Lec 11: Waves in shallow water/tsunamis

• Deep Water Waves


  • Crest-to-crest speed
  • Wavelength

  
• What happens when waves interact with seafloor

  1. Seafloor prevents water particles from moving in circular orbits

  2. Distorts orbits into elongated ellipses

  3. Compression and friction slows forward motion

  
• Shallow Water Waves


  Horizontal oval-shaped movement

  
• As water depth decreases

  Wave speed decreases

  
• Intermediate-water waves

  Wave speed equation is quite complex

  
• Shallow Water Waves


  Wave speed is controlled only by water depth

  
• As waves enter shallow water and are slowed

  Period does not change

  
• As waves enter shallow water and are slowed

  Wavelength decreases

  
• As waves continue towards shore

  Leading wave is in shallower water and moving slower, allowing trailing wave to catch up

  
• As waves enter shallow water

  Speed decreases, wavelength decreases, height increases, steepness increases

  
• Deep-water waves


  • Water depth greater than wave base, wave does not "feel" the bottom, speed varies only with wavelength

  
• Shallow-water waves


  • Water depth much smaller than wave base, wave "feels" the bottom, speed varies with water depth

  
• Intermediate-water waves


  • L/20 < D < L/2, mix between deep and shallow water waves, speed varies partially with water depth and partially with wavelength

  
• Wave Refraction


  Bending of shallow water waves due to changes in water depth

  
• Waves usually approach the shore at an angle

  
• Wave refraction

  Waves normally end up reaching the shore almost parallel to it

  
• Wave refraction can be as complicated as the seafloor topography

  
• Wave refraction in a bay flanked by headlands

  Wave slows first in shallow areas in front of headlands, continues at original speed over deeper water in center, ends up breaking almost parallel to coast

  
• Wave refraction


  Redistributes wave energy, reduces height in bays, increases height at headlands
• Surf Zone


  Area offshore within which waves are breaking

  
• Breaking Waves


  • Spilling, Plunging, Collapsing, Surging

  
• Surfers position their board on the upward moving part of the wave orbit
• Wave conditions for surfing generally better on west coast than east coast of North America
• Rip Currents

  Fast offshore currents caused by water dumped nearshore by breakers

  
• Tsunamis

  Caused by abrupt displacements of ocean water, originate from sudden changes in seafloor topography
• Majority of tsunamis caused by vertical displacements of seafloor along faults
• Tsunami characteristics

  • Typical wavelength exceeds 200 km, behave as shallow-water waves, speed determined by water depth, have much longer periods than wind waves, lose little energy over long distances
• In the open ocean

  Tsunamis move over 700 km/h, have heights of only 1 m or less
• A tsunami does not form a huge breaking wave at the shoreline
• Coastal Effects of Tsunamis

  Strong flood or surge of water, resembles a sudden high tide, may take several minutes to fully express, sea level may rise up to 40 m
• Tsunamis are a series of waves, with alternating surges and withdrawals of water
• The trough may arrive at the coast first, speed of advance can be up to 4 m/s
• Tsunami


  • Does not break at the shoreline
  • Instead, it is a strong flood or surge of water that causes the ocean to advance / retreat dramatically
  • Resembles a sudden, extremely high tide
  • Often misnamed "tidal waves" but have NO relation to tides
  • It may take several minutes for a tsunami to express itself fully
  • Sea level may rise up to 40 m above normal
• Tsunami arrival at shore

  1. Trough arrives first (on the side of the fault where the seafloor drops down)

  2. Water rapidly drains off the land

  3. Crest arrives next

  4. Tsunamis are a series of waves → alternating series of dramatic surges and withdrawals of water widely separated in time (5 to 10 minutes)

  5. The first surge is rarely the largest

  6. Speed of advance (up to 4m/s) is faster than any human can run
• Tsunami magnitude

  • Depends partly on the size of an earthquake
  • Earthquake intensity usually given as a Richter Scale magnitude
  • Magnitude is a measure of the strength of an earthquake or strain energy released by it
  • Non-linear scale: An increase of one unit of magnitude (for example, from 8.1 to 9.1) represents a 10-fold increase in wave amplitude on a seismogram or approximately a 30-fold increase in the energy released
• Tsunami examples

  • Krakatoa, 1883
  • Indian Ocean, 2004 Boxing Day
  • Japan, 2011
• Krakatoa tsunami, 1883


  • Volcano exploded with the greatest release of energy from Earth's interior ever recorded
  • Instantly blew a large fraction of the island's mass into the air
  • The sound of the explosion was heard throughout the Indian Ocean up to 4800 km away → loudest noise on human record
  • Brilliant red sunsets worldwide for nearly a year
  • The island was inhabited, but the tsunami generated (35 m high) took more than 36,000 lives
  • Detected by tide gouges in London and San Francisco
• Indian Ocean tsunami, 2004 Boxing Day


  • Earthquake was so large that it changed Earth's rotation a bit (magnitude 9.2)
  • 1200 km of seafloor was ruptured, thrusting seafloor upward and generating about 10 m of vertical displacement
  • Wavelength of about 500 km
  • Jason-1 altimeter was able to capture sea level two hours after the tsunami was originated
  • Fatalities: between 230,000 and 300,000
  • Lack of a warning system in the Indian Ocean (now operational since 2010)
• Japan tsunami, 2011

  • Earthquake magnitude 9.0
  • Shifted the coast of Japan 8 m eastward
  • Lifted the seafloor by 5 m
  • Initially, warning of 3-6 m tsunami
  • Warning reissued for 10 m tsunami – but by then power supply system was destroyed – nobody got the new forecast
  • At one place, tsunami reached 40 m
  • Fatalities: 19,508; displaced nearly half million people
  • Fukushima
• Waves

  • Energy and waveform travel through matter
  • Very small net transport of water due to waves – Stokes Drift
  • Crest, trough, wavelength (L), height (H), period (T), frequency (1/T), steepness (H/L), speed (C=L/T)
  • Wave motion: orbital movement of particles
  • Orbits get smaller with depth
  • Wave motion happen in the layer between the surface and wave base (L/2)
  • If the water depth is the same or smaller than wave base, wave starts to "feel" the bottom
  • Wave becomes unstable and break if they are steeper than 1/7