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This 7 page Class Notes was uploaded by Sidnee Notetaker on Wednesday September 23, 2015. The Class Notes belongs to BIOEE 1540 at Cornell University taught by Bruce C. Monger in Fall 2015. Since its upload, it has received 39 views.
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Date Created: 09/23/15
Wednesday September 23 2015 1127 AM I Ocean Tides A Equilibrium Model of Tides A highly idealized but very instructive view of tides 1 tide wave treated as a deepwater wave in equilibrium with lunarsolar forcing 2 no interference of the tide wave s propagation by continents B Daily Tidal Patterns 1 Diurnal one high tide and one low tide per day 2 Semidiurnal two equal high tides and two equal low tides per day 3 Mixed Semidiurnal two unequal high tides and two unequal low tides per day Em Diurnal Sevmi iurnal 7 Mixed SemiialDiurnal E Equot m I El 112 24 CI 12 241 Time hr Time hr Time hr 39 4 So What Forces are Responsible for the Two Tidal Bulges O The earth s rotation in conjunction with 1 the pull of gravity by the moon and 2 a second force to be discussed soon creates two quotTidal Bulges on opposite sides of the earth and causes the regular rise and fall of the tides over an approximately 24h hour period gt The tide rises when a point on the earth is aligned under the moon or on the opposite side of the earth from the moon gt The tide falls when a point on the earth is 90 away from the moon 0 houn centrifuga raw 1110011 00 la n I um ha In u u lu It 3 1 1 5 I quotl O O 1 I II II 0 5 Tidal Day 24h 50min Moon39s omit Moon a 24w 0 Moon 0 C Monthly Tidal Patterns The Tidal Force Exerted on the Earth by the Sun is About 46 of the Tidal Force Exerted on the Earth by the Moon 1 Spring Tides occur when the moon pulls along the same line as the sun new and full moon 2 Neap Tides occur when the moon pulls at 900 to the sun first and last quarter moon D Equilibrium Tide Theory 1 Daily Patterns diurnal semidiurnal and mixed semidiurnal tidal patterns 2 Monthly Pattern Tides Page 1 springneap tidal pattern 39 E Why do we get ocean tides but no tides in lakes and ponds 1 The earth s own gravity is always directed toward the center of the earth 2 Directly below the moon the earth s downward gravity is exactly inline with the moon s upward gravitational pull and the earths gravity almost completely balances the upward pull of the moon s gravity and this is what happens in a small lake 3 However the earth s gravity is not inline to the moon s gravity at locations not directly under the moon and so the earth s gravity cannot counterbalance the moon s gravity at these locations 4 The result is that the ocean tides are pinched upward from the cumulative lateral pull by the moon on all the ocean 5 Lakes are not large enough to experience this broad lateral pinch by the moon F Dynamic Theory of Tides A More Realistic View of Tides 1 Tide wave treated as a forced shallowwater wave gt not in equilibrium with lunarsolar forcing 2 Affected by the Coriolis Force 3 Continents interfere with the propagation of the tide wave 4 Tide Waves Are ShallowWater Waves i The tide wave has wavelength L on the order of 12 the diameter of the earth or about 20000 km ii The tide wave can be considered a ShallowWater Wave for depths lt L20 or in this case for bottom depths lt 1000km iii Since ocean bottom depths are typically only about 4 km it is safe to assume that a tide wave is a ShallowWater Wave 5 Tide Waves Are Actually Forced ShallowWater Waves i Under ideal conditions the tide wave speed if it were a freely propagating wave would be determined only by ocean bottom depth Because frictional drag by the shallow ocean bottom slows the tide wave down the earth will spin past and out from directly under the moon before the tide crest catches up The net result Is that the hth tide occurs sometime after the moon appears to pass overhead The red dot is at time 0 and the yellow dot it at a later time So the high tide is shown to come after the moon passes overhead 6 Since tidal waves are of the same length scale as the earth and motions are on the order of a day Coriolis Force also has a very significant effect on the direction of tidal wave propagation Coriolis Force illll Response to Meridi nal Motion Jig L 39 n tial northward motion T T T T T T T T T T T T T T T T T39galu Ehiri Fume arctic till the 135551 l i The Coriolis Force always acts exactly to the right of the direction of motion in the northern hemisphere and always directly to the left of the direction of motion in the southern hemisphere ii Rotary Tides Tides Page 2 Co Tidal l Amphidromic Point A N Mg m 3 N n 13 I MKS 39 Cmtwm CoRange w a w l lb AMM39DKOMK SV39SYIM I Dynamic Theory of Tides II Tide waves are forced shallow water waves that are subject to Coriolis force and constrained by the geometry of ocean basins III Explains why tidal bulge high tide occurs after the moon passes overhead III Explains the rotary motion of tides Tides Page 3 Monday September 21 2015 1119 AM I Ocean Waves A Fundamental Principles 1 Wave Parameters Wavelength W twat nmm l l l Ii DE IlT39rE39 a Ought mwmrg H ihl hi re a a Wavelength crest to crest distance units of length b Wave Speed distance a wave crest travels per unit time units of lengthtime c Wave Period time it takes a wave crest to travel one wavelength units of time d Wave Frequency number of crests passing a fixed location per unit time units of 1time 239 2 What Determines Wave Speed DeepWater Waves versus ShallowWater Waves a Overall Wave Speed Propagation is Function of Both 1 Wavelength and 2 Bottom Depth i Waves with longer wavelength travel faster than waves with shorter wavelength ii Waves traveling in deeper water travel faster than waves traveling in shallower water i b Under Certain Exceptional Circumstances only wavelength or only bottom depth will have the overriding dominate impact on wave speed In very deep water deep water waves small variation in bottom depth has little impact on overall wave speed and wavelength alone determines wave speed ii determines wave speed 3 Wave Speed In very shallow water shallow water waves small variation in bottom depth has a big impact on wave speed and variations in bottom depth alone i a DeepWater Waves bottom depth is deeper than 12 the wavelength Speed is a Function of Wavelength Only ii Longer Wavelength Waves Move Faster than Shorter Wavelength Waves i b ShallowWater Waves bottom depth is shallower than 120 the wavelength Speed is a Function of Depth Only ii All Waves in Shallower Water Move Slower than They Would for Deeper Water C as long as all depths less than 120 of the wavelength Intermediate Waves L20 lt Depth lt L2 i Wave Speed is a Complicated Function of Both Wavelength amp Depth This situation will not be covered in class 4 Wave Dispersion a SelfSorting of DeepWater Waves Leaving a Storm Region based on Wavelength b lt c It Occurs Because Longer Wavelength Waves Travel Faster than Shorter Wavelength Waves for Deep Water Fcuh DISquotquotCn 39 Map WIND View vr Suns Ocean swell Wave PMth NW 5 Wave Refraction a The Bending of ShallowWater Wave Fronts Due to Change in Bottom Depth i The leading edge of a wave front enters shallower water and slows down while the other end of the wave front continues at higher speed ii The net result is a bending of wave front L Am r quot 39 n 5 ll l 8 If a V39 n mm x S AV contour a I i 1 shoreline Waves Page 1 iii Consequence of Wave Refraction P Focusing and Defocusing of Wave Energy on Headlands and Bays Respectively hp 0 u 39 v is iv Longshore Sediment Transport P Longshore sediment transport occurs when wave strike the beach at an angle Breaking VVaves the top of the mo moves tum than gt Summer Gentle waves push offshore sandbar shoreward to create wide and gently sloping sandy summer beach V Winter Storm waves drag sand off the beach to be stored in offshore sandbar and frequently resulting in a rocky winter beach vi Ripe Currents P Initiated when large waves push water onto an elevated beach face P The beached water is funneled back off the beach through narrow breaks in underwater sand bars to form accelerated jets of wa ter rip currents P These jet like rip currents can pull a person hundreds of meters offshore P The currents are seldom wider than about 10 meters Waves Page 2 Beam b Wave Height of Wind Generated Waves is a Function of i Wind Speed P sets the upper possible limit on wave height for a fully developed sea ii Duration of the Wind Event P modulates the upper possible limit on wave height iii Fetch the distance over which wind can blow without obstruction P modulates the upper possible limit on wave height Wave Height as a Function of Wind Speed For a Fully Developed Sea for in nite wind duration 8 fetch 20 g 15 45 feet El E 5 10 a I co 0 I I I I 0 S 10 15 20 25 nd Speed meters secquot 50 mph P Once a wave is generated under the center of a storm region it begins to propagate outward and away from the region P If the spatial extent of the storm region is large ie if the fetch is large then it takes a long time before the wave finally reaches the outer edge of the storm region where the winds subside P So in a sense fetch is connected to the duration over which the wave experiences maximal winds P Larger fetch effectively gives the storm more time pump up the size of a given wave before the wave propagates out from under the storm center c Special Waves i Tsunami Wave Generation at a Convergent Plate Boundary 7K Before Earthquake 9 During Earthquake up ii Internal Waves Travel along Density Discontinuities in the Ocean Interior Waves Page 3 39 gt p 3 Waves Page 4
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