WATER LEVEL VARIATIONS III (TIDEINDUCED)

25/10/2014 WATER LEVEL VARIATIONS III (TIDE-INDUCED) Tide-Induced Water Level Variations Astronomical Tides 25/10/2014 Gravitational Force Attraction force between two bodies: Fg  f m1m2 r2 Individual water elements on Earth attracted by slightly different forces Departure from mean net force => tides Newton Schematized Distribution of Forces fa: local attraction force fa-F yields tidal-generating force Because of Earth’s rotation: two highs and two lows in a day (approximately) Moon’s orbital motion => about 12 hr 25 between highs 25/10/2014 Types of Tide semidiurnal diurnal mixed Influence of the Sun Sun has different mass and distance to Earth = > effect less than half the moon’s influence Spring and Neap Tides 25/10/2014 Typical Tidal Curves United States coast Equilibrium Theory Assume that water responds instantaneously to forces of sun and moon (no inertia and friction) Tide can be predicted as a sum of harmonic terms: N h(t )  ho   fi hi cos  t  (Vo  u )i   i  i 1 Compute coefficients from water level data Tidal Constituents and Arguments 25/10/2014 Time and Phase Shift Effects Dynamic Theory Tidal motion is viewed as a forced wave Basin shape + Coriolis important => Kelvin Waves Laplace Amphidromic Point IN THE NORTHERN HEMISPHERE: FLOOD TIDE CO-TIDAL LINES & AMPHIDROMIC POINT EBB TIDE (3/12)T (4/12)T (2/12)T (5/12)T (1/12)T (6/12)T t=0 (7/12)T (11/12)T (8/12)T (10/12)T (9/12)T t = t = (6/12)T cross-section cross-section AMPHIDROMIC POINT Co-range lines are concentric curves about the amphidromic point MOTION OF CREST 25/10/2014 Cotidal and coamplitude lines Global Tidal Variations Microtides: < m Mesotides: – m Macrotide: > m Tide Gage 25/10/2014 ADCIRC Model Simulates tidal motion + storm surge Application to Shinnecock, Long Island ... harmonic terms: N h(t )  ho   fi hi cos  t  (Vo  u )i   i  i 1 Compute coefficients from water level data Tidal Constituents and Arguments 25/10/2014 Time and Phase Shift Effects Dynamic Theory... and Neap Tides 25/10/2014 Typical Tidal Curves United States coast Equilibrium Theory Assume that water responds instantaneously to forces of sun and moon (no inertia and friction) Tide can be predicted...25/10/2014 Gravitational Force Attraction force between two bodies: Fg  f m1m2 r2 Individual water elements on Earth attracted by slightly different forces Departure from mean net force =>