Last time Wind generated waves and Tsunami These are wind and earthquake generated waves Today: Tides These are Gravity waves How are they generated What are their intersting complexities? Low tide (decrease in water level on coast) High tide (increase in water level on coast) Tides: this is what we see (bay of Fundy, CAN) 1
Tides: Periodic rise and fall of sea level along coastlines following phases of moon Earth Moon Moon s Gravity So, is this what causes tides? Consider Moon s Gravity Pulls all points on earth toward Moon s center of mass. near side of Earth is attracted more than far side because force of gravity decreases with increasing distance. This creates a bulge in oceans toward moon. Earth rotates through this bulge = high tide. Can this explain tides, or is this what we observe? Earth Moon s Gravity Moon 2
What we actually observe: Two tidal bulges (two daily high tides) One near moon Other opposite moon Earth Moon What force is this? Moon s Gravity First: Center of Mass Center of Mass (C m ) Equal mass in all directions Example: Teeter-totter C m 3
Consider Earth - Moon system Lunar mass = 1.2% of Earth mass! So the center of mass is within the Earth! So, BOTH Earth and Moon rotate about this point This rotation results in inertia Directed away from the center of mass Example: spinning figure skating couple. Combine Gravity & Inertia: Near side moon s gravity overcomes inertia Produce near bulge (crest of tide wave) Far side Moon s gravity is less than inertia Produce far-side bulge bulge 4
What we just described are called Lunar Tides: Earth rotates through bulges in oceans created by gravity and inertia of Earth-Moon system Prediction We should have two high tides 12 hours apart (twice daily) Complexities: Are there two tides 12 hours apart? Moon completes orbit in 29.5 days in other words it rotates 12.2º per day So, Earth must rotate and additional 12.2º to complete tidal day (372.2º or 24 hours + 50 minutes). So, no. Tides are not 12 hours apart, rather they are 12 hours 25 minutes apart. 5
What about Sun s effect Gravity & inertia in this system too - so, there must be solar tides too Combined with phases of the moon. Full & New Moon = Spring tide First and last 1/4 Moon = Neap tide Note: these occur twice monthly, not annually So, result of Earth - Moon -Sun Maximum tide level changes during the month! And varies with latitude (Earth-Moon tilted ) 6
Moon is not above equator: Bulges in the ocean & axis of Earth s rotation are not perpendicular. So, tides vary with latitude Diurnal tides (one daily high) Semidiurnal (twice daily) So, our second prediction was bad too - don t always have two high tides per day. That depends on latitude. More complexity Just for fun Recall Sun s angle in sky changes during year? 23.5ºN (Cancer) to 23.5ºS (Capricorn) Moon s angle also varies (28.5ºN to 28.5ºS) over 19 years Result: some places change from diurnal to semidiurnal Level of tides changes too 7
Dynamic Theory of Tides: Tidal wavelength = 1/2 circumference of Earth! Shallow water waves and their speed is proportional to water depth Slowed most where seafloor is shallow Tidal bulges splash against continents So, the idealized bulges we just described are not adequate to explain tides. In reality, the bulges cannot keep pace with the speed of rotation, so they are disrupted into tidal cells that rotate around point called an amphidromic point Amphidromic point Thus, tides rock around basins like water in pan Within a given rotating tidal cell, low tide falls 6 hours after high tide. Actually, there are > 150 factors influencing tides on a give coast. This is way to complex for us, lets just know the lunar-solar factors and this idea of tidal cells rotating in the oceans 8
Tidal Bore Occur on Shallow coast lines Tide rushes up into river Result: fast shallow-water wave Qiantang River, China - 8 m bore 9