The Hudson takes on a tremendous load of pollutants due to its proximity to New York City, yet typically disperses these pollutants without severe environmental degradation. Through field deployments on the Hudson, we have observed vigorous turbulent mixing driven by tidal currents in frictional boundary layers near the riverbed, by winds in surface boundary layers, and also in internal mixing layers by breaking of “internal waves” that travel on the density interface that divides the deep salty ocean waters from the surface freshwater outflow.

Above are two acoustic “images” showing turbulent mixing and internal wave breaking on this density interface in Haverstraw Bay, 10 km north of the Tappan Zee Bridge.  Much like meteorologists measure rain droplet concentration and velocity in the atmosphere using Doppler radars, oceanographers can use Doppler sonars to measure water velocity and acoustic backscatter off ambient particles or off small-scale variations in water salinity.  The vertical profile of water salinity during periods such as this shows sharp layering at about mid-depth, with a surface layer that is nearly undiluted river water, and a bottom layer that is saline and thus had a slightly higher density.

The first period (top panel) was before the period of peak tidal currents, ebbing toward the ocean, and the second period (bottom) was at the time of peak ebb currents, about half an hour later.  Mean water velocities were ~1.4 m/s near the Hudson’s water surface (about 3 miles per hour), and near zero in the lower half of the water column.  The vertical difference in water velocity, called shear, is likely the reason for the wave breaking into turbulence, and for the conversion to a completely turbulent state shown in the lower panel.

Twenty-foot waves on the Hudson – but can you body surf on them?

You would have to hold your breath for quite some time, as the waves are breaking under water between layers of different density.  The waves also move slowly; velocity data show that it would take about a minute just for the wave to pitch over.

Below is a more detailed image showing velocity vectors on top of the acoustic backscatter, for the breaking wave shown above.  The vectors show the deviations from the 10-minute average velocity at each height above the riverbed.  Similarly, the colors show the deviations from the 10-minute average acoustic backscatter at each height.  By showing the deviations from average conditions, the wave and its velocities are more clearly visible.  The longest vector corresponds to a 5 cm/s deviation velocity, and the vectors are stretched by a factor of five in the vertical dimension to more clearly show the vertical component of velocity.

As mentioned previously, mean velocities during this period were ~1.4 m/s near the Hudson’s water surface, and near zero in the bottom of the water column.  This is why the deviation velocity vectors in the wave crest point to the right even though the crest appears as though it would be “pitching” forward, toward the left – deep water is being brought upward, and is traveling slower than the near-surface water it’s displacing, so its deviation velocity (or relative velocity) is actually toward the right.  In this case, one constituent being “mixed” by turbulence is momentum, whereby the high average momentum of the upper layer is diluted by the low momentum of the bottom layer.  You can read more about this type of turbulent mixing in the Hudson in my recent paper in Continental Shelf Research.

Turbulent mixing in context

Fluid dynamics, the study of fluids in motion, lies at the heart of most questions that humans ask of the ocean.  Evaluating problems such as storm surges, climate change, and pollutant discharges requires a detailed knowledge of ocean and estuary transport processes.  Also, Earth’s climate is conditioned by the ocean’s vast capacity to hold and transport heat, and many of the greatest uncertainties in projections of climate change lie in its depths.

This topic of turbulent mixing is increasingly recognized as one of the most difficult, yet important, problems in ocean physics.  It is difficult because it occurs on a variety of scales from millimeters to hundreds of kilometers – it is impossible to observe all these scales, or simulate them with computers, so scientists seek to develop simple physical rules in the chaotic turbulent patterns.

Generally shear is one of the main variables considered in simplified models of ocean or atmospheric turbulent mixing.  The type of shear-driven instability shown above is likely a Kelvin-Helmholtz instability, which are also commonly found at density boundaries in the atmosphere, magnetosphere, and on other planets.