Some basic aspects of internal waves in the ocean & (Tidally driven internal wave generation at the edge of a continental shelf) Weifeng (Gordon) Zhang Applied Ocean Physics & Engineering Department Woods Hole Oceanographic Institution MOMSEI Summer School VI Phuket, Thailand 26-30 Oct. 2015
Some basic aspects of internal waves in the ocean (a math-minimum version)
Gravity wave fundamentals Vertical oscillations at the interface between fluids of different density, and the restoring force is gravity/buoyancy A special case is the air/water surface density discontinuity: surface gravity waves sea swell, tsunami Another example is the waves on the density interfaces underneath the ocean surface: Internal gravity waves? (Moum et al, Oceanography 2008)
Internal gravity waves in the ocean (internal waves) Harmonic oscillations in four-dimensions: Dispersion relation (the relationship between wave frequency, ω, and the wavenumbers, k, l and m): Wave frequency, ω, falls between f (inertial frequency; Coriolis parameter) and N (buoyancy frequency; stratification parameter): Internal frequency band: A peculiar property: The energy propagation is normal to the phase propagation on the vertical plane
z Lab experiment showing beam-like radiation from the wave source in continuously stratified fluid x (S. A. Thorpe The Turbulent Ocean Chapter 2) Energy propagation C g Phase propagation C p (online by Dale Durran)
z Lab experiment showing beam-like radiation from the wave source in continuously stratified fluid x Internal wave energy propagation characteristics: (S. A. Thorpe The Turbulent Ocean Chapter 2) Question: In both case, f = 0 and ω < N. Which case has greater ω? Free Internal waves:
Internal wave beams in the real ocean Cross-ridge velocity Density (Cole, et al, JPO, 2009) Beams Question: Why not straight?
One special form of internal waves riding on the thermocline: solitary internal waves Question: Which way are the waves going? Vertical temperature profile in East China Sea ~28 C ~14 C (Duda, et al, JMR, 2013)
Internal waves at the thermocline: Solitary Internal waves divergence convergence (Alpers, Nature, 1985)
Solitary internal waves in the Andaman Sea A space shuttle photograph on 5 May 1985 showing solitary internal waves (Jackson, 2004)
Solitary internal waves in the Andamen Sea The Observed ripplingsisotherms or bands on of choppy 25 water was mentioned Oct 1976 in the 1861 book of Mauray (The Physical Geography of the Sea and Its Meteorology): "The ripplings are seen in calm weather approaching from a distance, and in the night their noise is heard a considerable time before they come near. They beat against the sides of a ship with great A sequence violence, of and pass on, the spray sometimes photographs coming on of deck; a and by carrying out oceanographic passing rip band measurements from a ship, on a 27 small Oct boat 1976. could not always resist the turbulence The speed: of these remarkable ripplings". 2.2 m/s Perry and Schimke (JGR, 1965), the first oceanographic in situ measurements showing that the bands of choppy water in the Andaman Sea are associated with largeamplitude oceanic internal waves. (Osborne and Burch, 1980)
One form of internal waves riding on the thermocline: solitary internal waves Vertical temperature profile in East China Sea ~28 C ~14 C (Duda, et al, JMR, 2013)
Internal waves at the thermocline: Solitary internal waves Vertical temperature profile in East China Sea ~28 C ~14 C (Duda, et al, JMR, 2013)
Internal waves at the thermocline: Solitary internal waves Question: Which part of the water column can the solitary internal waves exist?
Internal waves at the thermocline: Solitary internal waves (Duda, et al, JMR, 2013)
Generation of internal waves in the ocean Tidal currents (ω M2 > f for most of the ocean) over sloping bottom Wind/storm-driven inertial motion (ω i = f) Sub-inertial flow (ω sub < f ) over steep topography Sub-harmonic evolution of shear instability Others?
Tidally-driven internal wave generation Isopycnals Tidal current (Lamb, 1994) Tidal currents pull/push stratified water at the shelf edge inducing vertical motions and creating potential energy anomaly that radiates away as internal waves
Wind/storm-driven generation of nearinertial internal waves Wind speed Inertial current speed Ice-covered Ice-covered Horizontal velocity shear could cause reduces effective inertial frequency inertial shear magnitude (Rainville and Woodgate, GRL, 2009) (Kunze, JPO, 1985)
Internal lee wave formation by sub-inertial flow over steep topography Available potential energy (Legg and Huijts, DSRII, 2006) Relaxation of the upstream inflow allows the available potential energy stored in the initially trapped lee waves to be released in the form of internal waves (Nakamura et al, JPO, 2000)
Sub-harmonic evolution of shear instability Acoustic backscatter images taken 30 minutes apart at Knight Inlet, British Columbia, Canada (Farmer and Armi, Science, 1999) Sub-harmonic evolution of the initially trapped fine-scale shear instability generates long waves, which have faster phase speed and escape the trapping.
Why do we care about internal waves in the ocean? They are a major conduit for energy cascading in the global ocean from large scale motions to small scale mixing Boundary turbulence and open ocean mixing created by internal waves are keys for maintaining abyssal stratification Internal waves can affect ecosystem dynamics on continental shelves through transporting marine species, facilitating upward nutrient supply, and affecting marine habitat Vertical motions of the isothermals and horizontal temperature gradient created by internal waves affect underwater sound propagation
Internal waves drive mixing in the ocean Question: which way is the wave propagating, to the left or right? C (Moum et al, Oceanography, 2008) Acoustic backscatter image
Internal waves drive mixing in the ocean C (Lamb, ARFM, 2014) Strong velocity shear associated with internal waves can generate shear instability and cause vertical mixing
Internal waves drive mixing in the ocean Vertical transection across the Hawai i ridge Vertical viscosity Vertical Diffusivity (Cole, et al, JPO, 2009) Strong velocity shear or breaking of the internal waves cause vertical mixing
Internal waves transport larvae (Pineda, Science, 1991)
Internal waves affect species behavior Internal waves Zooplankton
Internal waves affect marine habitat (Wall et al., PRSB, 2014) Temperature Internal waves
Influence of internal waves on sound propagation 3D ray tracing in a curved internal wave duct (Lynch et al, IEEE JOE, 2010 Inhomogeneous sound propagation caused by the horizontal temperature variation associated with the solitary internal wave