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Geography 104 - “Physical Geography of the World’s Oceans”. Ocean Waves what is a wave? wave characteristics ocean surface gravity waves. Readings (Ocean Waves): Text Chapter 10 (pgs 190 - 217) Reader pgs. 231 – 242 (wave related material). What is a wave?
Geography 104 - “Physical Geography of the World’s Oceans” • Ocean Waves • what is a wave? • wave characteristics • ocean surface gravity waves Readings (Ocean Waves): Text Chapter 10 (pgs 190 - 217) Reader pgs. 231 – 242 (wave related material)
What is a wave? “In its simplest scientific form, a wave is an expression of the movement or progression of energy through a medium.” (Chamberlin and Dickey) “A wave is a disturbance that propagates through space and time usually with transference of energy.” (Wikipedia)
Ocean Wave Characteristics • propagating disturbance • characteristic length scale (wavelength) • characteristic time scale (period) • low frictional losses – thus able to travel long distances • energy transport (not water transport like currents*) • oscillatory (or cyclical) flow • weak interaction with other waves • movement depends on wave period and water depth • many types of waves in the ocean
Types of ocean surface waves • waves need a generating mechanism, and a restoring force • at ocean surface, disturbing force is wind • capillary waves (wavelengths < ~1cm) are restored primarily by surface tension (of interest for remote sensing of the ocean) • surface gravity waves exist at air-sea interface and are restored by gravity • internal gravity waves (not wind driven) exist at density interfaces beneath the ocean’s surface and are restored by gravity
Types of wave motion • progressive waves oscillate uniformly and travel (progress) without breaking particles move back and forth in direction of wave motion; examples: sound waves, pressure waves particles move back and forth in direction perpendicular to wave motion; occurs primarily in solids particles move in “orbitals” with both “back-and-forth” and “side-to-side” movement; need interface to exist; surface gravity waves
wave crests wave crest
wave movement 90° motion of wave crests
Definitions: (do on board) • crest • trough • amplitude • height • wavelength • wave period • wave frequency • wave steepness • phase speed (Equation 10.1)
Geography 104 - “Physical Geography of the World’s Oceans” • Ocean Waves (con’t) • wave (phase) speed of deep, intermediate, and shallow water waves • Stokes drift or wave drift • group speed (1/2 the phase speed in deep water) • wave generation (should have been #1) • wave interference (should have been #2) • dispersion Readings (Ocean Waves): Text Chapter 10 (pgs 190 - 217) Reader pgs. 231 – 242 (wave related material)
wave speed depends on water depth (h) relative to wavelength (L) • deep water: h > 0.5L • speed determined by L or T (not h); cg = 0.5c • shallow water: h < 0.05L • speed determined by h (not L,T); cg = c • intermediate water: 0.05L < h < 0.5L • speed determined by h and L or T; • most surface gravity waves near shore are in intermediate water depths (more complicated math) • for L = 220 m (T = 12 sec.) h between 11 -> 110 m
tanh (“tanch”) hyperbolic tangent function x < 0.5 tanh(x) = x x > ~2 tanh(x) = 1
wave speed vs. water depth = √gL/2π L c =√(gL/2π) tanh(2πh/L)
deep water waves orbit diameter at surface = H L/2 - little motion below depth = 0.5L - orbit diameters decrease rapidly with depth to ~4% of surface • phase speed = c = (gL/2π)1/2 • - depth condition: h > 0.5L or L/2
shallow water waves • phase speed = c =√g h • - depth condition: h < 0.05L or L/20
intermediate or transitional waves • phase speed = c =√(gL/2π) tanh(2πh/L) • - depth condition: L/20 < h < L/2
Stokes Drift or Wave Drift– slight movement of water in the direction of wave propagation due to wave orbitals that are not exactly closed. Greatest near surface where orbital diameters are largest.
group velocity cg- deep water waves travel in “trains” individual waves in front of train constantly die, and are replaced by new waves at rear of train crests disappear at front of group crests appear at rear of group
group velocity cg- deep water cg = group speed = ½ c crests disappear at front of group crests appear at rear of group c = speed of individual wave cg = group speed = ½ c
Fig. 10.18 movement of individual waves through a wave group can be observed by throwing a rock in a still pond
wave development and evolution surface gravity waves are generated by wind wave generation is typically in deep water
wave height is controlled by three factors: • wind speed • duration (length of time wind blows) • fetch (length of ocean over which the wind blows) • fully developed sea • result of sustained winds over a fetch • energy input by wind is lost by wave breaking (some energy into surface current generation) and propagation of energy from the region of generation
wave formation - fully developed sea wind time increasing fully developed sea: energy input of wind = energy loss by breaking & wave propagation away from storm center
Fig. 10.16 as wind blows wave steepness changes fully developed sea when wave steepness exceeds 1/7 (H/L)
Fig. 10.17 wave energy exists in various frequencies (waves of varying periods) as wind is not constant
wave interference two wave trains - different wavelengths & heights
Fig. 10.11 idea of wave energy spectrum: waves of different characteristics (L,T,f) all exist at once
wave energy and direction spectra from data at Harvest platform (SBC) Energy ~ H2
Fig. 10.19 wave generation by wind dispersion – waves with longer T and L will travel faster. Dispersion is the separation of waves that travel with different speeds.