MAR 110 LECTURE #20 Storm-Generated Waves & Rogue Waves Wave Principles Review Figure 20.1 Wave Principles (ABOVE) A simple ocean surface wave is a sea level distortion that repeats itself over a distance called the wavelength (L - symbol for wavelength). The wave height (H) is the distance between the high-point or crest and the low-point or trough of the wave. (BELOW) Ocean waves propagate (to the right in this case). A stationary observer at the crest to the right will initially will see the sea surface drop until the trough passes and then rise as the second crest approaches. It takes the wave period (P) for this cycle. Thus the wave travels one wavelength during a wave period and thus the speed of a wave (C p ) the ratio L/P. During the wave propagates past our observer, a surface water parcel traces a circular trajectory with no net movement of the water. (ItO,???) 22 October 2007 Lec 20 Wind & Rogue Waves 1
Wave Principles Deep Water Waves Wave Speed Depends on Wavelength - L C p (ft/s) = 2.26 L (ft) Figure 20.2 Deep Water Waves Deep water waves are those waves that propagate in water with a depth (D) that is greater than ½ the wave length (L = the distance between wave crests). Notice that the size of the circular trajectories of the water parcels diminishes to nearly zero at a water depth of 1/2 L. The speed of a deep water wave is different for waves with different wave lengths, such that waves with longer wave lengths go faster; according to the formula given above. (ItO) Wave Speed Depends on Water Depth - D C p (ft/s) = 5.67 D (ft) Figure 20.3 Shallow Water Waves Shallow water waves propagate in water depths D, which are less than 1/20 L. The trajectories of shallow water (SW) wave parcels are elliptical (squashed circles) and their width is the same throughout the water column. Because shallow water waves feel the bottom, their speed depends only on the local water depth, according to the formula given above. Thus SW waves slow down as they propagate from deeper water to shallower water; (ItO) 22 October 2007 Lec 20 Wind & Rogue Waves 2
Wave Spectrum Figure 20.4 Spectrum of Ocean Surface Waves An ocean wave spectrum shows how the wave energy (proportional to the square of the wave height) is distributed among the waves with different wave periods. While most waves are generated by the wind and have periods less than a minute, there are important other wave categories, (e.g., tides) that have periods of hours. The shorter wave period & wave length waves are wind-generated waves are called chop (lower left); while the longer wave period & wave length waves are called swell (lower right) (ItO) 22 October 2007 Lec 20 Wind & Rogue Waves 3
Wave Energy Transmission via Wave Groups Figure 20.5 Wave Energy Transmission & Wave Groups Deep ocean waves with slightly different wavelengths superimpose to form wave groups with speeds (C g ) that are half that of individual wave speeds (C p ). Because the individual waves move faster than the wave group and energy (C p = 2 C g ), individual waves are seen to (a) appear at the back of the wave group (b) propagate through the slower-moving wave group; and finally (c) disappear at the head of the wave group. Wave Energy Transmission Speed Wave Group Deep Water Wave Group Speed C g Depends on Wavelength BUT C g = ½ C p This means that LONGER WAVES = 1.13 L go faster than SHORTER WAVES! Figure 20.6 Deep Water Wave Energy Transmission Deep ocean waves with slightly different wavelengths form wave groups which are distinguished by their wave height envelope; which contains the wave energy. The wave group speed for deep water waves (C g ) is ½ the wave speed C p. The form of the deep water wave group speed - given by the relation above - indicates that the longer wave length, deep water waves travel faster than shorter wave length waves. 22 October 2007 Lec 20 Wind & Rogue Waves 4
Wave Energy Transmission Speed Wave Group Shallow Water Wave Group Speed Depends on Water Depth AND C g = C p C g (ft/s) = 5.67 D(ft) This means that ALL Shallow Water Waves go the same speed! Figure 20.7 Shallow Water Wave Energy Transmission The shallow water wave group speed C g is equal to the wave speed C p and thus depends on only the local water depth D, according to the above. Figure 20.8 The Generation of Surface Waves by Winds Hurricane winds are very effective wave generators. In the northern hemisphere, the largest waves are on the right-hand quadrant of the hurricane because the winds there are the sum of the storm winds plus the forward movement of the storm. (ItO) 22 October 2007 Lec 20 Wind & Rogue Waves 5
STORM-GENERATED WAVES Figure 20.9 Open Ocean Wind Wave Generation and Dispersion (Upper) In the wind-generation region, the ocean is rough and chaotic because waves with all different wavelengths superimpose and interfere with each other (lower left). As the waves propagate toward the right and away from the generation zone, the waves sort according to wave group speed. The longer wavelength/longer period waves known as swell (lower right) race out ahead of the shorter wavelength/shorter period waves.. (ItO) Deep Water Wave Propagation Pacific Ocean - Summer WAVE PROPAGATION ZONE Longer Waves Outrace Shorter Waves STORM WAVE GENERATION ZONE Waves of ALL Wavelengths Figure 20.10 The strong winter storms in the Southern Ocean generate waves that have a long time (& distance) to sort themselves out according to wave length before they strike the southwest facing shores of California. (NH, ItO) 22 October 2007 Lec 20 Wind & Rogue Waves 6
Rogue Wave Measurement.by Satellite Figure 20.11 With satellite altimeters it is now possible to find-and measure-rogue waves. Since the satellites can cover far more of the ocean than can be observed by ships at any one time, it was discovered that rogue waves are a far more common occurrence than was previously thought (NH) Rogue Wave Hazard Figure 20.12 Rogue Wave Hazard Rogue waves are very large open ocean waves of sometimes can range in height from 60 ft (20m) to120 feet (40m) and thus a significant hazard to large tanker ships. (???) 22 October 2007 Lec 20 Wind & Rogue Waves 7
Figure 20.13 Constructive Wave Interference-Rogue Waves (RIGHT) The real ocean has waves of all wave heights and wavelengths, Occasionally, a long wave (wave #1) and a wave half its wavelength (wave #2) will constructively interfere with each other to form and exceptionally large wave a rogue wave). (LEFT) The probability of rogue wave generation is very high in the Agulhus Current region because of the environmental conditions there. (ItO) Rogue Wave Height Estimates 60 ft 112 ft! Figure 20.14 Rogue Wave Height Estimates Until recently it was believed that rogue waves were very rare events. The only records of wave height came from estimates of people onboard ships that used line of sight to the crest of the wave to calculate the height. (??) 22 October 2007 Lec 20 Wind & Rogue Waves 8
Rogue Waves in the Agulhas Current Figure 20.15 Rogue Waves in the Agulhas Current The region where the Agulhas Current meets Antarctic storm waves and West Wind Drift is known for having a relatively high occurrence of rogue waves. (ItO, LEiO) Shallow Water or Short Wave Characteristics Water Depth D is less than 1/20 L Figure 20.16 Shallow Water Waves (BELOW) As deep water waves shoal - that is propagate into water depths D that are less than ½ their wave length L - the wave and the ocean bottom interact or the wave is said to feel the bottom. When this happens, the wave slows and the water parcel orbits become more elongated. (ABOVE) At the point where the water depth D is les than 1/20 of the wave length L, the waves becomes a shallow water wave, which as it shoals further increases in height until the wave breaks as it approaches the beach. (LEiO) 22 October 2007 Lec 20 Wind & Rogue Waves 9
Breaking Waves Hawaiian Waves Figure 20.17 Wave Breaking As the water gets shallower, the wave height increases until the point where the wave breaks due to gravity. (LEiO) Note the misnomer riptide Rip Currents derive from the power of the incoming waves have little to do with the tides Figure 20.18 Rip Current Zones Tell-tale signs of rip current zones along this California beach. (ItO) 22 October 2007 Lec 20 Wind & Rogue Waves 10
Rip Currents.water accumulating on the beach MUST return and it does in concentrated jets.. Figure 20.19 Rip Current Mechanics The incoming water from waves breaking in the surf zone all along the beach returns to the ocean (as it must) in concentrated offshore current flows called rip currents. (ItO) Figure 20.20 Rip Current Patterns The Incoming waves move water inshore all along the beach front. Water accumulation creates sea level setup (pressure gradient forces) that drive the accumulated water back offshore in concentrated rip current zones at regular intervals along the shore. (LEiO) 22 October 2007 Lec 20 Wind & Rogue Waves 11
Santa Ana Wind-Wave Wave Generation 25 nm Figure 20.21 Wind-Generated Waves Scenario The southward flowing Santa Ana winds generate waves in the Santa Catalina Channel. However, because it is a fetch-limited generation zone, the waves are not very well sorted when they strike the shores of Santa Catalina island. 22 October 2007 Lec 20 Wind & Rogue Waves 12