Density Currents and Internal Waves

Outside Links: Lab Guide
Please leave tips, examples, and troubleshooting information in the comment section below.

Group 1 Tank Experiment: Density Currents

Alyssa Finlay, Bethany Kolody, Sara Rivera

Density currents (aka gravity currents) describe the horizontal displacement of a fluid due to a difference in density between two bodies. To model this effect, we used an experiment originally conducted by Marsigli in 1679. He was interested in why surface waters of the Bosphorous Strait moved from the Mediterranean to the Black Sea, but deeper waters moved in the opposite direction. He discovered that the key to the problem was that water originating from the Mediterranean Sea water is much denser than water originating from the Black Sea.

To model the situation, we placed a small tank with two vertically aligned holes (one just above the bottom, and one near the top) inside of a larger tank (see pictures below). We filled both tanks with room temperature tap water, until the water level equilibrated halfway through the top hole. We then increased the density of the water in the smaller tank by quickly and thoroughly mixing in 100mLs of salty water (room temperature tap water with 3 tablespoons of dissolved table salt, made visible by adding concentrated red food coloring). The red, dense water began flowing through the bottom hole into the larger tank, displacing the less dense water through the upper hole and into the smaller tank. Over a span of about 15 minutes, these two density counter-currents equilibrated, leaving one solid layer of dense red water below the less dense tap water.


Tips and Tricks:
In succeeding iterations of the experiment, we homogenized a few drops of yellow food coloring into the starting water in order to better visualize the flow of the less dense surface water into the smaller tank. To further this effort, after mixing in the salty red water and creating our density currents, we also added a drop of blue food coloring into the freshwater tank near the opening outside of the upper hole. Some of the dye was carried through the hole by the surface current which aided in the visualization of its motion (see pictures below). However, a large portion of the droplet sank vertically down the tank because it is denser than the surrounding water. When the dye reached the depth of the lower hole, it was pushed by the lower, salty water density current and clearly illustrated the motion of the deeper water.

Density currents


The Physical Theory:
We used the difference in vertical force being exerted in the salty versus the fresh tank to calculate horizontal force in the x direction from the salty tank to the fresh tank. From this, we could approximate the speed of the current (see calculations below).

ρfresh = 1.000 g/cm3
ρsalt = 1.025 g/cm3 (approximation)
ρavg= 1.013 g/cm3
h = 16.0 cm
L = 41.0 cm
g = 9.8 m/s2 = 980 cm/s2

An excellent example of a density current in an oceanographic setting is a turbidity current. A turbidity current is a gravity-driven density current in which clasts remain in suspension supported by upwelling fluid turbulence (Prothero and Schwab, 2004). They occur when an event stirs up a mixture of sediment on the bottom of a lake or the ocean. The liquefied mass of suspended sand and mud is denser than the lake or sea water that surrounds it, so it can move downhill under the force of gravity. An important distinction between turbidity currents and other bottom currents is that a turbidity current is not propelled by the water within it, but by gravity.
Turbidity currents result in depositional products called turbidites. Turbidites consist of thick sequences of alternating coarse sands and deep-water shales. For decades, these depositional sequences puzzled geologists, because the coarse sands suggested nearshore deposition, but were accompanied by deep-water shales. In the 1940s and 50s, the Dutch geologist Phillip Kuenen observed density currents with his own experimentsin a laboratory tank and showed that density currents could move enormous distances over relatively gradual slopes at velocities high enough to transport sand to the deep seafloor.
Understanding the underlying of turbidite deposition (turbidity currents) allows geologists to draw conclusions about paleoceanographic conditions. Sea-level changes appear to have a significant influence on turbidite deposition and there is a strong correlation between periods of increased deposition and low sea-level. Furthermore, turbidite sands are fairly coarse and are interbedded with impermeable shales, making them an important hydrocarbon source (Prothero and Schwab, 2004).
external image TurbidityCurrentFlowDiagram.jpg
external image continental_margin2.gif

external image TurbSD2.jpg
external image turbSunsetCl.jpg

Literature Cited:
Donald R. Prothero, Fred Schwab. (2004). Sedimentary Geology; An Introduction to Sedimentary Rocks and Stratigraphy (2nd ed.). New York: Freeman.

Group 2 Tank Experiment: Internal Waves

Caroline Lowcher, Irina Koester, Travis Courtney
Fall 2015

Theory + Brunt-Vaisala Frequency:
On any typical trip to the beach, an observer will notice surface waves as they approach the shore and break. However, these are not the only types of waves in the ocean. In fact there are waves that propagate thousands of kilometers in the ocean’s interior with amplitudes the size of skyscrapers (MIT News). These internal waves can be generated by tides, winds, storms, nonlinear interactions with waves of other frequencies, among other dynamics and can enhance mixing and nutrient exchange for biological productivity (Mackinnon, J.). In a stable fluid, one where density continuously increases with depth, internal waves can propagate along density interfaces. When an event occurs that causes a vertical perturbation or acceleration of a fluid parcel, gravity serves as a restoring force to return the particle to its original position. This restoration is influenced by the Brunt-Vaisala frequency, which is the angular frequency of oscillation for a vertically displaced fluid parcel, also known as the buoyancy frequency. Given that a column of water in the ocean has little compressibility with depth, we can assume an incompressible fluid in evaluating the buoyancy frequency.

Applying Newton’s second law, we can rearrange to solve for acceleration yields, a = F/m; where a is acceleration, F is force, and m is mass. Our interest is in the vertical, thus we will look at forces acting in this direction, namely a restoring gravitational force. This leads to a differential equation whose eigenvalues are the Brunt-Vaisala frequency, N, with a general solution involving cosines and sines which determines the oscillation of the fluid parcels when vertically displaced.
We can rearrange the equation for density to solve for mass and plug that into Newton’s second law. Then rewrite the acceleration as the second derivative of position in the vertical direction. Thus, we have a solvable differential equation whose solution shows the vertical motions of the fluid parcel and whose eigenvalue is the buoyancy, N.
ρ = m/V therefore m = ρV

a = -g(ρ1-ρ2)V/ρ1V

d2z/dt2 = -g(dρ/dz)z/ρ

z(t) = Acos(sqrt(-g/ρ*dρ/dz)) + B sin(sqrt(-g/ρ*dρ/dz))

Of interest is the buoyancy, N, which is sqrt(g/ρ*dρ/dz) that determines the Brunt-Vaisala frequency and indicates how stable the fluid is. Positive N describes a stable fluid column while negative N is an unstable column of fluid. N = 0 indicates no stratification, and larger positive numbers indicate a more strongly stratified fluid. The relationship of the Brunt-Vaisala frequency, N, to the internal waves equation is as follows:
d/dt2 𐌡2w + N2 𐌡2H w = 0

where 𐌡 is taken to be the del operator, w is the vertical velocity, and 𐌡2H is the Laplacian in the horizontal (MIT Open Course).
Aside from the physical principles of the Brunt-Vaisala frequency and internal waves, there are other processes in the ocean that arise from these dynamics. This includes mixing of water masses, nutrient exchange, distribution of pollutants, and propagation of sound waves.

The Experiment:

For our demonstration of internal waves we used a divided tank and filled the two compartments with water of different densities (see Fig. A). For the higher density water, we took seawater from the Scripps Pier, cooled it down, and dyed it with blue food coloring. For the lower density water we used warm fresh water and colored it yellow. Temperature and salinity were measured with a handheld YSI Professional Plus.

After slowly removing the divider, the high density water slides beneath the low density water and internal waves appear at the interface. The internal waves bounce back and forth in the stratification until they are dampened by drag.
For the second part of the experiment we divided the tank again in two compartments. We then mixed the water on one side to simulate wind-generated mixing and dyed it red (Fig. B). Upon removing the divider, the red mixed water formed a layer between the freshwater and seawater in the tank that allowed internal waves to propagate along. We also used a cardboard paddle to generate internal waves along the mixed layer, which is analogous to tides generating internal waves.

Troubleshooting and Tips:

Because the elongated rectangular tank designed for this experiment was broken, we used a 16"x16" square tank, which probably allowed for greater diffusion and mixing due to the larger surface area. Instead of a corresponding divider for the rectangular tank, we cut an improvised cardboard divider to fit the square tank. We had to quickly and simultaneously fill the water masses to avoid absorption of water by the cardboard, which decreased its ability to function as an effective divider.

To increase the density difference between the liquids we used hot freshwater and cooled the seawater with ice (Tip: use a bag for the ice to avoid lowering the salinity). We used seawater from the Scripps pier with additional salt in the form of Instant Ocean to increase the salinity and generate an even greater density gradient between the two water masses.

For good contrast between the different water masses we recommend using yellow and blue food coloring for the freshwater and seawater masses respectively. Thus red/ purple can be used for the mixed water in the second part of the experiment to provide a clear contrast between the upper and lower water masses. We affixed white sheets to the back side of the square tank to increase the contrast observed between the two water bodies.

To make a video of the experiment the GoPro has to be adjusted at the right angle- perpendicular to the front plane of the tank. Otherwise the water appeared as a mixing of the colors and the internal waves were not visible in the video.

In the table below, the Brunt-Vaisala frequency is calculated for three different cases. The first case is an ideal example of freshwater (no salinity) and seawater (containing averaged ocean density of 1025 kg/m3), the second is from our test run where the tap water had a salinity of 0.5 (2 kg/m3) and temperature of 19.4 ৹C and seawater had a salinity of 33.5 (23.8 kg/m3) and temperature of 19.4 ৹C, and the third case used potential density values (1027 kg/m3 and 1028 kg/m3) typically found in the ocean. Column 1 gives the density, columns 2 and 3 show the densities of different water masses subtracted from 1000 kg/m3, column 4 is the calculated difference in density, column 5 is the water column depth, column 6 is apparent gravity, and column 7 is the buoyancy frequency.
The N values show that for the first two cases, the buoyancy frequency is pretty high due to the large density change over a small water column range. Case three has a much smaller N value that is more typical of those found in the ocean, namely Nocean roughly between 0.2 and 6 cycles/hour. The high frequency values in the first two cases are more similar to Brunt-Vaisala values of surface waves.
BRUNT-VAISALA Frequency Calculations
Density (kg/m^3)
Less Dense Water (kg/m^3)
More Dense Water (kg/m^3)
Density Change in z (kg/m^3)
Water Column Depth (m)
Apparent Gravity (m/s^2)
N (cycles/s)

Internal waves progressing shoreward with periods ranging from 9 to 136 minutes have been documented off the coast of San Diego with slicks visible at the surface (Ufford 1947, Ewing 1950). These slicks are pictured here in a photograph taken from the International Space Station near the Caribbean island of Trinidad (NASA Earth Observatory).

NASA scientists hypothesized these interacting sets of internal waves were generated by tides moving over the shelf break near the island (NASA Earth Observatory, 2013). While these waves were driven by tidal forcings, other studies have also investigated the propagation of internal waves resulting from hurricanes (Price, 1983). As internal waves progress shoreward, they can break in shelf environments inducing mixing between stratified waters (Legg and Adcroft, 2003). The surface convergence zones (slicks) of internal waves also been shown to transport larval organisms shoreward (Shanks 1983, Shanks and Wright, 1987) with internal waves driving changes in temperature and phytoplankton in nearshore environments (Witman et al., 1993). An additional study by Zhou et al. (1991) found the density variations induced by internal waves to play a significant role in sound traveling through coastal waters. These studies collectively highlight some of the ecological and physical manifestations of internal waves that may be of interest to oceanographers studying in nearshore and shelf environments.

Ewing, G. (1950). Slicks, surface films and internal waves. J. Mar. Res., 9, 161-187.
Legg, S., & Adcroft, A. (2003). Internal wave breaking at concave and convex continental slopes*. Journal of Physical Oceanography, 33(11), 2224-2246.
Mackinnon, J.,
MIT News.
MIT Open Course.
Nasa Earth Observatory (2013). <>
Price, J.F. (1983). Internal wave wake of a moving storm. Part I. Scales, energy budget and observations. Journal of Physical Oceanography 13: 949-965.
Shanks, A.L. (1983). Surface slicks associated with tidally forced internal waves may transport pelagic larvae of benthic invertebrates and fishes shoreward. Mar. Ecol. Prog. Ser., Vol. 13, pp. 311-315.
Shanks, A. L., & Wright, W. G. (1987). Internal-wave-mediated shoreward transport of cyprids, megalopae, and gammarids and correlated longshore differences in the settling rate of intertidal barnacles. Journal of Experimental Marine Biology and Ecology, 114(1), 1-13.
Ufford, C. W. (1947). Internal waves measured at three stations. Trans. Amer. Geophys. Union, 28, 87-95.
Witman, J. D., Leichter, J. J., Genovese, S. J., & Brooks, D. A. (1993). Pulsed phytoplankton supply to the rocky subtidal zone: influence of internal waves. Proceedings of the National Academy of Sciences, 90(5), 1686-1690.
Zhou, J. X., Zhang, X. Z., & Rogers, P. H. (1991). Resonant interaction of sound wave with internal solitons in the coastal zone. The Journal of the Acoustical Society of America, 90(4), 2042-2054.