Chapter 4 Tide and tidal currents

Chapter 4 Tide and tidal currents Nội dung 1. Thuật ngữ thiên văn và thuỷ văn 2. Lực tạo triều 3. Phân tích thuỷ triều 4. Dự báo triều 5. Thuỷ triều Biển đông 6. Cửa sông và thuỷ triều vùng cửa sông 7. Bài tập Thuật ngữ thiên văn  Thiên cầu hay mặt cầu bầu trời  Trục vũ trụ  Thiên cực bắc và thiên cực nam  Thiên đỉnh và thiên đế  Mặt phẳng chân trời  Đ-ờng chân trời, xớch đạo trời.  Thiên cầu bắc và thiên cầu nam.  Kinh tuyến trời.  Điểm bắc và điểm nam, điểm đông và điểm tây.  Vòng giờ, vòng nhật động. Vòng hoàng đạo, bạch đạo.  Xuân phân (21/III),thu phân (23/IX),hạ chí (22/VI), đông chí (22/XII).  Ngày sóc th-ợng huyền , ngày vọng hạ huyền . Thuật ngữ 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 kém - “0 lục địa” , “0 độ sâu” Tidal Characteristics single waves - stretch across entire ocean basins. shallow-water waves –wavelengths greatly exceed the depth of the ocean. complex interactions of moon and sun Why Care About Tides? Aquaculture The Tides of the Bay of Fundy Origin of the Tides Unlike wind-driven surface waves 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, despite the fact that the Sun is much more massive than the Moon. x = ? Gravitational Effect of Moon Centrifugal Forces: Center of Rotation 2 Bulges from Gravitational Attraction & Centrifugal Force Gravitational forces  2sin K2 gM3 F 3s)sin()sin(   ams FFF Tractive force Distribution of tractive forces over the Earth surface. Ratio of the tractive forces od the Moon and the Sun. Symbol Moon Sun Dimension M 0.0123 333,000 (-) K 60.3 23,500 (-) 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 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.   h84.24 /h49.14 3602 T2 o o mE     T = 12.42 h = 12 h 25’ E = 15.041 o/h m = 0.549 o/h 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. Neap tide: phase when tidal range is minimal. There are 2 spring and 2 neap tides each month  sm 2   h708 /h508.0 360 T2 o o  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          n i iiios tAA K gM K gM F 1 33 )cos( 2 3 2sin 2 3  Ao = constant Ai = amplitude of component i i = angular speed of component i = jE + 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 = 0. Periods and angular speeds Origin Angular speed in o/hour Period Rotation Earth Rotation Earth 15.041069 0.997 days Moon around Earth 0.549016 27.32 days Earth around Sun 0.041069 365.24 days Perigeum Moon 0.004642 8.85 years Nodes lunar orbit 0.002206 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 speed (o/hour) Astronomi c coefficients Type of constituent 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 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 II P1 N2 K2 we-2ws 2we-wm+wp 2we 24.07 12.66 11.97 14.9589 28.4397 30.0821 0.176 0.174 0.115 diurnal solar declination tide semi-diurnal lunar elliptic tide semi-diurnal lunar-solar declination tide III Q1 L2 e-3m+p 2e-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 2m m-p 2s 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 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-m- 2s+p 2e-3s 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 constituents of the tide (conts) Shallow water tidal - Bottom friction; - Variable propagation speed of the tidal wave. - Variable propagation speed of the tidal wave. Symbol Origin Frequency Period (hrs) Angular speed (deg./h) Remarks MNS2 2MS2 2SM2 M2+N2-S2 2M2-S2 2S2-M2 2e-5m+2s+p 2e-4m+2s 2e+2m-4s 13.13 12.87 11.61 27.4238 27.9682 31.0159 semi-diurnal MK3 2MK3 SK3 SO3 M2+K1 2M2-K1 S2+K1 S2+O1 3e-2m 3e-4m 3e-2s 3e-2m-2s 8.18 8.39 7.99 8.19 44.0252 42.9271 45.0411 43.9430 terdiurnal M4 MS4 MN4 MK4 S4 2M2 M2+S2 M2+N2 M2+K2 2S2 4e-4m 4e-2m-2s 4e-5m+p 4e-2m 4e-4s 6.21 6.10 6.27 6.09 6.00 57.9682 58.9841 57.4238 59.0662 60.0000 quarter diurnal Shallow water tides Symbol Origin Frequency Period (hrs) Angular speed (deg./h) Remarks M6 2MS6 2MN6 2SM6 MSN6 S6 3M2 2M2+S2 2M2+N2 2S2+M2 M2+S2+N2 3S2 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 4.14 4.09 4.17 4.05 4.12 4.00 86.9523 87.9682 86.4079 88.9841 87.4238 90.0000 sixth diurnal M8 3MS8 2(MS)8 2MSN8 S8 4M2 3M2+S2 2M2+2S2 2M2+S2+N2 4S2 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 3.11 3.08 3.05 3.07 3.00 115.9364 116.9523 117.9682 117.4079 120.0000 eighth diurnal Shallow water tides Kiểu triều Bán nhật triều đều Triều hỗn hợp Nhật triềuBN triều không đều Nhật triều không đều 0.0 4.0 0.25  1.5 1.5 3. H h h h K O M  1 1 2 H + H H + H = F S2M2 01K1 Phõn loại thủy triều 3