lec 12: Tides

• Tide

  Periodic raising and lowering of sea level that occurs daily
• Tide

  • Very long (wavelength and period) shallow-water waves
  • High tides are associated with the wave crest
  • Low tides are associated with the wave trough
  • The vertical motion can be as much as 10-15 metres, twice a day in some areas

  
• Bay of Fundy, NS


  • Largest tidal range in the world (up to 17 meters)
• Flood currents

  Incoming currents associated with rising tides
• Ebb currents


  Outgoing currents associated with decreasing tides

  
• Importance of tides

  • Navigation
  • Marine creatures
  • Energy
  • Internal waves generated over topography / mixing
  • Re-suspension of bottom sediment
• Gravitational attraction


  Every object that has mass in the universe is attracted to every other object
• Gravitational force

  • Directly proportional to their masses
  • Inversely proportional to the square of the distance between the two bodies

  
• Barycenter


  The balance point of the Earth-Moon system, located ~1600 km beneath the Earth's surface

  
• The Earth-Moon system rotates about its centre of mass, with one complete revolution approximately every month (27.3 days)

  
• Orbital velocity


  The velocity required to maintain an orbit, balanced by the centripetal force
• If the centripetal force changes


  The motion also changes (the object either flies off tangentially or spirals in)
• Tide generating force (TGF)


  Proportional to the mass and inversely proportional to the cube of the distance between the objects (TGF ~ Mass/ Distance^3)

  
• The moon exerts over two times the gravitational pull of the Sun on tides, because the moon is much closer to Earth, although it is much smaller in size and mass compared to the Sun

  
• The tide generating forces are one-millionth of the Earth's gravitational acceleration (g)
• Tidal bulges


  • Water gets squeezed toward the equator by the tide generating forces, creating two bulges - one under and one opposite the moon
  • The bulges stay aligned with the moon as it rotates

  
• Solar day


  Time for a specific point on the earth to rotate from an exact point under the sun back to that same exact point (24 h)
• Lunar day


  Time it takes for a specific site on the Earth to rotate from an exact point under the moon to the same point under the moon (24h50min)

  
• Earth rotates through 2 tidal bulges each lunar day, thus giving two high tides
• The period between high tides is 12hr 25min, with high tide 50min later each successive day
• Spring tides

  Occur when the sun and moon are aligned, and their gravitational pulls combine to produce the highest (and lowest) tides
• Neap tides


  Occur when the sun and moon are at right angles, and their gravitational pulls partially cancel each other out, producing moderate tides
• Tides

  Periodic rise and fall of the sea level caused by the gravitational pull of the moon and sun

  
• Moon's rotation

  Causes tides to be aligned with the moon

  
• Tides

  • Many locations experience two high tides and two low tides each day
  • Extra length is because moon revolves around the earth in the same direction as the earth rotates around its axis, needing the extra 50 minutes to "catch up"

  
• If you moved to N or S of the equator, you would experience the same tidal period but the high tides would be less high
• Period between high tides


  12hr 25min
• High tide


  50min later each successive day (just as Moon rises 50min later in the sky every day)
• Spring tides


  When the sun and moon are aligned, the solar bulge has an additive effect on the lunar bulge, creating extra high and very low tides
• Neap tides


  When the sun and moon are at right angles to each other, their bulges partially cancel out, producing more moderate tides
• Monthly tidal cycle = 29.5 days (2 spring tides, 2 neap tides)
• Declination

  The angular distance of the Sun or Moon above or below Earth's equatorial plane

  
• Maximum declination of the Sun relative to Earth's equator is 23.5°
• The plane of the Moon's orbit is tilted 5° with respect to the ecliptic (plane around which the Earth revolves around the Sun)

  
• The maximum declination of the Moon's orbit relative to Earth's equator is 28.5°

  
• As a result, tidal bulges move from 28.5°N to 28.5°S during multiple lunar cycles within one year
• Elliptical orbits

  • The Earth has an elliptical orbit around the Sun (distance varies 2.5% over the year)
  • The moon's orbit is also elliptical, with an 8% variance in distance

  
• Elliptical orbits produce changes in tidal amplitude
• The net result is that spring tides have greater ranges during the NH winter and when they coincide with perigee
• Any location (except the poles) will have two high tides and two low tides per lunar day