Bài giảng hải dương học chương 4

Chapter Tide and tidal currents Ni dung Thuật ng ngữ ữ thiên văn thuỷ văn Lực tạo triều Phân tích thuỷ triều Dự báo triều Thuỷ triều Biển đô đông ng Cửa sông thuỷ triều vùng cửa sông Bài tập Thuật ng ngữ ữ thiên văn Thiên cầu hay mặt cầu bầu trời Trục vũ trụ Thiên cực bắc thiên cực nam Thiên đỉnh thiên đế Mặt phẳng chân trời Đ-ờng chân trời trời,, xớch o tri tri Thiên cầu bắc thiên cầu nam nam Kinh tuyến trời trời Điểm bắc điểm nam nam,, điểm đô đông ng điểm tây tây Vòng giờ,, vòng nhật động ộng Vòng hoàng đạo, bạch đạo đạo Xuân phân (21/III), (21/III),thu thu phân (23/IX), (23/IX),hạ hạ chí (22/VI), đô đông ng chí (22/XII) Ngày sóc th-ợng huyền , ngày vọng hạ huyền Thuật ng ngữ ữ thuỷ văn - Đỉnh triều - Chân triều - Chu kỳ triều - Độ lớn thuỷ triều - Biên độ triều - Tr, Td - Kỳ n-ớc c-ờng, kỳ n-ớc - lục địa , độ sâu Tidal Characteristics single waves - stretch across entire ocean basins shallow shallow water waves wavelengths greatly exceed the depth of the ocean complex sun interactions of moon and Why Care About Tides? Aquaculture The Tides of the Bay of Fundy Origin of the Tides Unlike wind driven surface waves wind and unlike tsunamis, tides are caused by two principal factors: Gravitational attraction Centrifugal force Gravitational Attraction All masses are drawn to each other The moon because of its closeness to the Earth exerts a greater gravitational effect on the Earth than the Sun, Sun, despite the fact that the Sun is much more massive than the Moon x=? Gravitational Effect of Moon Centrifugal Forces: Center of Rotation Gravitational forces Tractive force Fs Fm sin( ) Fa sin( ) Fs 3gM sin 2K Distribution of tractive forces over the Earth surface Ratio of the tractive forces od the Moon and the Sun Symbol M K Moon 0.0123 60.3 Sun 333,000 23,500 Dimension (-) (-) 3gM/(2K3) 0.82*10-6 0.38*10-6 (m/s2) The equilibrium theory assumed that the Earth is fully covered with water The plane of the moon is in the plane of the equator why not exactly 24 hours or 12 hours? Moon moves forward in its orbit each day Takes 50 additional minutes for a spot on the Earths surface to regain its position relative to the Moon E = 15.041 o/h m = 0.549 o/h 360o 2T 24.84h o E m 14.49 /h T = 12.42 h = 12 h 25 The plane of the moon makes an angle with the plane of the equator Joint effect of moon and sun on the tides Spring tides occur when the Earth, Sun, and Moon are aligned New Moon and Full Moon phases Constructive interference Neap tides occur when the Sun and Moon are aligned at right angles to one another Quarter Moon phases Destructive interference Spring tide:: phase when tidal range is maximal tide maximal Neap tide: tide: phase when tidal range is minimal minimal There are spring and neap tides each month m s 360o 2T 708h o 0.508 /h T = 354 h = 14.8 days Moving position of the perigeum Elliptical orbit of the Earth Relative motions of moon and sun in relation to the celestrial sphere 3gM 3gM Fs sin 2K 2K n A A cos( t ) o i i i i Ao = constant Ai = amplitude of component i i = angular speed of component i = jE + k m +l s + m p in which E m s p are the angular speeds of the Earth, the Moon, the Sun, perigeum of the moon i = phase of component i at t = Periods and angular speeds Origin Rotation Earth Rotation Earth Moon around Earth Earth around Sun Perigeum Moon Nodes lunar orbit Angular speed in o/hour 15.041069 0.549016 0.041069 Period 0.997 days 27.32 days 365.24 days 0.004642 0.002206 8.85 years 18.60 years The variation due to the revolution of the nodes is taken into account by multiplying the amplitude with a factor fi and adding a phase shift ui to the harmonic terms The number of harmonic terms is large: - The orbits are not in the plane of the equator, which cause declination tides (mainly diurnal); - The distance between the Earth and the moon and sun are not constant, as their orbits are ellipses The distances vary and also the angular speed That causes the elliptical tides (both diurnal and semi-diurnal) Main astronomic constituents of the tide Gro up Sym bol Frequency Period (hours) Angular Astronomi Type of constituent speed c (o/hour) coefficients I M2 S2 K1 O1 2we-2wm 2we-2ws we we-2wm 12.42 12.00 23.94 25.80 28.9841 30.0000 15.0411 13.9430 II P1 N2 K2 we-2ws 2we-wm+wp 2we 24.07 12.66 11.97 14.9589 0.176 28.4397 0.174 30.0821 0.115 0.908 0.423 0.531 0.377 semi-diurnal principle lunar tide semi-diurnal principle solar tide diurnal lunar-solar declination tide diurnal lunar declination tide diurnal solar declination tide semi-diurnal lunar elliptic tide semi-diurnal lunar-solar declination tide constituents of the tide (conts (conts)) III Q1 L2 e-3m+p 2e-m-p 26.87 12.19 13.3987 29.5285 0.072 0.026 diurnal lunar elliptic tide semi diurnal lunar elliptic tide IV Mf Mm Ssa 2m m-p 2s 328 661 4383 1.0980 0.5444 0.0821 0.156 0.083 0.026 long periodic lunar tide long periodic lunar tide long periodic solar tide V Sa Msm Msf Mtm M1 1 J1 001 2N2 m2 n2 l2 T2 s m-2s+p 2m-2s 3m-p e-m+p e-3s e+2s e+m-p e+2m 2e-4m+2p 2e-4m+2s 2e-3m+2sp 2e-m2s+p 2e-3s 8759 764 354 219 24.83 24.13 23.80 23.10 22.31 12.91 12.87 12.63 12.22 12.02 0.0411 0.4715 1.0159 1.6424 14.4967 14.9179 15.1232 15.5854 16.1391 27.8954 27.9682 28.5126 29.4556 29.9590 0.012 0.012 0.008 0.030 0.030 0.010 0.008 0.030 0.016 0.024 0.022 0.034 0.007 0.025 long periodic solar tide Shallow water tidal - Bottom friction; - Variable propagation speed of the tidal wave - Variable propagation speed of the tidal wave Shallow water tides Symbol Origin Frequency Period (hrs) Angular speed (deg./h) MNS2 2MS2 2SM2 MK3 2MK3 SK3 SO3 M4 MS4 MN4 MK4 S4 2e-5m+2s+p 2e-4m+2s 2e+2m-4s 3e-2m 3e-4m 3e-2s 3e-2m-2s 4e-4m 4e-2m-2s 4e-5m+p 4e-2m 4e-4s 13.13 12.87 11.61 8.18 8.39 7.99 8.19 6.21 6.10 6.27 6.09 6.00 27.4238 27.9682 31.0159 44.0252 42.9271 45.0411 43.9430 57.9682 58.9841 57.4238 59.0662 60.0000 M2+N2-S2 2M2-S2 2S2-M2 M2+K1 2M2-K1 S2+K1 S2+O1 2M2 M2+S2 M2+N2 M2+K2 2S2 Remarks semi-diurnal terdiurnal quarter diurnal Shallow water tides Symbol Origin Period Angular speed (hrs) Frequency Remarks (deg./h) M6 2MS6 2MN6 2SM6 MSN6 S6 M8 3MS8 2(MS)8 2MSN8 S8 3M2 2M2+S2 2M2+N2 2S2+M2 M2+S2+N2 3S2 4M2 3M2+S2 2M2+2S2 2M2+S2+N2 4S2 6e-6m 6e-4m-2s 6e-7m+p 6e-2m-4s 6e-5m-2s+p 6e-6s 8e-8m 8e-6m-2s 8e-4m-4s 8e-7m-2s+p 8e-8s 4.14 4.09 4.17 4.05 4.12 4.00 3.11 3.08 3.05 3.07 3.00 86.9523 sixth diurnal 87.9682 86.4079 88.9841 87.4238 90.0000 115.9364 eighth diurnal 116.9523 117.9682 117.4079 120.0000 Phõn loi thy triu Kiểu triều H Triều hỗn hợp Bán nhật BN triều Nhật triều Nhật triều triều không không đều h K hO1 0.0 < 0.5 hM + F = H K1 H 01 H M2 + H S2 < 0.25 0.5 2.0 2.0 4.0 0.25 1.5 1.5 > 4.0 >3 [...]... (hrs) Angular speed (deg./h) MNS2 2MS2 2SM2 MK3 2MK3 SK3 SO3 M4 MS4 MN4 MK4 S4 2e-5m+2s+p 2e -4 m+2s 2e+2m -4 s 3e-2m 3e -4 m 3e-2s 3e-2m-2s 4 e -4 m 4 e-2m-2s 4 e-5m+p 4 e-2m 4 e -4 s 13.13 12.87 11.61 8.18 8.39 7.99 8.19 6.21 6.10 6.27 6.09 6.00 27 .42 38 27.9682 31.0159 44 .0252 42 .9271 45 . 041 1 43 . 943 0 57.9682 58.9 841 57 .42 38 59.0662 60.0000 M2+N2-S2 2M2-S2 2S2-M2 M2+K1 2M2-K1 S2+K1... 2MSN8 S8 3M2 2M2+S2 2M2+N2 2S2+M2 M2+S2+N2 3S2 4M2 3M2+S2 2M2+2S2 2M2+S2+N2 4S2 6e-6m 6e -4 m-2s 6e-7m+p 6e-2m -4 s 6e-5m-2s+p 6e-6s 8e-8m 8e-6m-2s 8e -4 m -4 s 8e-7m-2s+p 8e-8s 4. 14 4.09 4. 17 4. 05 4. 12 4. 00 3.11 3.08 3.05 3.07 3.00 86.9523 sixth diurnal 87.9682 86 .40 79 88.9 841 87 .42 38 90.0000 115.93 64 eighth diurnal 116.9523 117.9682 117 .40 79 120.0000 Phân loại thủy triều KiÓu triÒu... 43 83 1.0980 0. 544 4 0.0821 0.156 0.083 0.026 long periodic lunar tide long periodic lunar tide long periodic solar tide V Sa Msm Msf Mtm M1 1 1 J1 001 2N2 m2 n2 l2 T2 s m-2s+p 2m-2s 3m-p e-m+p e-3s e+2s e+m-p e+2m 2e -4 m+2p 2e -4 m+2s 2e-3m+2sp 2e-m2s+p 2e-3s 8759 7 64 3 54 219 24. 83 24. 13 23.80 23.10 22.31 12.91 12.87 12.63 12.22 12.02 0. 041 1 0 .47 15 1.0159 1. 642 4 14. 4967... Period (hours) Angular Astronomi Type of constituent speed c (o/hour) coefficients I M2 S2 K1 O1 2we-2wm 2we-2ws we we-2wm 12 .42 12.00 23. 94 25.80 28.9 841 30.0000 15. 041 1 13. 943 0 II P1 N2 K2 we-2ws 2we-wm+wp 2we 24. 07 12.66 11.97 14. 9589 0.176 28 .43 97 0.1 74 30.0821 0.115 0.908 0 .42 3 0.531 0.377 semi-diurnal principle lunar tide semi-diurnal principle solar tide diurnal lunar-solar declination tide diurnal... The plane of the moon is in the plane of the equator  why not exactly 24 hours or 12 hours?  Moon moves forward in it’s orbit each day – Takes 50 additional minutes for a spot on the Earth’s surface to regain it’s position relative to the Moon E = 15. 041 o/h m = 0. 549 o/h 2 360o 2T    24. 84h o E  m  14. 49 /h T = 12 .42 h = 12 h 25’ The plane of the moon makes an angle with the plane of the... 2e-m2s+p 2e-3s 8759 7 64 3 54 219 24. 83 24. 13 23.80 23.10 22.31 12.91 12.87 12.63 12.22 12.02 0. 041 1 0 .47 15 1.0159 1. 642 4 14. 4967 14. 9179 15.1232 15.58 54 16.1391 27.89 54 27.9682 28.5126 29 .45 56 29.9590 0.012 0.012 0.008 0.030 0.030 0.010 0.008 0.030 0.016 0.0 24 0.022 0.0 34 0.007 0.025 long periodic solar tide Shallow water tidal - Bottom friction; - Variable propagation speed of the tidal wave -... t = 0 Periods and angular speeds Origin Rotation Earth Rotation Earth Moon around Earth Earth around Sun Perigeum Moon Nodes lunar orbit Angular speed in o/hour 15. 041 069 0. 549 016 0. 041 069 Period 0.997 days 27.32 days 365. 24 days 0.0 046 42 0.002206 8.85 years 18.60 years The variation due to the revolution of the nodes is taken into account by multiplying the amplitude with a factor fi and adding a... when tidal range is maximal tide maximal  Neap tide: tide: phase when tidal range is minimal minimal  There are 2 spring and 2 neap tides each month 2 m  s  360o 2T   708h o 0.508 /h T = 3 54 h = 14. 8 days Moving position of the perigeum Elliptical orbit of the Earth Relative motions of moon and sun in relation to the celestrial sphere 3gM 3gM Fs  sin 2   2K 3 2K 3 n   A  A cos(  t ... loại thủy triều KiÓu triÒu H TriÒu hçn hîp B¸n nhËt BN triÒu NhËt triÒu NhËt triÒu triÒu kh«ng ®Òu kh«ng ®Òu ®Òu h K 1  hO1 0.0 < 0.5 hM 2 + F = H K1 H 01 H M2 + H S2 < 0.25 0.5  2.0 2.0  4. 0 0.25  1.5 1.5 3 > 4. 0 >3  ... SK3 SO3 M4 MS4 MN4 MK4 S4 2e-5m+2s+p 2e-4m+2s 2e+2m-4s 3e-2m 3e-4m 3e-2s 3e-2m-2s 4e-4m 4e-2m-2s 4e-5m+p 4e-2m 4e-4s 13.13 12.87 11.61 8.18 8.39 7.99 8.19 6.21 6.10 6.27 6.09 6.00 27 .42 38 27.9682... e+2m 2e-4m+2p 2e-4m+2s 2e-3m+2sp 2e-m2s+p 2e-3s 8759 7 64 3 54 219 24. 83 24. 13 23.80 23.10 22.31 12.91 12.87 12.63 12.22 12.02 0. 041 1 0 .47 15 1.0159 1. 642 4 14. 4967 14. 9179 15.1232 15.58 54 16.1391... 2M2+N2 2S2+M2 M2+S2+N2 3S2 4M2 3M2+S2 2M2+2S2 2M2+S2+N2 4S2 6e-6m 6e-4m-2s 6e-7m+p 6e-2m-4s 6e-5m-2s+p 6e-6s 8e-8m 8e-6m-2s 8e-4m-4s 8e-7m-2s+p 8e-8s 4. 14 4.09 4. 17 4. 05 4. 12 4. 00 3.11 3.08 3.05 3.07