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Lagrangian versus Eulerian Tracers

In oceanography and in fluid dynamics in general, our observations can be made in two ways: Lagrangian measurements and Eulerian measurements.

Lagrangian measurements involve following a parcel of fluid as it moves. For example, we could measure temperatures from a weather balloon or from a free-floating buoy.

The other way to make measurements is to have an observation site geographically fixed. For example, we can measure temperature at a fixed weather station or from an anchored buoy in the ocean. Measurements made in this manner are known as Eulerian measurements.

Eulerian Current Observations

Measurements of ocean current are collected using a variety of methods. One popular way to measure ocean currents is to determine the water's velocity at one fixed place in the ocean. This type of measurement is called Eulerian, in honor of the Swiss mathematician Leonhard Euler. This is typically accomplished using an electro-mechanical current meter (which measures the velocity at a single depth) or Acoustic Doppler Current Profiler (ADCP) (which can provide a profile of velocity with depth). Current meters are usually on a wire of a mooring, which is deployed from a ship. ADCPs can be mounted on a mooring, the ocean bottom, or the underside of a vessel. Both will provide a time series of the velocity of the ocean's water at a single geographic location. Current measurements are also obtained using High-Frequency Radar.cean Tower off Georgia coast where an ADCP is deployed on the ocean bottom for Eulerian current measurements.

Acoustic Doppler Current Profiler (ADCP) shown before deployment on ocean bottom.

Lagrangian Current Observations

Drifting profiler shown before deployment. Instruments of this type make Lagrangian measurements as they are swept along by ocean currents. Satellites track their positions with Global Positioning Systems (GPS).

Another direct way to measure ocean currents is by tagging a water material with either floats or dyes. This viewpoint of following a tagged water parcel is called Lagrangian, named in honor of Joseph Louis Lagrange, a French mathematician. Near-surface ocean currents are measured by so-called drifters, which is a buoy that rides at the ocean surface and is usually weighted at some depth to negate the direct effects of wind on the buoy itself. Tracking this drifter (by satellite, radar, radio, sound, etc.) will give a description of the ocean current.

The animation below shows the tracks of many drifters through time. Each half second frame of the animation represents 12 hours of drifter movement. The animation loops after representing two weeks of drifter movement. Notice the drifter dragged along by the Loop Current until it is ejected through the Straits of Florida and picked up by the Gulf Stream. Also notice the drifter trapped in a mid-Atlantic Gyre at the upper right of the map.

The short and straight arrows near shore represent current measurements taken by fixed Eulerian stations either on shore, on ocean towers, or on moored bouys. The changing splotches of color off the northern coast of North Carolina and the southeastern tip of Florida represent hundreds of simultaneous current measurements taken by high frequency radar. The lively background colors represent sea surface temperature as measured by satellites. More red means warmer water. More blue means cooler water.

Notice how the drifter pulled along by the Loop Current is following the edge of a temperature gradient in the Gulf of Mexico. The Loop Current trapping a mass of warmer water. Notice how the Gulf Stream pushes warmer water from the tropics northward along the coast. The Gulf Stream is part of the Global Conveyor Belt distributing heat around the world by means of flowing ocean currents.

Scientists often use Eulerian and Lagrangian measurements together to learn about the flowing ocean. Scientists have launched thousands of Lagrangian drifters into the ocean and deployed hundreds of fixed Eulerian stations near shore to observe ocean circulation. The animation below superimposing Eulerian and Lagrangian measurements was constructed by Jesse Cleary of the North Carolina Coastal Ocean Observing System, a SECOORA partner.

Drifter tracks and HF Radar current readings plotted on top of remotely sensed Sea Surface Temperature (SST).