Tides, Gravity, Centripetal force

Fig. 10-7

Fig. 10-6

Tide-producing forces

Gravity and motions among Earth, Moon, and Sun.

Barycenter, and centroid Fig. 10-2

Centripetal force “tethers” Moon to Earth Directed away

from barycenter

Fig. 10-4 a,b

Resultant tidal forces

Gravitational force, Earth and Moon

Centripetal force, Earth and Moon

Resultant force moves ocean water horizontallyFig. 10-7

Fig. 10-6

Tidal bulges Two equal and

opposite tidal bulges

Earth rotates beneath tidal bulges

Two high tides Two low tides Per day Fig. 10-8

Complications to simplest equilibrium theory

Oceans do not cover entire Earth Oceans do not have uniform depth Friction between ocean and

seafloor Continents Moon not always in same place

with respect to Earth Lunar day longer than solar day

Lunar day Moon revolves around Earth Earth has to “catch up” with Moon

to reach same position

Fig. 10-9

Time between successive high tides shifts day after day

Moon rises later each successive night

Solar tidal bulges

Tide-producing force of Sun less than half of Moon’s since Sun much farther away

Month tidal cycle Spring tides

New Moon, Full Moon

Earth, Moon, Sun align (syzygy)

Higher than usual high tides

Fig. 10-12

Neap tide First Quarter,

Last Quarter Earth, Moon,

Sun quadrature

Lower than usual high tide

Fig. 10-12

Declination of Sun and Moon

Orientation of Sun, Moon to Earth’s equator Sun 23.5o N and S, yearly cycle Moon 28.5o N and S, monthly

cycle Unequal tides

Successive tides different tidal range

Unequal tidal range

Fig. 10-15

Elliptical orbits Perigee

Lunar tidal force greater

Higher high tides

Apogee Lunar tidal force

lesser Lower high tides Fig. 10-16

Dynamic theory of tides

Tide shallow-water wave Speed varies with depth Lags behind Earth’s rotation

Rotary flow in open ocean basins Amphidromic point (‘panning for

gold’) Cotidal lines

Rotary flow

Crest (high tide) rotates Counterclockwise in

Northern Hemisphere Clockwise in Southern

Hemisphere

Tidal patterns

Diurnal One high, one low tide per lunar day Period of tidal cycle 24 hours 50

minutes Semidiurnal

Two high, two low tides per lunar day Period 12 hours 25 minutes Equal range

Mixed Two high, two low tides per lunar day

Unequal range Most tides are mixed

Standing waves

Forced standing wave caused by tides

Free-standing waves caused by strong winds or seismic disturbances Fig. 10-22

Node maximum horizontal flow

Antinode maximum vertical flow

Fig. 10-23

Bay of Fundy Largest tidal range

(spring tide max 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)

Fig. 10-24

Tidal bores

Wave created by tide rushes upstream

Large tidal range Low-lying coastal

river Max 8 m = more

than 25 feet high