Lecture 8 Tides, tidal mixing and internal waves

The Physics of Tides

• Tides result from a slight imbalance between two forces:

(1) Gravitational pull of the moon and sun, (2) Centripetal force required to keep the

ocean’s water along with earth and sun rotating in the earth-moon pair.

1. Gravitational force exerted by the moon and sun vary over the earth's surface;

2/ rGMMF

me=

Mass of earth

Mass of sea water

Distance between moon (or sun) and waters on earth.

Constant

Only experience on high an low tides once a day, not realistic

2. Total centrifugal force: the force that maintains the circular motion and in the case of the earth –moon system, it keeps the earth at their nearly constant distance apart and supplied by the gravitational between two bodies.

The force is always directed toward the center of the circle and has equal size for every particle.

About 29.5 day for one circle

•On the half closest to the moon, the gravitational force is greater than the centripetal that causes the ocean to pile up.

•On the half of the earth away from the moon, the gravitational force is not strong enough to supply all the centrifugal force required to keep that water particles moving in the required circle so that a mass will behave as though there were a outward force as it rotates in earth-moon pair

1. Fb and Fd: F/Me=GMm/r2

Fa>Fc (3% diff.)CF: Centripetal force

2. F(a,b,c,d)-CF=Tide-producing forcesis slightly less thanCF so that a mass Will behave as thoughthere were a outward force

•The earth and moon rotate around one another in a lunar month is roughly 29.5 days.

•Since earth spins on its axis at about 4 minutes per degree the tides will appear about 50 minutes later every day.

•Moon’s orbit around the earth is tilted at an angle to the equator.

•Observer at O notices that there are two high and two low tides but that the high tides are of unequal height, as are the low tides. This s called diurnal inequality.

•The mass of the sun is 27x106 times the mass of the moon, but its distance from the earth is 400 times that of the moon.•The gravitational force is only half that due to the moon.•When the tidal bulges (both from moon and sun) coincide they create the extra high tides called the spring tides. On the contrary, it is called neap tides.

• Tides produced by the moon • M2 (semi-diurnal lunar) 1/2 lunar day =

12h 25min • O1 (diurnal lunar) 1 lunar day = 24h

50min• Tides produced by the sun • S2 (semidiurnal solar) 1/2 solar day =

12h • K1 (diurnal solar) 1 solar day = 24h

• The form factor F is used to classify tides. It is defined as

• F = ( K1 + O1 ) / ( M2 + S2 ) • where the symbols of the constituents

indicate their respective amplitudes. Four categories are distinguished : F: 0 - 0.25 semidiurnalF: 0.25 - 1.5 mixed, mainly semidiurnalF: 1.5 – 3 mixed, mainly diurnalF: > 3 diurnal

Tidal currents:

• In narrow passage, tidal currents, in general, are strong and the max. current speeds will be at the middle of the rise or fall, with slack water near high or low water.

• Flood current: tide is rising and Ebb current: tide is falling

Coastal trapped waves and other oscillations

• The local convergence or divergence along the coast increases or decrease local sea level, which leads to the formation of local pressure gradient

• The resulting currents from the local pressure gradient lead to the propagation of these local increased or decreased sea level (i.e. wave propagation)

Kelvin Wave• largest amplitude at the coast, amplitude

falls off exponentially towards the open ocean;

• Propagate in the direction with coastline on its right in the NH and on its left in the SH;

• Its existence requires coastline, but not shelf.

• Tidal bulge moves with Kelvin waves.

Tides in real ocean

Internal Waves

The convergence and divergence has significant biological impacts

The Biological Significance of Internal Waves

• Internal waves as a nutrient pumps

Convergence: Cause floating organic matter to accumulate. Trajectories of water particles and breaking wave enhance mixing in the water.

The inorganic nitrate and chlorophyll are significant higher in the waters with internal waves.

Internal waves and phytoplankton production

• Internal waves traveling the pycnocline are likely both to increase turbulent transport of nutrients and to cause the phytoplankton to oscillate in depth, thereby increasing the light intensity experienced by light-limited phytoplankton cells at the lower layer.

Internal waves concentrate and transport planktonic organisms

Concentration of organisms (no net advection of cells and no net shoreward movement of water)

•Increase of organism concentration and aggregations.

•Planktonicorganisms become associated with the aggregations.

Aggregation and transport of organisms:

Shoreward accumulation of crab larvae and fish larvae during the‘downwelling’ phase’

The breaking internal waves (or bores) will enhance vertical mixing.

Transport (upwelling and downwelling) related to arrival of tide-induced internal wave (bore)

Major currents, gyres, rings, and eddies (basin scale)

• Winds and wind-driven basin circulation• Meanders, rings, eddies and gyres• The thermohaline circulation

Winds and wind-driven basin circulation

Winds

Unevenly heating by the sun

Spinning sphere

Subtropical gyre

Strong and narrow western boundary current

Subtropical gyre

Subpolar gyre

1. The Coriolis force causes the moving water to be deflected to the right of the right of the wind (in NH). The net effect of winds in the upper ocean is a flow perpendicular to the wind (i.e. Ekman transport).

2. The strong western boundary currents are formed due to the variation of the Coriolis parameter with latitude.

Meanders, rings, eddies and gyres

gyre

•Meanders: Jet stream develop large oscillations caused by its unstable.

•Rings: Eddy pinched off from meander as it become too large.

Anticlockwise and clockwise rotating rings are cold and warm rings, respectively.

They contain water from the opposite side of the stream having the other side’s physical, chemical and biological properties.

The interaction of meander and rings create significant vertical transports of nutrient and plankton which enhance biological activity

•Eddies: The closed circulation with horizontal scale of 10-100km and time scale of 10-30 days. The upward and downward vertical velocities in cyclonic and anticyclonic will enhance biological productivity, respectively.

High surface Chl-a

•Gyres: A circular current that is confined by or associated with bathymetric features and covers a wide range of spatial scales.

The Thermohaline Circulation (north-south vertical circulation

Sinking of dense water due to cooling in mid to high latitude.