Terminology • Spring tide- (from old English Springere- to rise, not season) high tide

range when sun and moon are inline at full or new moon. – MHWS : Mean High Water Spring

– MLWS : Mean Low Water Spring

• Neap tide- (Near Even As Possible) low tide range when moon & sun effect cancel each other

– MHWN : Mean High Water Neap

– MLWN : Mean Low Water Neap

MSL : Mean Sea Level (need a reference level)

• Semi-diurnal Tide- The most common tidal pattern, featuring two highs and two lows each day

• Diurnal Tide- Only a single high and a single low during each tidal day

• Flood- The tidal current when it is coming from the sea to the shore

• Ebb- The tidal current when it is coming from shore and returning to the sea

• Slack- The point between flood and ebb (or ebb and flood) currents when there is no flow.

Why we have

these different

tides?

Later…

Tidal

Range Tidal

Amplitude

Tidal water level and biological zonation along the shore

(supratidal) • never covered by

water (maybe

splash from waves)

• covered/ exposed

with the tidal cycle

• always covered by

water

(intertidal)

shore

Deep ocean

Neap

tid

e r

an

ge

Sp

rin

g t

ide r

an

ge

Why do we need to predict tides?

Example: ship navigation and access to harbor

(Cairns Harbour, Australia)

water level too low,

danger for grounding

of ships

u

Ebb Tide

Flood Tide

t

t

Low Tide

Slack water before flood

High Tide

Slack water after flood

tAt fcos)(Tide water level can be described by:

A = tidal amplitude (tidal range=2A)

= tidal frequency

= tidal phase

A

2cos)( tUtu f

The relation between tidal water level () and tidal current (u)

max & max u are “out of phase”

EQUILIBRIUM TIDE

The forces between two moving bodies (Moon & Earth)

• Centrifugal forces: push bodies away from each other

• Gravitational forces: push bodies toward each other- stronger on the side

facing the moon

• The difference between the two forces is uneven over the earth

• generate tides (if forces are in equilibrium)

Moon

Earth

What are the physical forces of tides?

Balance of forces:

2234

2

22 2

2)(

)( RPRPP

RPRGmM

P

mMG

RP

mMGFF

aatforcelcentrifuga

aatattractionnalgravitatio

ca

M

Since the Moon is relatively far compared to Earth’s radius, P>>R

33

2)(;

2)(

P

RGmMFF

P

RGmMFF cbca

m

Since F~M/P3, effect of Sun vs. Moon:

Msun=2.5x107Mmoon ; Psun=400Pmoon

Fsun ~ (2.5x107)/(400)3Fmoon ~ 0.4Fmoon

Tides in average: 60% moon and 40% sun

Gravitational Constant

G = 6.67×10-11 N m2/kg2

P=distance between center of Earth and center of Moon

R= radius of Earth

EQUILIBRIUM TIDE

However, the combined effects of lunar and solar, diurnal and

semidiurnal is more complex in the real ocean…

Why tides are different at different latitudes?

Declination (tilt) angle between the moon

and earth axis.

a useful way to characterize the tide is:

The Form factor

F = [ K1 + O1 ] / [ M2 + S2 ]

0.25 < F < 1.25 the tide is mixed

- mainly semidiurnal

F > 3 the tide is diurnal

F < 0.25 the tide is semidiurnal

1.25 < F < 3.00 the tide is mixed

- mainly diurnal

F=0.1

F=0.9

F=2.1

F=19

Equilibrium vs. Dynamic theories of tides Equilibrium theory of tides: If the entire globe

is covered with water and we sum up the forces

along the surface, the maximum “Spring Tide”

when the Moon & Sun are in line would be

always 55cm (M)+24cm(S)=79cm

However, in reality tides in different places are

very different!

Dynamic theory of tides: shallow-water waves

driven by periodic forcing- amplified when basin

in resonant with dominant periods, affected by

coastline topography and Coriolis.

Actual tides in Chesapeake Bay

The tide propagation involve both,

progressive free waves in the open

ocean and waves running along

coasts (mostly Kelvin Waves):

- long waves that travel parallel to

the coastline

- geostrophic balance with higher

sea level near the coast

- in N. Hemisphere generate

counterclockwise propagation

direction-in x decays lev-sea

direction-yin propagates wave

0 )cos(),,(gh

fx

etkytyx

Pressure

Gradient

Coriolis

x

y

Kelvin waves

propagating in opposite

direction would create a

rotating Amphidrome

Semidiurnal tide in the North Sea (“Amphidromic System”)

Amphidromic

point

Tidal propagation

(anti-clockwise in

N. Hemisphere)

Co-tidal lines: points with the same

tidal stage (phase)

Co-range lines: points with the same

tidal range (amplitude)

Tidal Patterns Vary with Ocean Basin

Shape and Size: shallow-wide basin

(a) An amphidromic system in a broad, shallow basin.

(b) The amphidromic system for the Gulf of St. Lawrence

Tidal Patterns Vary with Ocean Basin

Shape and Size: narrow basin

(a) True amphidromic systems do not develop in narrow basins because there is no space for rotation. (b) Tides in the Bay of Fundy, Nova Scotia (one of the largest tides)

How can tides be predicted? Most common: Harmonic Method

• For shallow water:

– Use long-term tide gauge

data

– Do harmonic analysis of

basic tidal constituents

(i.e., find the amplitude and

phase of each component)

– Use astronomical tables or

tidal calculators for future

tides at each location

...)sin()sin()(

12

222111 KM

tAtAt

http://tidesonline.nos.noaa.gov/

Useful resources for tidal data: NOAA Tides Online

(Data: http://tidesonline.nos.noaa.gov/)

Why are the predicted and observed tides different?

How well can we predict tides?

What about wind-driven (storm surge) variations?

November-09

Nor’Easter

Water Level:

Tides+ storm surge

Tides only

Wind:

Floods in Hague area (Nowbray St., Norfolk, VA) Minor flood: high tide (~4ft; 8-25-2012) Major flood: Hurricane Sandy (~7ft; 10-29-2012)

M2

http://www.esr.org/polar_tide_models/Model_TPXO62_load.html

useful tools for global tide prediction:

TPXO6.2 Load Tide: Global Inverse Tide Model 1/4x1/4 developed at Oregon State University, based on

assimilation of T/P altimetry with corrections for coastal oceans.

(code available in Fortran and Matlab)

Run Matlab Tide

Model simulations in Cook Inlet, Alaska,

where the inlet size creates a perfect

resonant with the tidal period (M2)

(Oey & Ezer et al., 2007)

H=50m depth; L=250km long

C=(gH)½ = 22 m/s propagation speed

Resonant: T=4L/C = ~12h

(M2 period=12.42h)

The amplification of the tides in the inlet are simulated quite well

Kodiak Island

Seldovia

Nikiski

Anchorage

mod

obs

Tidal Bores over the mud flats in

Turnagain Arm of Cook Inlet:

big tourist attraction (and a

challenge for surfers…)

2m high, 3-5 m/s propagation speed

ebb

flood

m/s

Velocity and tide level in Turnagain Arm

Cook Inlet, Alaska Low Tide

High Tide

Bay of Fundy: Max. Spring Tide: 17 m

•Shape of basin

•Oscillation period close to tidal period

•Shoals and narrows to north

•Basin oriented toward right (Coriolis

moves water toward right)

finished with waves and tides…

Next Classes:

• Monday 25-November

– Coastal processes and estuarine circulation

• Wednesday 27-November: Happy Thanksgiving

• Monday 02-December: Review for Final Exam

• Wednesday 04-December 5:00pm Final Exam?