Tides II Outline Tides Part I (Wednesday) Why Study Tides Equilibrium Theory of Tides diurnal, semidiurnal and mixed semidiurnal tides spring and neap tides Tides Part II (Friday) Dynamic Theory of Tides rotary tidal motion larger tidal ranges in coastal versus open-ocean regions Forcing ocean water into a narrow embayment Tidal forcing that is in resonance with the tide wave Special Cases 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. The earth s gravity is only inline with the moon s gravity directly below the moon it almost completely balances the upward pull of the moon s gravity 2. 3. 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. The result is that the ocean tides are pinched upward from the cumulative pull by the moon on all the ocean. Lakes are not large enough to experience this broad pinch by the moon. 4. 5. 1 Dynamic Model of Tides A More Realistic View of Tides Tide wave treated as a forced shallow-water wave not in equilibrium with lunar/solar forcing Continents interfere with the propagation of the tide wave Affected by <a href="/keyword/coriolis-force/" >coriolis force</a> Tide Waves Are Shallow-Water Waves The tide wave has wavelength (L) on the order of 1/2 the diameter of the earth or about 20,000 km The tide wave can be considered a ShallowWater Wave for depths &lt; L/20 or for bottom depths &lt; 1000km. Since ocean bottom depths are typically only about 4 km, it is safe to assume that a tide wave is a Shallow-Water Wave Tide Waves Are Actually Forced Shallow-Water Waves Under ideal conditions, tide wave speed (as a free wave) would be determined by ocean bottom depth alone. However, this would only be the case if tides were briefly generated and then allowed to propagate freely on their own - but this is not the case 2 Tidal waves are Forced shallow-water waves because tidal forces exerted on the ocean by the moon constantly interfere with the free propagation of the shallow water wave. note that the wave speed for a shallow water wave in 4km of water is 200m s-1 (400 miles h-1). The speed that the earth rotates under the moon at the equator is 463m s -1 (1044 miles h-1). In other words The moon tries to move the tide wave along at 1044 mph, but the bottom drag tries to limit the wave propagation speed to 400 mph. The net result is that the tide wave moves slower than it would if there was no shallow-water bottom drag to slow it down. 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 high 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 Since tidal waves are of the same length scale as the earth and motions are on the order of a day, <a href="/keyword/coriolis-force/" >coriolis force</a> also has a very significant effect on the direction of tidal wave propagation. 3 <a href="/keyword/coriolis-force/" >coriolis force</a> 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 Rotary motion of a tide wave in an ocean basin caused by <a href="/keyword/coriolis-force/" >coriolis force</a> Amphidromic Point of a Rotary Tide 4 Theoretical and Actual Rotary Tide Depicted using Cotidal Lines (solid) and Corange Lines (dashed) Earth s Rotary Tides Depicted with Cotidal Lines Earth s Corange Lines (i.e., Color Contours) Note that coastal regions generally exhibit largest tidal ranges 10 8 6 4 2 5 Dynamic Theory of Tides Tide waves are forced shallow water waves that are subject to <a href="/keyword/coriolis-force/" >coriolis force</a> and constrained by the geometry of ocean basins Explains why tidal bulge precedes the moon s orbit Explains the rotary motion of tides Explains why coastal regions experience larger tides than open ocean regions A Couple of Other Interesting Features of Tides Tidal Forcing of Shallow Embayments can Enhance Tidal Ranges 6 For certain coastal geometries tidal forces can be in Resonance with the tide wave and this can lead to exaggerated tidal variation Summary Points Equilibrium Theory Explains: diurnal, semidiurnal and mixed semidiurnal tides spring neap tide series Dynamic Theory Explains: rotary motion of tides why coastal regions experience larger tides than open ocean regions Tidal Ranges can be exaggerated by: Forcing ocean water into a narrow embayment Tidal forcing that is in resonance with the tide wave 7