Capillary Waves, Wind Waves, Chapter 10 Waves Anatomy of a Wave more like a real wave Tsunamis, Internal waves big waves huge waves rogue waves small waves more like a sine wave Wave direction Wave wave energy NOT the water particles moves across the surface of the sea * Wavelength * height * Crest * trough * amplitude Parts of a Wave wave form moves and with it, energy is transmitted * Frequency - # of waves passing a fixed point in a given length of time * Period - time for successive crests or troughs (1 wavelength) to pass a fixed point Direction of wave motion Direction of wave motion A Wavelength Height B Wave-length Still water Crest Trough level Crest Still water level Crest Trough Frequency: Number of wave crests passing point A or point B each second Period: Time required for wave crest at point A to reach point B Orbital path of individual water molecule at water surface 1/2 wavelength depth Fig. 10-2, p. 266 1
If we had this below, then there would be no net mass transport and no contribution of waves to the surface currents No mass transport BUT Wave in reality orbits are not exactly closed and waves DO contribute to mass transport Stokes drift (mass transport) Wave Disturbing force Restoring force Gravity Seismic disruption landslides Gravity Wind Surface tension Type of wave Tide Tsunami Seiche Wind wave Capillary wave (ripple) Amount of energy in ocean surface Period (& wavelength) and Wave Energy 2412 hr. hr. 100,000 sec (1 1/4 days) 10,000 sec 1,000 sec 100 sec 10 sec 1 sec 1/10 sec 1/100 sec (3 hr) (17 min) Closed orbit after one period Open orbit after one period Period (time, in seconds for 1 10 100 two successive wave crests to pass a fixed point) Frequency (waves per second) How do a waves form? Wind blowing across calm water if gentle breeze capillary waves. Generating force = wind; restoring force = surface tension (cohesion); grow up to a wavelength of about 2 centimeters As wind speed increases - wave becomes larger. Generating force = wind; restoring force changes from surface tension to gravity Types of waves - (1) progressive & (2) standing waves (1) progressive = have a speed and move in a direction surface waves: deep-water & shallow-water waves big waves: large swells, tsunamis & episodic waves internal waves at the pycnocline (2) standing waves or seiches - do not progress, they are progressive waves reflected back on themselves and appear as alternating troughs and crests at a fixed position called antinodes, oscillating about a fixed point called node. They occur in ocean basins, enclosed bays and seas, harbors and in estuaries. Deep- to Shallow-Water Waves Progressive Waves Wave Speed L A H Keep in mind: wave energy, NOT the water particles move across the surface of the sea. Wave propagates with C, energy moves with V Wave Speed is C - Group Speed is V wave speed = wavelength / period or C = L / T T is determined by generating force so it remain the same after the wave formed, but C changes. In general, the longer the wavelength the faster the wave energy will move through the water. 2
Deep Water Waves Period to about 20 seconds Wavelength to at most 600 meters (extreme) Speed to about 100 kilometers/hour (70 mi/hr) (extreme) gl gt C = = 1.25 L = = 1. 56T 2π 2π For example, for a 300 meters wave and 14 sec period, the speed is about 22 meters per second Shallow-Water Waves surface waves generated by wind and progressing in waters of D less than (1/20) L wave motion: as the wave moves through, water particles move in elliptical orbits diameter of orbits remains the same with depth, orbits do reach the bottom where they flatten to just an oscillating motion back and forth along the bottom * The wave speed and the wavelength are controlled by the depth D of the waters only: C = gd =3. 1 D * Group Speed (which transport the energy) is the same as the wave speed for shallow-water waves: V = C Deep Water Waves * surface waves progressing in waters of D larger than 1/2 L * as the wave moves through, water particles move in circular orbit * diameter of orbits decrease with depth, orbits do not reach bottom, particles do not move below a depth D = L/2 * The wave speed can be calculated from knowledge of either the wavelength or the wave period: C = 1.56 m/s 2 T or C 2 = 1.56 m/s 2 L * Group Speed (which really transport the energy) is half of the wave speed for deep-water waves: V = C/2 Wind Blowing over the Ocean Generates Waves Waves development and growth are affected by: Wind Speed: velocity at which the wind is blowing Fetch: distance over which the wind is blowing Duration: length of time wind blows over a given area Larger Swell Move Faster waves separate into groups wave separation is called dispersion Shallow-Water Waves C = gd =3. 1 D Storm centers and dispersion Winds flow around low pressure Variety of periods and heights are generated grouped into wave trains Seismic Sea Waves Shallow-Water Waves Period to about 20 minutes Wavelength of about 200 kilometers Speed of about 750-800 km/hr (close to 500 mi/hr!!) Waves with longer period (T) and larger length move faster - these get ahead of the pack. Wave sorting of these free waves is dispersion 3
Wave Train ( pack, group) wave 1 transfers ½ of its energy to water (gets orbital motion going) and ½ to wave 2 (to keep that going) wave 1 disappear later 2 and 3 and so on will disappear also as wave 6, 7, etc. form waves 1, 2, 3, etc. move at their deep-water wave speed C but the wave train moves at ½ of C = V, the group velocity, speed at which energy moves forward Dispersion only affects deepwater waves, as depth decreases waves become shallow-water waves, they slow down until C=V 5 4 3 2 1 6 5 4 3 2 1 6 5 4 3 2 7 6 5 4 3 7 6 5 4 3 7 6 5 4 8 7 6 5 8 7 6 5 Wave Height, Wavelength & Wave Steepness Typical ratio wave height to wavelength in open ocean = 1:7 = wave steepness angle of the crest = 120 Exceed these conditions and wave will break at sea whitecaps 120 7 across 1 high Wave Height is controlled by (1) wind speed, (2) wind duration and (3) fetch (= the distance over water that the wind blows in the same direction and waves are generated) Significant Wave Height - average wave height of the highest one-third of the waves measured over a long time Fetch: uninterrupted distance over which the wind blows without significant change in direction. Wind Speed, Fetch & Duration Wave Interaction - Interference Wave size increases with increased wind speed, duration, and fetch. A strong wind must blow continuously in one direction for nearly three days for the largest waves to develop fully. Pacific Ocean: wind speed of 50 mi/hr, blowing steadily for about 42 hours over a region of size 800 miles will results in 8 meters waves can get to 17 meter waves! (see Table 10.2) 1 2 a b Constructive interference (addition) Destructive interference (subtraction) Constructive interference (addition) 4
Wave interaction Constructive interference; (b) crests of waves coincide Destructive interference; (c) crest of one coincides with trough of other Wave Refraction slowing and bending of waves as they approach shore at an angle part of wave in shallow water depth contours slows down crests oblique angle between direction of motion of waves and depth contours ask surfers about the surf beat, or impress them explaining that it is just wave interference! part of same wave still in deep water hence faster Deep-water waves change to shallow-water waves as they approach the shore and they break Wave refraction- propagation of waves around obstacles, for example over a shallow ridge energy is focused (waves get interrupted, waves generate other waves) 1 2 4 5 3 Depth = 1/2 wavelength Surf zone (1) The swell feels bottom when the water is shallower than half the wavelength. (2) The wave crests become peaked because the wave s energy is packed into less water depth. (3) Water s circular motion due to wave is constrained by interaction with the ocean floor and slows the wave, while waves behind it maintain their original rate. (4) The wave approaches the critical 1:7 ratio of a wave height to wavelength. (5) The wave breaks when the ratio of wave height to water depth is about 3:4. The movement of water particles is shown in red. Note the transition from a deep-water wave to a shallow-water wave. Breaker Types Wave refraction in a shallow bay energy is spread 5
Wave Reflection when???? Tsunamis Vertical sea floor displacement Shallow water waves Long wavelength Low period Wave height changes (quite dramatically!) At point of origin Close to shore where depth decreases Wave Diffraction narrow opening diffraction and wave interaction Review: Refraction: waves approaching shore are refracted (bent) as they move from deep to shallow water - change in wavelength and wave speed Diffraction: spread of wave energy sideways to the direction of wave travel. Reflection: Waves that encounter a solid vertical surface (such as a seawall) will abruptly change direction without much loss of energy. Though not as simple as a ball bouncing off a wall, the reflection of a wave obeys the same principles, where the angle of incidence is equal to the angle of reflection. When the angle is zero (as measured from a line perpendicular to the reflecting surface), reflection may generate standing waves. This numerical simulation by the US Geological Survey shows the spreading for the tsunami triggered by the quake. http://walrus.wr.usgs.gov/tsunami/sumatraeq/tectonics.html 6
Satellite images of a coastal village in Banda Aceh, Indonesia, before and after the December 26, 2004 tsunami. http://www.seed.slb.com/en/scictr/watch/living_planet/tsunami.htm Site of potential collapse Cumbre Vieja Volcano-Potential Collapse and Tsunami at La Palma, Canary Islands (Ward and Day, GRL, 2001) 7