TRAPPED-FETCH WAVES The Theory from an Observational Perspective

Transcription

1 TRAPPED-FETCH WAVES The Theory from an Observational Perspective Peter J Bowyer Allan W MacAfee System Speed (kt) System Speed (kt) Fetch Enhancements Wind Speed vs System Fetch Speed Enhancements for 250 nmi Fetch Length Wind Speed vs System Speed for 250 nmi Fetch Length Fetch Reduction Fetch Reduction Extreme Enhancement Extreme Enhancement Significant Enhancement Significant Enhancement Fetch Enhancement Fetch Enhancement Wind Speed (kt) Wind Speed (kt)

2 BACKGROUND Since 1990 a significant number of TCs have moved through eastern Canadian waters, accompanied by extreme waves (H SIG m and/or H MAX m) generated by a dynamic ( trapped ) fetch (Bowyer & MacAfee) 1995 Interest in trapped-fetch waves spawned 2000 Basic theory & model developed 2003 Theory & model significantly refined 2004 Papers submitted to WAF (awaiting 2 nd review)

3 Cyclone Motion WIND 1 WIND XO 3 4 WIND 2 WIND

4 Winds Perpendicular to Fetch Motion 1 XO Which waves will remain in in the the fetch the the longest? P C P E P B P D P A Time T 0

5 Winds Perpendicular to Fetch Motion 1 XO 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 P C P E P B P D P A Time T 1

6 Winds Perpendicular to Fetch Motion 1 XO Waves from P B moved outside the fetch after 1 time-step Waves from P D grew for almost 2 time-steps Time T 2 P C P E P B P D P A

7 Winds Perpendicular to Fetch Motion XO Which waves will remain in in the the fetch the the longest? 2 P C P D P E P B Time T 0 P A

8 Winds Perpendicular to Fetch Motion XO 2 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 P D P B P C P E P A Time T 1

9 Winds Perpendicular to Fetch Motion XO Waves from P B moved outside the fetch after 1 time-step Waves from P C have grown for 2 time-steps 2 P D P B P C P E P A Time T 2

10 Winds Perpendicular to Fetch Motion Waves from P C grew for more than 2 time-steps before moving outside the fetch XO 2 Time T 3 P C P D P B P E P A

11 Winds Opposing Fetch Motion 3 XO Which waves will remain in in the the fetch the the longest? P C P D P B P E P A Time T 0

12 3 Winds Opposing Fetch Motion XO 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 P C P D Time T 1 P E P B P A

13 Winds Opposing Fetch Motion Waves from P C & P D moved outside the fetch before growing for even 2 time-steps 3 XO P C P E P B P D P A Time T 2

14 Winds With Fetch Motion XO 4 Which waves will remain in in the the fetch the the longest? P C P D P E P B Time T 0 P A

15 Winds With Fetch Motion Waves from P A fell behind the fetch before even 1 time-step XO 4 P C P B P D Time T 1 P E P A

16 Winds With Fetch Motion Waves from P E grew for more than 1 time-step but were then outrun by the fetch XO 4 P C P B P D Time T 2 P E P A

17 Winds With Fetch Motion XO 4 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 Time T 3 P C P B P E P D P A

18 Winds With Fetch Motion Waves from P C & P D are still growing after 4 time-steps XO 4 Time T 4 P C P B P E P D P A

19 Winds With Fetch Motion Time T 5 XO 4 P C P B P E P D P A 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

20 Which fetch generates the the smallest waves? Cyclone Motion Fetch Reduction always occurs in Quadrants as long as the cyclone is moving WIND 1 WIND XO 3 4 WIND 2 WIND

21 Cyclone Motion Fetch Enhancement may occur in Quadrant 4 depending on the speed of the cyclone WIND 1 WIND XO 3 4 WIND 2 WIND

22 Waves Moving in Same Direction as Their Storm Potential for Resonance

23 A Fetch moving much faster than waves Mid-latitude systems

24 A Fetch moving much faster than waves Mid-latitude systems B Waves moving much faster than fetch Tropical storms in the tropics

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

26 Fetches moving with constant speed

27 All of the waves quickly outrun the slow- moving storm system The steady-state state solution is reached in 7+ hours

28 Most of the waves still outrun the slower moving storm system The steady-state state solution is reached in 10+ hours

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

30 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

31 All waves are quickly outrun by the much quicker wind system and growth is very limited The steady-state state solution is reached in under 5 hours

32 Maximum wave growth occurs for a constant system speed of 207 knots All speeds greater or less than this will result in lower wave heights The steady-state state solution is not reached until 34 hours

33 Even for speeds only slightly greater, there is a significant difference in the resonance of the storm- waves system

34 Maximum Enhancement Ratio Fetch Enhancement Fetch Reduction m s -1 Storm Speed (kt / m s -1 )

35 kt Maximum Wave Growth (h) kt 60 kt 80 kt 100 kt 120 kt 140 kt m s -1 Storm Speed (kt / m s -1 )

36 35 Maximum Enhancement Ratio kt 40 kt 60 kt 80 kt 100 kt 120 kt 140 kt Observation The greater the wind speed, the greater the enhancement m s -1 Storm Speed (kt / m s -1 )

37 Maximum Possible Significant Wave Heights 35-knot winds

38 Maximum Possible Significant Wave Heights 50-knot winds

39 Maximum Possible Significant Wave Heights 65-knot winds

40 Maximum Possible Significant Wave Heights 80-knot winds

41 Maximum Possible Significant Wave Heights 95-knot winds Observation The smaller the fetch, the greater the enhancement

42 3 Optimum Enhancement Fetch 150 Fetch 250 Fetch m s -1 Wind Speed (kt / m s -1 )

43 25 Wind Speed vs Storm Speed for Maximum Fetch Enhancement 50 nm Fetch Area 20 Optimum Storm Speed (kt) Observation The greater the wind speed, the greater the optimum storm speed y = -0001x x R 2 = Wind Speed (kt)

44 45 Fetch Enhancements Wind Speed vs System Speed for 50 nmi Fetch Length System Speed (kt) Fetch Reduction Extreme Enhancement Significant Enhancement Fetch Enhancement Wind Speed (kt) 146 Fetch Enhancements Wind Speed vs System Speed for 250 nmi Fetch Length System Speed (kt) Fetch Reduction Extreme Enhancement Significant Enhancement Fetch Enhancement Wind Speed (kt)

45 Maximum Wave Growth (h) Fetch 150 Fetch Observation Optimum fetch-enhancement is more probable for high wind / small fetch events than low wind / high fetch events because the required durations are on the order of 1-day (ie: these events can actually occur) Fetch m s - 1 Wind Speed (kt / m s -1 )

46 Conclusion 1 Sub-synoptic scale storm systems, like tropical cyclones and polar lows, have the greatest potential for optimum resonance

47 VCRIT (kt) Average speed of TCs north of 40 N 50 Fetch 150 Fetch 250 Fetch Average speed of TCs south of 30 N m s -1 Wind Speed (kt / m s -1 ) Observation Fetch enhancement for TS or Hurricanes is greater in mid latitudes than in the tropics 5

48 As tropical cyclones undergo extratropical transition (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

49 Conclusion 2 Very high waves with TCs should be expected in mid latitudes as these systems become ET

50 Example: Three 50-kt tropical storms identical in in all all ways except translation speed 30kt 15kt 10kt

51 Maximum H sig generated is 53 m

52 Maximum H sig generated is 91 m

53 Maximum H sig generated is 63 m

54 30kt 15kt 10kt Storm speed is is very important 53m 91m 63m

55 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 kt wind 25 Wave Group Speed (kt) kt wind 60-kt wind 40-kt wind 20-kt wind Duration of Wave Growth (h)

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

57 The Worst-Case Scenario is 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

58 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 (little or 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