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ZOn moonward side of Earth, gravitational attraction is greater, so particles are accelerated toward moon On side of Earth facing away from moon, inertial effects related to earth s circular path exceed gravitational attraction, so particles are accelerated away from the moon Accelerations perpendicular to earth s surface are miniscule - on the order of one millionth of Earth s gravitational attraction Accelerations parallel to Earth s surface are more effective  they displace water into two bulges, one on side facing moon & one on side away from moonx.C&~,4  . teEquilibrium tide&$   If Earth rotates beneath the two bulges, points experience semidiurnal tides Call this the equilibrium tide Refinements to equilibrium theory include: Plane of moon s orbit is inclined 61.5 to Earth s rotation axis - expect daily inequity that varies with a monthly cycle Moon s orbit is elliptical - expect variation in magnitude of bulge with a 27.55 day cycle 4.)2 A n ufSolar equilibrium tide&$   Earth-sun interactions produce ocean tides Earth-moon distance = 59 x RE; Mass of moon 1/82 mass of earth Earth-sun distance = 23,000 x RE; Mass of sun 330,00 x mass of earth Solar tide is 47% of that generated by earth moon interactions Solar tide has 12 hr period; see effects of tilt of rotation axis & elliptical orbit, too Add lunar & solar equilibrium tides together to get spring & neap tide+ZZGZ+ B 30ff #  vg%Shortcomings of the equilibrium model&&%$  & [It predicts semidiurnal tides at all locations - not observed It predicts that high tides should occur when moon passes overhead or 12 hours 25 minutes later - rarely observed Calculations suggest that tidal ranges should be 20-50 cm - observed tidal ranges are often much larger It predicts values for daily inequities that are rarely observed \Z1 d>,1 \ }o4What is wrong with equilibrium model for the tides? "53(( 5 It ignores the fact that ocean basins have irregular shapes, that bulges must respond to friction in moving through basins, & that water itself has inertia once it is movingj+3  whDynamic theory for tides&$   Begins where equilibrium model ends, i.e. with two bulges created by gravitational/inertial interactions of Earth & moon Explains real tides by envisioning tidal bulges as tidal wave Tidal wave has small wave height - about 50 cm in open ocean Tidal wave has very long wavelength, about one half earth s circumference = 20,000 kmxL -3 L ~pThe tidal wave&$   Wavelength (L) of tidal wave = 1/2 Earth s circumference = 20,000 km Water depth of oceans = 4 km <<< L/2 Tidal wave is a shallow water wave everywhere, i.e. it interacts continually with the ocean bottom As a shallow water wave, tidal wave feels the bottom, slows, steepens, & sometimes breaks Tidal wave reflects, refracts, & interferes with other waves or with reflections of itselfLZ P m  0  xiStanding waves&$   Have a wave with long wavelength (L) in a rectangular basin of uniform depth (D) Wave advances across basin, reflects off boundary, & travels back across basin Given enough time, a regular wave will interfere to produce a standing or stationary wave Where water level does not change = nodal line (node) Where water level changes the most = antinodal lines (antinodes) Oscillation period for standing wave with one node = [2 x L]/ [g x D]1/2 (depends on basin length & depth) Length & depth dependence holds for all standing wavesV$ ( K   7  qyjTidal standing waves&$   (Tidal standing waves are not free waves, where generating force acts only at the outset Tidal standing waves are forced waves, where the wave generating force(s) continue(s) to act as the system responds Each passage of the moon overhead is another disturbing force Complicated wave motion in any basin is the sum of latest disturbance interacting with waves generated by numerous previous passes overhead Depending on the shape of a basin, the net result may be a standing wave that corresponds to a diurnal tide, a semidiurnal tide, or a mixed tide)Z K     ) zk Kelvin waves& $   Special kind of standing wave seen in large basins where masses of water experience the Coriolis effect Wave crest swings about the basin margin like water swirling in a glass Nodal point, called an amphidromic point, occurs near the center of the basin Co-tidal lines - connect points that have high tides at the same time, typically measured in hours after the moon crosses the Greenwich meridian Co-range lines connect points that have equal tidal ranges&f-6X  h    rs  ?Amphidromic point (node) occurs near center of the basin Co-tidal lines connect points that have high tides at the same time (denoted by hours after the moon crossed the Greenwich meridian) Co-range lines connect points that have equal tidal ranges Co-tidal lines are spokes; co-range lines are closed loops about node v@Z(vs  5 {lTidal currents&$    Can understand tidal currents by envisioning tide as one of three types of wave Progressive wave tide - where coast is too irregular to give pronounced reflection, so no standing wave High tide = wave crest; low tide = wave trough Flood current coincides with high tide; ebb current coincides with low tide Standing wave tide - in confined rectangular basin Slack water coincides with high or low water level Flood and ebb currents coincide with mean water level Kelvin wave tide - azimuth & magnitude of currents may varyZ|Z3ZjZ<ZPS|!j+  W  ` ̙33` ` ff3333f` 333MMM` f` f` 3` ):@+H` ):@+H`  4@+H>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> +#(    6  P P V Click to edit Master title style! !   0$   P RClick to edit Master text styles Second level Third level Fourth level Fifth level!     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