Nonlinear Internal Waves

enlargeSurface Expression of NLIW

Long bands frequently appear at the sea surface in coastal waters. These are visible to the eye, as well as to both shipboard and satellite radar. These are the surface expressions of waves that are internal to the fluid and have the special property that they do not disperse as surface gravity waves and internal gravity waves do. They are called by the generic term nonlinear internal waves (NLIWs). The surface patterns in the photo are NLIWs that we have sampled from ship over the New Jersey shelf.

Measurements and Observations

enlargeKH Billow
The internal structure of these waves can sometimes be illuminated by acoustics, if sufficient acoustic scatterers are present. Here, acoustic scattering is primarily due to small-scale sound speed fluctuations created by turbulence in the wave. Roll-ups within the wave indicate internal instability, which leads to turbulence.
enlargeCHAMELEON Launch
We make in situ measurements of these waves with our turbulence profiler, Chameleon, here being delicately launched from the deck of R/V Oceanus over New Jersey's continental shelf. R/V Knorr is in the background. Scientists onboard the Knorr are busy observing alterations to acoustic propagation caused by the waves we are tracking.
enlargeTurbulence Profiles
These in situ measurements tell us how the density is perturbed (2nd panel) and how energetic the turbulence is in the waves (3rd panel). The line plots overtop the acoustic images represent Chameleon profiles. All of the above waves propagate along near-surface stratification and are termed waves of depression.
enlargeElevation wave
Bottom-trapped waves of elevation can occur in the presence of a near-bottom density interface. Although these are less amenable to surface observation, a bottom lander fixed to the seafloor provides a rock steady viewpoint and captures water column velocity (top panels), and near bottom density and turbulence (lower panels). These types of measurements have led the way in deciphering some of the elusive physics of the waves. This image shows 30-m amplitude waves that precede a near-bottom density increase and induce significant near-bottom turbulence. This feature thus has characteristics of both a wave and bore.

From these detailed seafloor-based measurements we have computed the wave-induced pressure throughout the water column. The pressure signal is made up of 3 terms inferred form the equations of motion, that when summed, provide excellent agreement with measured seafloor pressures. And because the pressure plays a big role in the energy transport, our ability to accurately determine it has allowed a meaningful assessment of the energy transported by the waves.


During one experiment (at the mouth of the Columbia River that separates Oregon and Washington) we were fortunate enough to observe the process by which waves are formed by the buoyant river plume issuing into the coastal ocean. The front of the tidally-pulsing river plume grows in amplitude as it decelerates with the changing of tide. Wave fission occurs when the front's speed matches that of the allowable wave speed in the fluid ahead. Thereafter, freely-propagating waves were observed ahead of the front.


enlargeEnergy Loss
Wave tracking experiments that follow one wave group over extensive distances across the shelf help illuminate the evolution process that nonlinear internal wave trains may undergo on their shoreward journeys. During one such experiment performed off the Oregon shelf, microstructure and density measurements through the lead depression wave of the group allowed for an energy budget to be estimated. For this particular wave, we observed a loss in energy that was approximately balanced by the measured turbulent dissipation in the wave.
As part of the SW/NLIWI 2006 (Tang et al., 2007), another wave tracking experiment was performed off the New Jersey coast. Here, detailed measurements reveal a possible outcome of the structural evolution of shoaling depression waves. As mentioned above a pycnocline located near the surface supports depression waves, while a pycnocline located closer to the bottom will result in elevation waves. As a nonlinear internal wave of depression shoals, the depth of the water column decreases and a point where the fluid switches from supporting depression to elevation waves may exist. As a depression wave approaches this critical point the wave develops an asymmetry, with the lead edge traveling faster than the rear face. The slope of the leading face becomes less and less steep, until its signature is no longer discernible. At this point, an elevation wave emerges as the leading wave in the train.
More about our work on nonlinear internal waves:

Observations of polarity reversal in shoaling nonlinear waves, submitted, J. Phys. Oceanogr. (E.L. Shroyer, J.N. Moum, and J.D. Nash) [pdf]

Seafloor pressure measurements of nonlinear internal waves, J. Phys. Oceanogr., 38(2), 481-491, doi:10.1175/2007JPO3736.1, 2008 (J.N. Moum and J.D. Nash) [pdf]

Shallow Water 2006: a joint acoustic propagation/nonlinear internal wave physics experiment, Oceanography, 20(4), 156-167, 2007(D.J. Tang, J.N. Moum, J.F. Lynch, P. Abbot, R. Chapman, P. Dahl, T. Duda, G. Gawarkiewicz, S. Glenn, J.A. Goff, H. Graber, J. Kemp, A. Maffei, J. Nash and A. Newhall) [pdf]

Dissipative losses in nonlinear internal waves propagating across the continental shelf, J. Phys. Oceanogr., 37(7), 1989-1995, 2007 (J.N. Moum, D.M. Farmer, E.L. Shroyer, W.D. Smyth and L. Armi) [pdf]

Energy transport by nonlinear internal waves, J. Phys. Oceanogr., 37(7), 1968-1988, 2007 (J.N. Moum, J.M. Klymak, J.D. Nash, A. Perlin and W.D. Smyth) [pdf]

The pressure disturbance of a nonlinear internal wave train, J. Fluid Mech, 558, 153-177, 2006 (J.N. Moum and W.D. Smyth) [pdf]

River plumes as a source of large-amplitude internal waves in the coastal ocean, Nature, 437, 400-403, 2005 doi:10.1038/nature03936 (J.D. Nash and J.N. Moum) [pdf]

Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward over the continental shelf, J. Phys. Oceanogr., 33, 2093-2112, 2003 (J.N. Moum, D.M. Farmer, W.D. Smyth, L. Armi and S. Vagle) [pdf]

Internal solitary waves of elevation advancing on a sloping shelf, Geophys. Res. Lett., 30, OCE 3-1 - 3-4, 2003 (J. M. Klymak and J.N. Moum) [pdf]