Erratic internal waves at SIO Pier data and wavelet analysis courtesy of E. Terrill, SIO
Internal Surface Waves warm water Slow f ω N ~1day ~hours cold water Big tens of meters
Internal Waves warm water Slow f ω N ~1day ~hours cold water Big tens of meters
Simple interfacial internal wave h = h 0 cos(kx ωt) 2π/k = one wavelength U 1 = ωh 0 cos(kx ωt) H 1 k H 1 U 1 h U 2 = ωh 0 cos(kx ωt) H 2 k H 2 U 2 after Gill, Atmosphere-Ocean Dynamics
Internal wave equations Linearize equations of motion u = u u + fv 1 p ρ x + ν 2 u v = u v fu 1 p ρ y + ν 2 v w = u w 1 p ρ z + ν 2 w g ρ = u ρ + κ 2 ρ u = 0
Internal wave equations Linearize equations of motion u = u u + fv 1 p ρ x + ν 2 u v = u v fu 1 p ρ y + ν 2 v w = u w 1 p ρ z + ν 2 w g ρ = u ρ + κ 2 ρ u = 0
Internal wave equations Linearize equations of motion u = u u + fv 1 p ρ x + ν 2 u v = u v fu 1 p ρ y + ν 2 v w = u w 1 p ρ z + ν 2 w g ρ = u ρ + κ 2 ρ u = 0 Try a solution of the form u(x, y, z, t) = ûe i[kx+ly+mz ωt] Get polarization and dispersion relationships ω 2 = (k2 + l 2 ) N 2 + m 2 f 2 k 2 + l 2 + m 2
Internal wave equations Linearize equations of motion u = u u + fv 1 p ρ x + ν 2 u v = u v fu 1 p ρ y + ν 2 v w = u w 1 p ρ z + ν 2 w g ρ = u ρ + κ 2 ρ u = 0 Try a solution of the form u(x, y, z, t) = ûe i[kx+ly+mz ωt] Get polarization and dispersion relationships ω 2 = (k2 + l 2 ) N 2 + m 2 f 2 k 2 + l 2 + m 2 (Glenn Flierl)
Continuous stratification Z U Mode-1 wave (approx two-layer) U = Ψ(z)cos(kx ωt) Wave propagation direction Allowable frequency range f ω N days to minutes
What generates internal waves? 1) Wind makes near-inertial internal waves 116 118 120 122 124 126 128 130! / N m!2 0.4 0.2 Wind Stress 0 15 8 T z / m 35 7 T / C 55 6 V bc S 2 z / m z / m 15 35 55 15 30 45 116 118 120 122 124 126 128 130 yearday 0.2 0!0.2!3!4!5!6 log 10 (S 2 / s!2 ) V bc / m s!1 (MacKinnon and Gregg, JPO, Dec 05) a good offense p.15
What generates internal waves? 2) Barotropic tide sloshing over topography Internal Tide: An internal wave with a tidal frequency, usually once in 12.4 hours = M2 Often generated at the continental shelf break, with waves propagating both on and off shore. (J. Nash)
Internal-tide generation in Monterey Bay courtesy of Oliver Fringer
Internal-tide generation in Monterey Bay courtesy of Oliver Fringer
Global pattern of internal tides Simmons et al 2004
Complicating factors: higher-mode waves Waves propagate in beams......or wave packets (Oliver Fringer) (Glenn Flierl)
Complicating factors: complex topography
SIO Pier temperatures
Strength of surface and internal tide (SIO pier) Eric Terill semi-diurnal diurnal Time in hours Barotropic tide: regular beating of semi-diurnal (12 hour) and diurnal (24 hour) signals Time in hours Internal tide: a mess! C h a n g i n g s t r a t i f i c a t i o n, mesoscale currents, eddies,...
More local internal tides Lerczak, Winant and Hendershott, 2003 Figure 1. Internal Waves on the Continental Margin (IWAVES) study site. Circles mark the locations of
Complicating factors: nonlinearity U 1 U 2 h Linear waves h + c h 0 x =0 h(x, t) =cos(x c 0 t) Non-linear waves h +(c 0 + h) h x =0 When wave amplitude gets large (shallow water), crest of wave moves faster, so wave starts to steepen. This can take several forms...
Solitons: internal waves of unusual size nonlinear steepening balanced by dispersion 24 hours Stanton and Ostrovsky GRL 24(14) 1998 100 minutes
Nonlinear internal tides: bores courtesy of S. K. Venayagamoorthy and O. Fringer, Stanford
Nonlinear internal tides: bores courtesy of S. K. Venayagamoorthy and O. Fringer, Stanford
Why you should care Internal-wave fluctuations often dominate any signal you measure. Up/down CTD casts. Moorings. Internal-wave shear produces turbulence and mixing. Most mixing at interface / thermocline, can bring nutrients up into the euphotic zone. (next week) May create net on or offshore transport of mass / nutrients / larvae /???
Consequences of Internal Waves Wave breaking mixes the ocean (next week). FIG. 14. Example acoustical snapshot of a propagating ISW within which is embedded a sequence of rollups identical in nature to Kelvin Moum et al 03
Hawaiian Ocean Mixing Experiment (HOME) Huge overturns as internal tide sloshes up and down a steep slope Klymak et al 07 Levine and Boyd 06 Aucan et al 05 Velocity Temperature Dissipation rate Klymak et al 07
Hawaiian Ocean Mixing Experiment (HOME) Huge overturns as internal tide sloshes up and down a steep slope Klymak et al 07 Levine and Boyd 06 Aucan et al 05 Velocity Temperature Dissipation rate Klymak et al 07
Hawaiian Ocean Mixing Experiment (HOME) Huge overturns as internal tide sloshes up and down a steep slope Klymak et al 07 Levine and Boyd 06 Aucan et al 05 Velocity Temperature Dissipation rate Klymak et al 07
100 200 IW transport larvae/nutrients N A The Southern California Bight Point Conception log chlorophyll concentration (µmol L -1 ) 0.05 0.2 1 4 8 Los Angeles San Diego B N 32 o 50` # - CTD station and bottle sample CTD station C 32 o 40` N ADCP w WW 32 o 45` 500 50 1 2 3 4 75 50 SIO 10 25 117 o 20` 117 o 10` 10 20 w San Diego 117 o 15` 117 o 10` W w meters above bottom 20 15 10 5 20 15 10 5 20 15 10 5 20 15 10 5 u p N u p 0.1 0-0.1 50 0-50 5 0-5 2 0 m s -1 Pa µmol L -1 W m -2-2 Drew Lucas, SIO 20 15 10 5 u N 05!Aug 09!Aug 13!Aug 17!Aug 22!Aug 0.3 0-0.3 µmol m L -1 s -1
Larvae transport onshore Convergence at the front of a wave train Only strong upward swimmers can stay in the front Pineda 99