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JCOMM Workshop – June 2003 CanadianHurricaneCentre Waves-Storm Resonance Lab Why Do Waves Get So Big ? Peter Bowyer Allan MacAfee

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JCOMM Workshop – June 2003 Between Oct. 91 and Sept. 95, ECs East Coast NOMAD buoys reported some extraordinary waves events, with the 100-year waves being greatly exceeded 3 times in those 4 years

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JCOMM Workshop – June 2003 The Perfect Storm - October 1991 Storm of the Century - March 1993 Hurricane Luis - September each reported significant wave heights of 17+ metres, and maximum wave heights 30+ metres

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JCOMM Workshop – June 2003 Our work that has followed has focussed on the problem of what makes big waves?

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JCOMM Workshop – June 2003 Basics of Waves = cT = cT

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JCOMM Workshop – June 2003 SPEED OF WAVES IN WATER c = g tanh 2 d 2 () [ ] g = gravitational constant = wavelength d = water depth In deep water, d / gets very large, so tanh (big #) 1, therefore, c = g c = g 2 2 ( )

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JCOMM Workshop – June 2003 SPEED OF WAVES IN DEEP WATER = cT Since = cT c = gT 2 2 = gT = gT Therefore, speed (c) and wavelength ( ) are only a function of period (T). Since the speed is a function of the period, deep water is a dispersive medium.

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JCOMM Workshop – June 2003 BASIC DEEP WATER WAVE FORMULAE c = gT 2 c (m/s) = 1.56 T (sec) c (kts) = 3.03 T (sec) (m) = 1.56 T (sec) (ft) = 5.12 T (sec) S = H = H (m) 1.56 T (sec) 2 2 2

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JCOMM Workshop – June 2003 COMPOSITION OF WAVES Any observed wave pattern on the ocean can be shown to be comprised of a number of simple waves, which can differ from each other in height, wavelength and direction. The above profile is the result of two waves differing in only.

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JCOMM Workshop – June 2003 COMPOSITION OF WAVES In reality, the sea is a superposition of many wave sets.

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JCOMM Workshop – June 2003 WAVE GENERATION & DECAY

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JCOMM Workshop – June 2003 WIND-WAVES...depend on: Wind speed - the speed of the wind Fetch - the area of sea surface over which a wind of constant direction (within 30 o ) and steady speed is, or has been blowing Duration - the length of time the wind persists from a certain fetch

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JCOMM Workshop – June 2003 SIGNIFICANT WAVE HEIGHTS H sig V 2 tanh [ (F/V 2 ) a ] V = wind speed F = fetch length Law of Diminishing Returns is at work

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JCOMM Workshop – June 2003 WIND FETCH of the wind SEA CHANGING TO SWELL FULLY DEVELOPED SEA RIPPLES CHOP WIND WAVES

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JCOMM Workshop – June 2003 THE WAVE SPECTRUM For a simple sine wave, the energy is proportional to the square of the wave height. However, the real sea is a combination of many sine waves of varying and T. The simplest way of determining the energy of the sea is to examine the relative amounts of energy contained within different period ranges in the sea surface. The plot here of energy vs. frequency (1/T) is a typical energy (or wave) spectrum. ENERGY PERIOD

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JCOMM Workshop – June 2003 WAVE SPECTRA FOR DIFFERENT WIND SPEEDS As wind speed is increased, not only is more energy available (higher wave heights), but longer waves (longer period or lower frequency) are also present. Also, the period of maximum energy shifts to longer period waves. SPECTRAL ENERGY PERIOD (sec) 40 knots 30 knots 20 knots

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JCOMM Workshop – June 2003 WAVE ENERGY vs. WIND SPEED Wave energy is very sensitive to wind speed: Wave Energy (Wave Height) Wave Height (Wind Speed) Wave Energy (Wind Speed) Best Wave Model Uses Good Winds

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JCOMM Workshop – June 2003 STATISTICAL DESCRIPTION OF WAVE HEIGHTS H = significant wave height = average height of highest 1/3 waves in record (corresponds roughly to visually observed heights) H = average of all height values.625 H H = average height of (1/n)th highest waves H = 1.3 H H = 1.8 to 2.2 times the H SIG AV SIG 1/n 1/10 MAX SIG

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JCOMM Workshop – June 2003 WAVE GROUPS Although individual crests advance at a speed corresponding to their wavelength (as a coherent unit), the group advances at its own speed, called the GROUP SPEED....C g. The group speed is the speed at which the energy propagates (moves with the speed of the middle of the pack...slower than leading waves and faster than trailing waves.) The energy is equally split between KE and PE, however, the KE is associated with movement of particles in nearly closed orbits....therefore, the KE is not propagated. The PE is associated with net displacements of particles and this moves along with the wave at the wave speed.

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JCOMM Workshop – June 2003 WAVE GROUPS Therefore, only 1/2 of the energy (PE) is propagated at the wave speed which is the same as the total energy moving at 1/2 of the wave speed. C (kts) = C = 1.51 T (sec) 2 g

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JCOMM Workshop – June 2003 Period (sec)Group Speed (kts) m waves developed by a marginal gale Long swell well ahead of a storm system 16m fully-developed seas in a big storm TYPICAL WAVE PERIODS

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JCOMM Workshop – June 2003 Bretschneider Wave Calculator

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JCOMM Workshop – June 2003

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STATIONARY FETCHES - Example 1 Coast-lines - The fetch at point B is the distance AB. The fetch at point D is the distance CD. Since AB > CD, a wind from the coast would generate greater waves at B than at D because of the proximity of the coastline.

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JCOMM Workshop – June 2003 Curvature - The fetch at point B is limited by the curvature of the flow upwind. The fetch is now the distance upwind from B to the point where the wind direction becomes more than 30 o different from that at B. STATIONARY FETCHES - Example 2

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JCOMM Workshop – June 2003 Fanning out of flow The fetch at point B is limited by the fanning out of the isobars upstream, therefore giving decreasing wind speeds. In this case, the criterion that is recommended is for wind-speed reductions > 20%. STATIONARY FETCHES - Example 3

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JCOMM Workshop – June 2003 Moving Fetches Most interesting wind systems are not stationary. Determining fetches in a moving system can be complex and time consuming. As it turns out, the determination of the fetch is as critical as the determination of the wind speed

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JCOMM Workshop – June 2003 X O Cyclone Motion WIND

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JCOMM Workshop – June 2003 Time T 0 PBPB... PAPA PCPC. PDPD. PEPE Winds Perpendicular to Fetch Motion X O 1

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JCOMM Workshop – June 2003 Time T 1 PBPB. PAPA PCPC PDPD. PEPE.. Waves from P A & P C & P E grew for less than 1 time-step before moving outside the fetch Waves from P B & P D have grown for 1 time-step Winds Perpendicular to Fetch Motion X O 1

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JCOMM Workshop – June 2003 Time T 2 PBPB. PAPA PCPC PDPD. PEPE.... Waves from P B moved outside the fetch after 1 time-step Waves from P D grew for almost 2 time-steps Winds Perpendicular to Fetch Motion X O 1

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JCOMM Workshop – June 2003 Winds Perpendicular to Fetch Motion Time T 0 PBPB... PAPA PCPC. PDPD. PEPE X O 2

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JCOMM Workshop – June 2003 Time T 1 PBPB... PAPA PCPC. PDPD. PEPE..... Waves from P A & P D & P E grew for less than 1 time-step before moving outside the fetch Waves from P C & P B have grown for 1 time-step Winds Perpendicular to Fetch Motion X O 2

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JCOMM Workshop – June 2003 Time T 2 PBPB... PAPA PCPC. PDPD. PEPE Waves from P B moved outside the fetch after 1 time-step Waves from P C have grown for 2 time-steps Winds Perpendicular to Fetch Motion X O 2

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JCOMM Workshop – June 2003 Time T 3 PBPB... PAPA PCPC. PDPD. PEPE Waves from P C grew for more than 2 time-steps before moving outside the fetch Winds Perpendicular to Fetch Motion X O 2

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JCOMM Workshop – June 2003 Time T 0 PBPB.. PCPC. PDPD. PEPE PAPA. X O 3 Winds Opposing Fetch Motion

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JCOMM Workshop – June 2003 Time T 1 PBPB.. PCPC. PDPD... Waves from P C & P D grew for 1 time-step Waves from P E & P B & P A grew for less than 1 time-step before moving outside the fetch... PEPE PAPA... X O 3 Winds Opposing Fetch Motion

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JCOMM Workshop – June 2003 Time T 2 PBPB... PAPA PCPC. PDPD. PEPE Waves from P C & P D moved outside the fetch before growing for even 2 time-steps X O 3 Winds Opposing Fetch Motion

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JCOMM Workshop – June 2003 Winds With Fetch Motion Time T 0 PBPB.. PCPC. PDPD. PAPA. PEPE X O 4

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JCOMM Workshop – June 2003 Time T 1 PBPB... PAPA PCPC. PDPD. PEPE..... Waves from P A fell behind the fetch before even 1 time-step Winds With Fetch Motion X O 4

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JCOMM Workshop – June 2003 Time T 2 PBPB... PAPA PCPC. PDPD. PEPE Waves from P E grew for more than 1 time-step but were then outrun by the fetch Winds With Fetch Motion X O 4

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JCOMM Workshop – June 2003 Time T 3 PBPB... PAPA PCPC. PDPD. PEPE Waves from P C & P B & P D are still growing after 3 time-steps... although those from P B will soon be outrun by the fetch Winds With Fetch Motion X O 4

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JCOMM Workshop – June 2003 Time T 4 PBPB... PAPA PCPC. PDPD. PEPE Waves from P C & P D are still growing after 4 time-steps Winds With Fetch Motion X O 4

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JCOMM Workshop – June 2003 Time T 5 PBPB... PAPA PCPC. PDPD. PEPE Waves from P D were finally outrun by the fetch after more than 4 time-steps Waves from P C are still growing after 5 time-steps Winds With Fetch Motion X O 4

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JCOMM Workshop – June 2003 Fetch Reduction always occurs in Quadrants as long as the cyclone is moving

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JCOMM Workshop – June 2003 Fetch Enhancement may occur in Quadrant 4... depending on the speed of the cyclone

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JCOMM Workshop – June 2003 Waves Moving in Same Direction as Their Storm Potential for Resonance

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JCOMM Workshop – June 2003 Fetch moving much faster than waves Mid-latitude systems A

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JCOMM Workshop – June 2003 Fetch moving much faster than waves Mid-latitude systems A Waves moving much faster than fetch Tropical storms in the tropics B

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JCOMM Workshop – June 2003 Fetch moving much faster than waves Mid-latitude systems A Waves moving much faster than fetch Tropical storms in the tropics B Some waves in harmony with fetch Strong wind systems in mid-latitudes C

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JCOMM Workshop – June 2003 Fetch moving much faster than waves Mid-latitude systems A Waves moving much faster than fetch Tropical storms in the tropics B Perfect Waves-Storm Resonance REAL The REAL Perfect Storms D Some waves in harmony with fetch Strong wind systems in mid-latitudes C

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JCOMM Workshop – June 2003 NASA Scanning Radar Altimetry data for Hurricane Bonnie (98) as it tracked northward off the US east coast.

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JCOMM Workshop – June 2003 Courtesy of Ed Walsh, NASA (runs automatically in SlideShow mode)

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JCOMM Workshop – June 2003 The dominant waves are in the front right quadrant where a degree of resonance exists in a single spectral mode. This allows for ease of modelling and parametrization.

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JCOMM Workshop – June 2003 Fetches moving with constant speed

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JCOMM Workshop – June 2003 All of the waves quickly outrun the slow- moving storm system The steady-state solution is reached in 7+ hours.

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JCOMM Workshop – June 2003 Most of the waves still outrun the slower moving storm system The steady-state solution is reached in 10+ hours.

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JCOMM Workshop – June 2003 Waves leaving the trailing edge of the fetch are outrun by the wind system... however, all others move out ahead. The steady-state solution is reached in 17+ hours.

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JCOMM Workshop – June 2003 Most waves are soon outrun by the initially quicker moving wind system... however, waves starting at the leading edge hold on long enough until their speed catches up to the system speed... and eventually outruns the system. Steady state is reached in 30 hrs.

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JCOMM Workshop – June 2003 All waves are quickly outrun by the much quicker wind system... and growth is very limited. The steady-state solution is reached in under 5 hours.

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JCOMM Workshop – June 2003 Maximum wave growth occurs for a constant system speed of 20.7 knots. All speeds greater or less than this will result in lower wave heights. The steady-state solution is not reached until 34 hours.

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JCOMM Workshop – June 2003 Even for speeds only slightly greater, there is a significant difference in the resonance of the storm- waves system.

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JCOMM Workshop – June 2003 Consider... - a fixed fetch length (eg. 50 nmi) - fixed wind speed throughout fetch (eg. 50 kts) (eg. 50 kts) What is the relationship between fetch-enhancement and storm speed?

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JCOMM Workshop – June 2003 Storm-Wave Resonance Calculator

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JCOMM Workshop – June 2003

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Fetch Enhancement Fetch Reduction

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JCOMM Workshop – June 2003 Fetch Reduction Enhancement Significant Enhancement Extreme Enhancement

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JCOMM Workshop – June 2003

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Enhancement Reduction

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Observation: 1. The greater the wind speed, the greater the enhancement the greater the enhancement

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JCOMM Workshop – June 2003 Maximum Possible Significant Wave Heights 35-knot winds

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JCOMM Workshop – June 2003 Maximum Possible Significant Wave Heights 50-knot winds

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JCOMM Workshop – June 2003 Maximum Possible Significant Wave Heights 65-knot winds

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JCOMM Workshop – June 2003 Maximum Possible Significant Wave Heights 80-knot winds

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JCOMM Workshop – June 2003 Maximum Possible Significant Wave Heights 95-knot winds

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JCOMM Workshop – June 2003 Observations: 2. The smaller the fetch, the greater the enhancement greater the enhancement 3. The greater the wind speed, the greater the optimum the greater the optimum storm speed storm speed

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Unlikely durations

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Observation: 4. Optimum fetch-enhancement is more probable for high wind / small more probable for high wind / small fetch events than low wind / high fetch events than low wind / high fetch events... because the fetch events... because the required durations are on the order required durations are on the order of 1-day (ie: these events can of 1-day (ie: these events can actually occur) actually occur)

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JCOMM Workshop – June 2003 Conclusion 1 Observations 1-4 select sub-synoptic scale storm systems for the greatest potential for optimum resonance (tropical cyclones and polar lows)

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JCOMM Workshop – June 2003

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Optimum Enhancement

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JCOMM Workshop – June 2003 Optimum Enhancement

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Average speed of TCs south of 30 o N Average speed of TCs north of 40 o N 50 nm Fetch 100 nm Fetch

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JCOMM Workshop – June 2003 Observation: 5. Fetch enhancement for tropical cyclones of TS or Hurricane strength is greater in mid latitudes than in the tropics.

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JCOMM Workshop – June 2003 Conclusion 2 The highest waves with tropical storms or hurricanes could be expected in mid latitudes a unique problem with ETs

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JCOMM Workshop – June 2003 As tropical cyclones become ET, they are typically increasing in speed under the influence of a mid-latitude stream. The seas associated with these systems (and even minimal hurricanes that move quickly) can be greater than those associated with major hurricanes.

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JCOMM Workshop – June 2003 For example: A Hurricane in the Tropics Moving 5 kts... area of 65-kt winds over a fetch length of 100 nm... can generate H sig of almost 11 m. A Tropical Storm in Mid-Latitudes Moving 19 1 / 2 kts... area of 50-kt winds over a fetch length of 100 nm... can generate H sig of almost 15 m. -27

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JCOMM Workshop – June 2003 Accelerating Fetches If the storm system accelerates with a speed matching that of the waves it generates, the conditions for perfect resonance exists and wave growth is more easily maximized.

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JCOMM Workshop – June 2003

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Storms moving in a straight line, at the optimum speed, can result in the potential for phenomenally large waves to develop

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JCOMM Workshop – June 2003 Luis (95) Felix (95) Bonnie (98) Danielle (98)

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JCOMM Workshop – June 2003 HURRICANE LUIS Sept , knots 10 / 06Z knots 10 / 12Z 10 / 18Z 85 knots 95 knots 11 / 00Z 11 / 06Z 105 knots

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JCOMM Workshop – June 2003 Max Reported Sig. Waves 17+ metres HURRICANE LUIS Sept , knots 10 / 06Z knots 10 / 12Z 10 / 18Z 85 knots 95 knots 11 / 00Z 11 / 06Z 105 knots Wave Field at Sept Z * For 17 metres, 85 kts is required throughout this box for about 14 hours QEII

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JCOMM Workshop – June 2003 Nearest point to storm Storm speed 40+ knots andincreasing

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JCOMM Workshop – June 2003 Since Luis was quickly outstripping the waves generated by its wind-field, the waves were not as large as they might of been, had Luis moved considerably slower.

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JCOMM Workshop – June knots 55 knots 50 knots 21 / 00Z 21 / 06Z 21 / 12Z 21 / 18Z 22 / 00Z 22 / 06Z 22 / 12Z TS FELIX Aug , 1995

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JCOMM Workshop – June knots 55 knots 50 knots 21 / 00Z 21 / 06Z 21 / 12Z 21 / 18Z 22 / 00Z 22 / 06Z 22 / 12Z TS FELIX Aug , Max Reported Sig. Waves 13+ metres * Wave Field at Aug Z For 13 metres, 50 kts is required throughout this box for about 36 hours 7

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JCOMM Workshop – June 2003 Nearest point to storm Storm speed 30+ knots andincreasing

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JCOMM Workshop – June 2003 The waves in Felix were quite large, considering the wind field. However, like Luis, Felix began outstripping the waves... which might have eventually grown larger, had Felixs translation remained below 30 knots.

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JCOMM Workshop – June 2003 TS BONNIE Aug , knots 29 / 00Z 45 knots 29 / 06Z 45 knots 29 / 12Z 45 knots 29 / 18Z 45 knots 30 / 00Z 45 knots 30 / 06Z 45 knots 30 / 12Z 45 knots 30 / 18Z

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JCOMM Workshop – June 2003 TS BONNIE Aug , knots 29 / 00Z 45 knots 29 / 06Z 45 knots 29 / 12Z 45 knots 29 / 18Z 45 knots 30 / 00Z 45 knots 30 / 06Z 45 knots 30 / 12Z 45 knots 30 / 18Z Max Reported Sig. Waves 11 metres * 2 For 11 metres, 45 kts is required throughout this box for about 42 hours Wave Field at Aug Z

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JCOMM Workshop – June 2003 Nearest point to storm Storm speed 25+ knots andincreasing

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JCOMM Workshop – June 2003 The waves with Bonnie were close to being fully-developed for the wind field associated with the storm. The proximity of the wave max with the storm centre shows that the two moved in reasonable harmony. A slightly slower translation speed for the storm might have resulted in slighly larger waves.

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JCOMM Workshop – June 2003 HURRICANE DANIELLE Sept. 2-3, knots 02 / 18Z 70 knots 03 / 00Z 70 knots 03 / 06Z 70 knots 03 / 12Z 65 knots 03 / 18Z 65 knots 04 / 00Z *

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JCOMM Workshop – June 2003 HURRICANE DANIELLE Sept. 2-3, knots 02 / 18Z 70 knots 03 / 00Z 70 knots 03 / 06Z 70 knots 03 / 12Z 65 knots 03 / 18Z 65 knots 04 / 00Z 2 Max Reported Sig. Waves 16 metres * Wave Field at Sept Z For 16 metres, 70 kts is required throughout this box for about 16 hours

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JCOMM Workshop – June 2003 Nearest point to storm Storm speed 25 knots andslowing

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JCOMM Workshop – June 2003 Like Bonnie, the max in the wave-field with Danielle was very close to the storm centre... showing that the two were moving in reasonable harmony. Danielle actually began slowing, allowing the wave-field to catch up and grow larger what might be expected.

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JCOMM Workshop – June 2003 The Worst-Case Scenario is, therefore, a storm centre... - moving in a straight line, - covering a large distance over open ocean, - increasing in speed, continually matching the speed of the waves that corresponds closely with the peak in the energy spectrum

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JCOMM Workshop – June 2003 The Pattern... - area of maximum waves to the right of track - very tight gradient in the wave field at the leading edge... as the trapped-fetch arrives, it brings with it a wall of water (no forerunners to warn of storm) - waves can subside rather quickly in the wake of these storms, however, the trailing gradient is usually much weaker

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JCOMM Workshop – June 2003 Exercise Using the Wave Resonance Calculator on the Workstation, what significant wave heights would you expect along the coastline of Atlantic Canada with different fetch scenarios A-N?

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JCOMM Workshop – June 2003 Modelling the Problem Specifically for TCs Resonance is, uniquely, a unidirectional problem, so the spectral issues simplify considerably Resonance is, uniquely, a unidirectional problem, so the spectral issues simplify considerably Since wind is, by far, the most critical issue, even a simple first generation parametric approach will give superior results, if the wind field is treated accurately. Since wind is, by far, the most critical issue, even a simple first generation parametric approach will give superior results, if the wind field is treated accurately.

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JCOMM Workshop – June 2003 Currently, we are tackling this problem by coupling the CHCs hurricane wind model with a single-purpose wave model that looks only at the maximum possible H sig with a given storm

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JCOMM Workshop – June 2003

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The output of the trapped-fetch model shows trajectories, maximum H sig, and duration of wave growth from independent fetch areas within the tropical cyclone

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JCOMM Workshop – June 2003

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For Bonnie, the CHC model predicts a maximum H sig passing through southern Maritime waters of 10.3m. Compare this to the maximum H sig of 10.8m reported by a weather buoy.

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JCOMM Workshop – June 2003 For Luis, the CHC model predicts a maximum H sig of 18.9 m to the right-of-track. A weather buoy reported a maximum H sig of 17.1 m.

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JCOMM Workshop – June 2003 For Danielle, the CHC model predicts a maximum H sig of 15.5 m passing through southern Maritime waters. A weather buoy reported 15.8 m.

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JCOMM Workshop – June 2003

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