Mixing a Stratified Fluid: Flux Laws and the Resulting Circulation

Jack Whitehead, Physical Oceanography

OCCI Funded Project: 2006

Proposed Research

A correct representation of the mixing rate from small-scale turbulence within the ocean is a major unsolved problem in physical oceanography.  We are conducting a set of laboratory experiments that measure mixing-driven transport rates for a salt-stratified fluid. A relation between mixing rate, the intensity of the turbulence, and the strength of stratification is often conjectured but experiments do not give clear and precise measurements of this relation because the turbulence changes as the density field evolves in time. In addition, most previous experiments are not in the range of values for application to the ocean. In our new experiments, layered salt water is mixed with a rod going back and forth at a fixed velocity and a precise micro-salinity probe measures the vertical density distribution.  The first experiments are time-evolving experiments starting from two layers of water with differing salinity and mixing them up while recording the evolution of the vertical distribution of mean density.  As the layers mix up, the data from many experiments collapse into one curve using a similarity theory, which is consistent with the conjectured flux relation, but as with other experiments the relation is not clearly documented.  This has led to a second steady experiment (in oprogress) with two pumps supplying different salinity water pumped in at the same flux rate at two ends of the top of a tank.  Mixed water exits in the middle at the same level to keep the water volume constant in time.  The salt water descends to the bottom and the fresher, lighter water remains near the top, but the mechanical mixing conveys salt water up and fresh water down.  The result is a large-scale circulation and a vertical salinity distribution, both of which vary in strength with rod velocity, pumping rate, and density difference between the two waters that are pumped in. Scaling theory of fluid mechanics is used to analyze the experimental data.  Profiles for many experiments are shown in the lower left figure, representing about a month of continuous running.  A relation between, local stratification, pumping rate, density difference of the two waters pumped in, and energy of the mixing source collapses reasonable well to the relation shown in the lower right figure.  The symbol Ri1 is a scaled measure of the strength of stratification after the experiment has come to steady state.  It is equivalent to the vertical temperature difference of the ocean.  Mixing rate greatly increases as stratification decreases, a result consistent with direct measurements of ocean mixing.

Progress Report

The ocean has a very slow overturning circulation, with deep-water renewal estimated to take approximately 1500 years.  An understanding of the dynamics of the overturning is required if we are to quantify its contribution to Earth’s climate.  It is well known, for example, that equator-to-pole heat flow is central to the explanation of past climate changes.  Therefore, quantifying the heat flow rate of the overturning circulation is required for any prediction of future climate change.  In addition, ocean circulation has important consequences to biological and chemical changes within the ocean, including sequestering CO2.

Xin Huang of the Physical Oceanography Department has pointed out that turbulence inside the ocean serves as the energy source for the very deep overturning circulation of the ocean. We are conducting laboratory studies of deep overturning driven by turbulence. The experiment has fresh water pumped in at the top of one end of a long tank, salt water pumped in at the top of the other end, and an overflow at the top of the middle.  With no mechanical mixing, the salt water fills the entire tank except for a thin layer of fresh water at the top.  However, upon mixing with a rod (Figure 1), salt water from below is mixed with the layer of fresh water, which deepens.  The deepened layer spreads across the entire tank.  At the end with salt water entering, we observe that a turbulent plume descends from the top to the bottom of the tank (visible in Figure 2).  This corresponds to a deep overflow in the ocean, with the plume being the descending portion of the overturning circulation.  The rising portion is spread over the entire tank.  In summary, the turbulence produces the overturning circulation, and part of that circulation is a descending plume, which possesses additional turbulence. 

We have completed these experiments over a wide range of parameters that determine the strength of the circulation.  These parameters are the rod velocity, rod diameter, the pumping rates, and the density difference between salt and fresh water. A theory has been developed that can be tested by the data; one comparison is shown in Figure 3.  Our future objective will be to measure the speed of the overturning circulation and to estimate the mixing rate of the rod compared to the mixing rate on the plume. 

The results to date are quite unexpected and interesting.  As figure 2 shows, the light scattering seems to be about the same intensity in the two regions with turbulence.  In fact, we are excited by the possibility that the two rates are comparable, and are even developing an argument that the two are always equal.  (Two things being equal is called equipartition in physics, the possible equipartition of dissipation in the ocean would be very useful to know about if true!)  The graduate student shown in figure 1 will conduct an experiment to test the equipartition hypothesis in January 2007.