Oceanic Internal Waves: global patterns and open questions Jennifer MacKinnon Scripps Institution of Oceanography.

Transcription

1 Oceanic Internal Waves: global patterns and open questions Jennifer MacKinnon Scripps Institution of Oceanography

2 Internal wave equations for the ocean u t = u u +2Ω u 1 ρ p gẑ + ν 2 u ρ t = w ρ z + κ 2 ρ u = Incompressible Traditional approximation Boussinesq ρ = ρ + ρ(z)+ρ (x, y, z, t) ρ, ρ(z) << ρ Inviscid (at least until they break) Linear (surprisingly often, some nonlinear examples shortly)

3 Vertically propagating waves Try a solution of the form u(x, y, z, t) =ûe i[kx+ly+mz ωt] Get polarization and dispersion relationships Internal wave equations ω 2 = (k2 + l 2 )N 2 + m 2 f 2 k 2 + l 2 + m 2 f<ω<n

4 Vertically propagating waves Try a solution of the form u(x, y, z, t) =ûe i[kx+ly+mz ωt] Get polarization and dispersion relationships Internal wave equations ω 2 = (k2 + l 2 )N 2 + m 2 f 2 k 2 + l 2 + m 2 f<ω<n

5 Vertically propagating waves Try a solution of the form u(x, y, z, t) =ûe i[kx+ly+mz ωt] Get polarization and dispersion relationships Internal wave equations ω 2 = (k2 + l 2 )N 2 + m 2 f 2 k 2 + l 2 + m 2 f<ω<n (Glenn Flierl)

6 Vertically propagating waves Try a solution of the form u(x, y, z, t) =ûe i[kx+ly+mz ωt] Get polarization and dispersion relationships Internal wave equations ω 2 = (k2 + l 2 )N 2 + m 2 f 2 k 2 + l 2 + m 2 f<ω<n (Glenn Flierl) Vertically standing waves u(x, y, z, t) =û Ψ(z)e i[kx+ly ωt] rigid upper and lower boundaries similar to two-layer interfacial waves ocean stratification typically decreases with depth horizontal wavelength 1-1 km

7 Motivation - breaking waves mix the ocean Waves break by shear instability and/or convective overturning. (see Staquet and Sommeria 4 for a review) Moum et al 3 FIG. 14. Example acoustical snapshot of a propagating ISW within which is embedded a sequence of rollups identical in nature to Kelvin

8 Motivation - breaking waves mix the ocean Waves break by shear instability and/or convective overturning. (see Staquet and Sommeria 4 for a review) heat conveyor Moum et al 3 FIG. 14. Example acoustical snapshot of a propagating ISW within which is embedded a sequence of rollups identical in nature to Kelvin P E K E Low Latitudes High Latitudes (Munk and Wunsch)

9 Patchiness of Deep Mixing matters Spatial distribution of mixing reflects geography of internal wave generation, propagation and breaking Kunze et al 6

10 Patchiness of Deep Mixing matters Spatial distribution of mixing reflects geography of internal wave generation, propagation and breaking Kunze et al 6 Palmer et al. (27): bottom-enhanced diffusivity => deep overturning Constant κ = Bottom-enhanced diffusivity

11 Cant explicitly resolve internal waves in climate models. Climate Process Team: Funded to combine theory, observations and simulations to develop and implement improved parameterizations of internalwave driven mixing in global climate models The Team: Matthew Alford (UW) Brian Arbic (U Michigan) Frank Bryan (NCAR) Eric Chassignet (FSU) Gokhan Danabasoglu (NCAR) Peter Gent (NCAR) Mike Gregg (UW) Steve Griffies (GFDL) Robert Hallberg (GFDL) Steve Jayne (WHOI) Markus Jochum (NCAR) Jody Klymak (UVic) Eric Kunze (Uvic) William Large (NCAR) Sonya Legg (GFDL/Princeton) Jennifer MacKinnon (SIO) Rob Pinkel (SIO) Kurt Polzin (WHOI) Harper Simmons (UAF) Lou St. Laurent (WHOI)

12 Cant explicitly resolve internal waves in climate models. 1) Wave generation 3 steps to parameterize their role: Latitude / Latitude / JFM AMJ JAS 1997 Internal-Tide Generation OND Longitude / Π(<H>) / Wm -2 Egbert and Ray 1 Wind-generated near-inertial internal waves Alford 1 <H> / m Π(5 m) / mw m Π(<H>) / mw m a [St. c Laurent, Nycander talks] 37.5 N 37.5 S Generation where barotropic (astronomical) b tides are large and topography is rough. Fairly steady in time. Generation J F Mby Arotating M J Jcomponent A S O Nof D Month wind stress, mirrors storm tracks. NOT steady in time (episodic storms + Figure 6. (a,c) The monthly mean flux is seasonal cycle), but seasonally averaged plotted for each year (thin lines, solid=1996,dashed=1997,dashdot=1998,dotted=1999), pattern reasonably(?) consistent and for the 4-year mean (heavy line). Black lines are from 37.5 N, and gray[simmons lines are fromtalk] 37.5 S. (a) The flux without mixed-layer-depth correction, Π(5 m). (b) The

13 Cant explicitly resolve internal waves in climate models. 1) Wave generation 3 steps to parameterize their role: 2) Some waves break locally, leading to a global pattern of mixing that mirrors wave generation. This can be roughly broken down into weakly and strongly nonlinear dynamics A: wave action = E/ω A t + r (C g + u)a + p RA = T r + S o S i flux divergence refraction by mesoscale energy transfer to other internal waves sources and sinks ordinate, the wavenumber vector, = the Primary wave

14 Cant explicitly resolve internal waves in climate models. 1) Wave generation 3 steps to parameterize their role: 2) Some waves break locally, leading to a global pattern of mixing that mirrors wave generation. This can be roughly broken down into weakly and strongly nonlinear dynamics A: wave action = E/ω [polzin 4] A t + r (C g + u)a + p RA = T r + S o S i flux divergence refraction by mesoscale energy transfer to other internal waves sources and sinks ordinate, the wavenumber vector, = the Primary wave As a wave propagates upwards from a source region, it steadily looses energy to other internal waves (+mesoscale effects), which in turn lose energy to other waves... which dissipate locally. So an internal tide leaves behind a wake of dissipation Secondary (smaller scale?) waves Tr=ε

15 Nearfield: strongly nonlinear wave breaking Internal hydraulic jumps, strong bores, solitons etc [Akylas, Carr, Farmer, Helfrich, Shroyer, Staquet, Weidman talks] Strong tidally driven overturning in the South China Sea [Alford, Simmons, Nash, MacKinnon, Klymak, Pinkel] 22 N MP/ADCP mooring PIES LADCP/CTD station Yang mooring 5 4 lat o 3 P6 2oN 3. 2 lat 21oN 3 P2 P5 A1 P1 121oE 2 4 MPS 48 lat S S8 121oE lon oE 15 3 S4 S5 Observed Model 3 kw/m 12 depth / m FS S6b S6a e 12oE 122oE P3 in 119oE NR 2oN MPS S7 FS S6b So S6a ut he S4 rn S8 S5 L 19oN P7 P4 P3 3 MPN lon Northern Line 2oN N2a N2b Observed Model 3 kw/m 4 N2aMPN P7 NR P6 N1b N1a N2b P1 A1 Y1 N1b N1a oE 15 3 lon Figure 1: Model bathymetry and all IWISE stations. Measured (black) and modeled fluxes (yellow) are (Alford also plotted. The regions shown in close-up at right are shown with boxes at left. talk on Wednesday)

16 Farfield wave breaking (a) / mixing 5 o N Most (7-9%) internal tide energy escapes to propagate thousands of km away. 4 o N 2 kw/m Where do these waves break? [St. Laurent and Nash 4] 3 o N Altimetric tidal fluxes 2 o N Northbound Zhao and Alford 1 o N 17 o E 18 o W Southbound 17 o W 16 o W 15 o W 14 o W (a) 5 o N (b) 5 o N 2 kw/m 4 o N 4 o N 3 o N 3 o N 2 o N 2 o N 1 o N 17 o E 18 o W 17 o W 16 o W 15 o W 14 o W 1 o N 17 o E 18 o W 17 o W 16 o W 15 o W 14 o W (b) 5 o N 4 o N

17 The waves that get away... Energy lost to strong wave-wave interactions like Parametric Subharmonic Instability (PSI) Propagating low-mode waves lose some energy through a slow bleed to ambient internal wave field through wave-wave interactions, supplying the background dissipation rate. Some energy lost through interaction with mesoscale, trapping in regions of high vorticity (e.g. Kuroshio) or high shear (e.g. equatorial undercurrent) Whatever isn t lost in transit breaks when waves crash into continental slope or other topography How important is each?

18 Convergence of numerical internal tide fluxes (MacKinnon and Winters et al 5) Parametric Subharmonic Instability (PSI) Strong resonant instability near 29 º where f = M2/2 Energy loss from M2 internal tide to small-scale M2/2 motions Subharmonic waves have equal amounts of upward and downward propagating energy Parametric Subharmonic Instability Convergence of altimetric internal tide fluxes (Tian et al 6) Diffusivity / m 2 s -1 Atlantic Indian Pacific Hibiya and Nagasawa 4 MacKinnon and Winters 5 Furuichi et al 5 Young, Tsang and Balmforth 7 Hibiya et al 7 Young et al 8 Munroe talk Latitude Latitude Latitude

19 Observations of PSI Internal Waves Across the Pacific Alford, MacKinnon, Pinkel, Klymak, Peacock TOPEX Altimetry 38 PEZHAT Filtered Vmean MP6 2 kw/m 36 Raw Vmean TOPEX Pass kw/m Surface generation Phase Energy Mooring 2 kw/m 34 Vertically standing (PSI generation) Ri =.7 Neap MP5 Latitude 32 TS2 3 MP4 TS1 MP3 28 MP2 Spring TS3 26 MP SSHA / cm 24 Surface generation Phase Energy French Frigate Shoals Nihoa Island 22-6 Kauai Channel Longitude Depth / 1 m (Alford et al 7 24 F IG. 6. Top row: amplitude of the first three modes, based on a full-depth fit to standard vertical mode shapes for horizontal velocity. Bottom row: direction of the energy flux for the first three modes. Bispectra show significant phase-locked energy transfer from tidal to subharmonic motions B: Triple product for (-f,-f, M2) triad C: Bicoherence for subset of data D: Biphase 2 4 Depth / m A: Bispectra Biphase / radians (MacKinnon et al 11a,b)

20 IWAP continued / cpm signal does not meet the bicoherence significance test. Depth / m A B C D x k z / cpm However, net transfer rate and local dissipation rate are quite modest Rate of energy transfer to subharmonic Local dissipation rate k z / cpm FIG. 7. Spectral comparisons for various depth windows at 28.9 N. Here all data h TS1 time series. Depth / m MP3 / TS1: 29N at which they It is unclear w or something process model c. Mixing imp Working w mates (Thorpe the Pacific is sivity is close m towards lower torwards of th et al. (27) h these new esti in larger-scale the backgroun a huge drain o propagation ob Acknowledg This work w tireless captain our two month 5 5 W kg 1 x yearday 1.5 Discrepancy between observations and predicted catastrophe likely due to Multiple tidal modes going various directions Internal tide changes in time, due to both mesoscale refection and S-N cycle, both of which limit PSI growth rates (Hazewinkel and Winters 11) (MacKinnon et al 11a,b) / m 2 s 3 FIG. 5. Average dissipation rate plots at 29 N from various instruments. Here all daata is averaged ONLY over the time range during which the Fast CTD was operating. Alford, M., and M strain and m in press. mode-1 mode-3

21 The waves that get away... Some energy lost to PSI, but probably not much (~1-2% in a few specific places...?) Propagating low-mode waves lose some energy through a slow bleed to ambient internal wave field through wave-wave interactions, supplying the background dissipation rate. Some energy lost through interaction with mesoscale, trapping in regions of high vorticity (e.g. Kuroshio) or high shear (e.g. equatorial undercurrent) Whatever isn t lost in transit breaks when waves crash into continental slope or other topography How important is each?

22 Fate of internal tides II: nonlinear wave-wave interactions Empirical observations show a remarkably universal distribution of energy in wavenumber and frequency space, with energy spectra in both directions tending towards -2 slopes (McComas and Muller 81, Muller et al 86, Lvov and Tabak 1, Lvov and Tabak 4, Lvov et al 4, Polzin 4 (x 2) Low-mode internal tide Dynamics: energy loss to continuum [Pinkel talk] What we have: Mixing parameterizations based on MEASUREMENTS of a broadband wavefield Broadband spectrum Dynamics: Gregg- Henyey-Polzin scaling for rate of down-scale energy Diffusivity What regional-global models need: predictive knowledge of dissipation rate based only on low-mode internal waves (canʼt resolve continuum)

23 Numerical studies of energy transfer early later steady state Energy flows to smaller scales, till a broadband spectrum is created in which continued tidal forcing is balanced by down-scale energy transfer and dissipation. Vertical wavenumber Frequency spectrum -2 slope -2 slope [Mackinnon, in prep. Also Winters and D Asaro 97, Hibiya et al 2, Lvov and Yokoyama 9]

24 Question: Empirical results (MacKinnon and Gregg, 2,5) show that the relationship between low-mode shear and turbulent dissipation scales differently in the open ocean and shallow water. Why? MG suggest that either the lower vertical bandwidth or the higher tidal variability in coastal water might be to blame Changing the forcing: Wavenumber spectra (left) and dissipation rate (right) are shown for 5 simulations run to steady state with different levels of wave forcing (black lines/dots). For the fifth simulation, the forcing tide is abruptly changed, and the evolution over 2 days is shown in color (red to blue). 1 1 GM 1 9 slope=2 / cpm 1 1 / W kg slope=1/2 } ~ 1 days Wavenumber / cpm Energy / J kg 1 [MacKinnon, in prep] Steady state: The dissipation rate scales quadratically with the spectral level (ε ~ E 2 ), in agreement with numerous previous theories and simulations (e.g. Winters and D Asaro) Variable tide: When the forcing is changed, it takes time (~ 2 days here) for the small-scale waves to adjust to the new equilibrium. Initially, dissipation increases with increasing tidal energy, but more slowly (ε ~ E 1/2 ). This is the same scaling observed by MacKinnon and Gregg, perhaps because in coastal areas internal tides are highly variable and the wavefield is never in steady state.

25 Latitude / JAS Near-Inertial wave generation and decay OND Longitude / Π(<H>) / Wm -2 [Alford 1,3, Plueddemann and Farrar] igure 5. Seasonally averaged maps of energy flux from he wind into near-inertial mixed-layer motions for the year 997. Variability in mixed-layer depth is included by seaonally averaging the Levitus climatology. Π(<H>) / mw 1 J F M A M J J A S O N D Month How and where do wind-generated near-inertial waves break? Figure 6. (a,c) The monthly mean flux is plotted for each year (thin lines, solid=1996,dashed=1997,dashdot=1998,dotted=1999), and for the 4-year mean (heavy line). Black lines are from 37.5 N, and gray lines are from 37.5 S. (a) The flux without mixed-layer-depth correction, Π(5 m). (b) The monthly mean, zonally averaged Levitus and Boyer [1994] mixed layer depth, < H >, at 37.5 N (black) and 37.5 S (gray). (c) Mixed-layer-depth corrected flux, Π(H). What sorts of waves are generated? Low mode? High mode? Do we know? How does interaction with mesoscale upper ocean vorticity (eddies etc) affect the importance of the inertial component of the wind fields, nd the model gives zero currents. A few (< 1%) seasonallyveragedgeneration values are < (loss rather than their overall magnitude, in generating near-inertial and ofpropagation? energy to the atmosphere), (Young and motions. Ben Jelloul 97, Balmforth et al 98, Balmforth and ut all ofyoung these have 99, magnitudes Klein and less Llewellyn than.1smith mwm 2 1,, and Klein et al 4, Danioux et al 8, Elipot and Lumpkin 9) o are also plotted in blue. The rough land edges reflect the.5 grid spacing Seasonal Cycle The largest What inputs percentage occur from 3-5 of near-inertial N during northern energy The dissipates seasonal cycle locally? is examined by computing the zonal emispheric fall/winter, in bands across the western North average across the bands 37.5 N and 37.5 S. Examining the tlantic and Pacific, associated with northern midlatitude cycle of Π(5 m) (Figure 6a), a strong maximum is seen near torms. Large What fluxes happens also occurto at 3-5 the low-mode S during southern near December/January inertial waves? in the Clearly northern hemisphere seen in the (in agreement deep inter, particularly ocean (Alford in the Indian and Whitmont Ocean. 7), but we don t with know D Asaro how [1985]), far and they nearget June (Simmons in the southerntalk hemi-osphere. This pattern is consistent with primary forcing by Broad minima span the central and eastern portions of xx) ach basin. Interestingly, D Asaro s [1985] eastern Pacific winter storms. nalysis was conducted in a relatively low-flux region. He The zonally averaged mixed-layer depth (Figure 6b) is

26 High-frequency waves in the upper ocean Langmuir-cells create high-frequency (~1 min) internal waves that extract energy from the ML and break to produce mixing in the stratified layer below D surface streaks wind, waves drift, U ML c p = ω k = U ml Thermocline U ML (m.s -1 ) Uml direction depth (m) time (mins) phase direction of waves below * ML [Polton et al 8] These high-frequency waves may be trapped (and dissipate) in high-n transition layer separating upper ocean from main thermocline

27 High-frequency waves generated by convection Similar high-frequency waves generated by convection banging on the base of the ML. Similar equatorial measurements [ McPhaden and Peters 1992; Moum et al. 1992, Gregg et al. 1985; Wijesekera and Dillon 1991, Moum et al 9] Other studies of high-frequency internal waves generated by turbulent motions: Data from equatorial Pacific, N 14 W [R.-C. Lien] Dohan and Sutherland 5, Taylor and Sarker 7 Diamessis talk

28 Conclusions Two species of internal waves dominate the energy (and energy flux) of the oceanic internal wave band - internal tides and wind-forced near-inertial waves. In both cases, most of the energy radiates away from the generation site. Candidate dissipation mechanisms include topographic scattering, wavewave interactions (PSI), interaction with the mesoscale...?? Other types of waves (lee waves, high-frequency waves from turbulent motions) may be important parts of local energy and mixing budgets Mixing due to wave breaking is patchy in both space and time. Understanding and predicting these patterns is important for proper modeling of heat and other tracer distributions.

29 Open questions Near-inertial waves in the ocean? What kinds of waves does the wind make? How far do they go? How do they break? How do internal waves interact with the mesoscale? Some energy lost through interaction with mesoscale, trapping in regions of high vorticity (e.g. Kuroshio) or high shear (e.g. equatorial undercurrent) [Buhler, Williams talks] Seems likely that much of the propagating low-mode energy is dissipated where waves scatter off topography [Holmes-Cerfon, Kelly] or crash into the continental shelf or other large topography. Do we understand this process? [Eriksen 82, Johnston et al 3, Johnston and Merrifield 3, Legg and Adcroft 3, Nash et al 4, Martini et al 11, Kelly, et al 11, Klymak et al 11]

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