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Home , Tidal force

EAS 220 Spring 2009 The System Lecture 22

Waves, , and Coasts How do waves & tides affect us? Navigation & Shipping Coastal Structures Off-Shore Structures (oil platforms) Beach erosion, sediment transport Recreation Fishing Potential energy source Waves - Fundamental Principles Ideally, waves represent a propagation of energy, not matter. (as we will see, waves are not always ideal). Three kinds: Longitudinal (e.g., sound wave) Transverse (e.g., seismic “S” wave) - only in solids Surface, or orbital, wave Occur at the interfaces of two materials of different densities. These are the common wind-generated waves. (also seismic Love and Rayleigh waves) Idealized motion is circular, with circles becoming smaller with depth. Some Definitions Wave Period: Time it Takes a Wave Crest to Travel one Wavelength (units of time) Wave Frequency: Number of Crests Passing A Fixed Location per Unit Time (units of 1/time) Frequency = 1/Period Wave Speed: Distance a Wave Crest Travels per Unit Time (units of distance/time) Wave Speed = Wave Length / Wave Period for deep waves only Wave Amplitude: /2 Wave Steepness: Wave Height/Wavelength Generation of Waves Most surface waves generated by wind (therefore, also called wind waves) Waves are also generated by Earthquakes, landslides — Atmospheric pressure changes (storms) Gravity of the and — tides Generation of Wind Waves For very small waves, the restoring force is surface tension. These waves are called capillary waves For larger waves, the restoring force is gravity These waves are sometimes called gravity waves Waves propagate because these restoring forces overshoot (just like gravity does with a pendulum). Height of Wind-Generated Waves depends on: Wind Speed Duration of Wind Event

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Fetch - the distance over which wind can blow without obstruction Waves and Once generated, waves can propagate as swell without wind : Waves of different sizes travel at different speeds Large ones travel faster Damping Because waves are not ideal, energy is dissipated and waves die out Small ones die out, or damp out, faster. Large waves can easily travel across an ocean without damping out. Deep- and Shallow-Water Waves Deep-Water waves travel in water that is deeper than 1/2 the wave’s wavelength Depth > L/2 Deep water waves have nearly ideal shape and thus propagate energy but very little mass. Shallow-Water waves travel in water that is shallower than 1/20 of the wave’s wavelength Depth < L/20 Shallow water waves are not ideal and propagate both energy and mass. Intermediate waves are neither purely “deep” nor “shallow”. L/20 < Bottom Depth < L/2 Wave Speeds Deep-Water Waves (Bottom Depth > L/2) Speed is a Function of Wavelength Only Speed = Wave Length / Wave Period Waves with Longer Wavelength move faster than Waves with Shorter Wavelength Shallow-Water Waves (Bottom Depth < L/20) Speed is a Function of Depth Only Speed = 3.13 × (depth)1/2 At intermediate depths (L/20 < Depth < L/2) Wave Speed is a Complicated Function of Both Wavelength & Depth Breaking Waves As waves approach the shore, drag of the bottom slows the water motion near bottom wavelength decreases, while height and steepness increase Consequently, there is net forward transport at the surface as the waves steepens. Once height reaches 1/7 wave length, the wave becomes unstable and breaks. Tsunamis Tsunamis (sometimes improperly called tidal waves) are large amplitude, long wavelength waves that propagate on the ocean surface Tsunamis can be generated by Earthquakes Explosive Volcanic Eruptions (where are these most likely to happen?) Landslides Meteorite/Asteroid Impact Properties of Tsunamis Tsunamis have long periods and long wavelengths (as long as 1 hour and 100 km

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respectively). Water motion is primarily horizontal (back & forth) Wavelength is always greater than twice the water depth for tsunamis. Therefore, tsunamis always behave as shallow water waves everywhere (speed depends on depth). In water of average depth (4000 m), a will travel at 700 km/hr. What areas are vulnerable to tsunamis? Pacific Rim is most vulnerable Hawaii is particularly vulnerable Japan, Alaska, S. America Pacific Northwest The plate boundary system in the Pacific NW is behaves very similarly to the Indonesia one, with very large, very infrequent earthquakes. Geologic evidence and Japanese historical records indicate a very large tsunami was generated there in 1700. Indian Ocean Atlantic and Caribbean Many of the Caribbean islands are zone volcanoes - in addition to earthquakes, volcanic eruptions and volcanic landslides could generate tsunamis Eastern Mediterranean Both volcanically and seismically active Salt beds beneath Mediterranean are particularly subject to landslides. Tides Equilibrium model of Tides wave treated as a deep-water wave in equilibrium with lunar/solar forcing No interference of tide wave propagation by continents No Effect. Combined effects of gravitational and centrifugal forces on produce simple diurnal tides Tidal Day = 24h + 50min Complications Tides vary by location and through time. Diurnal : 1 daily cycle Semidiurnal: 2 cycles Mixed: 2 unequal cycles Why don’t we see simple diurnal tidal patterns always and everywhere? The moon’s is inclined up to 28.5o relative to the Earth’s equator and this produces different tidal patterns at different latitudes (varies between 18.5 & 28.5° over 18 years). The Sun Wave-like behavior of tides The Sun and Spring & Neap Tides The tidal force exerted on the Earth by the Sun is about half (46%) that the exerted on the Earth by the Moon. Spring Tide is a higher than normal that occurs when the Moon is aligned with the Sun and pulls in the same direction (new and ). Neap Tide is a lower than normal tidal range that occurs when the Moon pulls at 90˚ to the Sun (first and last quarter moon). Dynamic

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A more sophisticated view of tides Tidal wave treated as a shallow-water wave not in equilibrium with lunar/solar forcing (a forced wave). considered Continents interfere with tidal wave propagation Tide Waves Are Shallow-Water Waves The tidal wave has wavelength (L) on the order of 1/2 the circumference of the earth or about 20,000 km. A wave will behave as a shallow water wave when depth < L/20 — in this case, for depth < 1000km. Since ocean bottom depths are typically only about 4 km, it is safe to assume that a tide wave is a shallow-water wave everywhere Since speed depends on depth, tidal wave can be refracted by Tidal Waves Are Forced Shallow-Water Waves As a free shallow water wave, tide wave speed would be determined by ocean bottom depth alone but this is not the case… The wave speed for a shallow water wave in 4km of water is 200m/sec (400 miles/hr). The speed that the earth rotates under the moon at the equator is 463m/sec (1044 miles/hr). As a consequence, ocean depth alone does not determine the tide wave. Earth’s rotation and frictional bottom drag on the Tidal Wave causes the tidal bulge to be pulled in front of the direct line to the Moon Coriolis Force causes rotation of tidal wave and currents Tidal current rotate clockwise in northern hemisphere (as expected), but tidal wave rotates counter clockwise! Areas of Extreme Tidal Range Examples: Northwestern Europe (Mont St. Michel) Bay of Fundy (Maine, New Brunswick) Tidal Bores, e.g., Seine, Amazon, Qiantang Why are tides so large? Resonance When the forcing frequency matches free wave frequency, a phenomenon called resonance occurs – The free wave interacts with the forced wave to produces a much larger wave than would otherwise occur. Other factors… Basin geometry Reflects and focuses tidal wave Wave cannot rotate in narrow basins, just sloshes back & forth Shoaling water depths Types of Coasts Primary Coasts shaped by non-marine (subaerial) processes Including

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Faulting, Folding, Volcanism Subaerial erosion (e.g., drowned river valleys, glacial erosion) Subaerial deposition (e.g., river deltas, landslides) Secondary Coasts shaped by marine processes Including those shaped by: Wave erosion Marine deposition Marine biological activity (corals, mangroves, etc). Secondary coasts are more mature, closer to equilibrium. Example of Primary Coasts Fjord Drowned River Valley Examples of Secondary Coasts Wave Eroded Cliffs Barrier Islands Marine Terraces on the California Coast Terraces are common along the California coast. Reflect a combination of quick uplift (e.g., in an earthquake) and slow work of waves, hence are strictly neither primary nor secondary.

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