Equilibrium Model of Tides, Study notes of Geometry

Download Equilibrium Model of Tides and more Study notes Geometry in PDF only on Docsity! 1 Tides • Equilibrium Theory of Tides — diurnal, semidiurnal and mixed semidiurnal tides — spring and neap tides • Dynamic Theory of Tides — rotary tidal motion — larger tidal ranges in coastal versus open-ocean regions • Special Cases — Forcing ocean water into a narrow embayment — Tidal forcing that is in resonance with the tide wave Outline • Tide wave treated as a deep-water wave in equilibrium with lunar/solar forcing • No interference of tide wave propagation by continents Equilibrium Model of Tides Highly Idealized, but very instructive, View of Tides Tidal Patterns for Various Locations 2 The Earth’s Rotation Under the Tidal Bulge Produces the Rise and Fall of Tides over an Approximately 24h hour period Looking Down on Top of the Earth Note: This is describing the ‘hypothetical’ condition of a 100% water planet moon Tidal Day = 24h + 50min It takes 50 minutes for the earth to rotate 12 degrees of longitude Earth & Moon Orbit Around Sun 5 Effect of Moon Orbit Declination on Tidal Pattern The Tidal Force Exerted on the Earth by the Sun is About 46% of the Tidal Force Exerted on the Earth by the Moon 6 Combined Effects of the Moon & Sun Induced Tides Spring Tides Occur When the Moon Pulls along the same Line as the Sun. (new and full moon). Neap Tides Occur When the Moon Pulls at 90o to the Sun (first and last quarter moon) 7 Equilibrium Tide Theory Roughly Explains: • diurnal, semidiurnal and mixed semidiurnal tides • spring/neap tide series 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 of tide wave propagation • Affected by Coriolis Force • 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 Shallow- Water Wave for depths < L/20 or for bottom depths < 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 Shallow-Water Waves 10 Earth’s Rotary Tides Depicted with Cotidal Lines Earth’s Corange Lines Note that coastal regions generally exhibit largest tidal ranges 8 6 4 2 10 • 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 Dynamic Theory of Tides Tide waves are forced shallow water waves that are subject to Coriolis force and constrained by the geometry of ocean basins 11 A Couple of Other Interesting Features of Tides… Tidal Forcing of Shallow Embayments can Enhance Tidal Ranges For certain coastal geometries tidal forces can be in Resonance with the tide wave and this can lead to exaggerated tidal variation 12 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