Measurements of internal waves and turbulence in two-dimensional stratified shear flows

Abstract

A turbulent stratified shear flow is generated in a towing tank by towing a grid or a circular cylinder through a tank of stratified salt water. The internal waves and turbulence generated in these flows are visualized with shadowgraphs and measured with quartz-coated hot-film probes (up to four probes for velocity fluctuations) and single-electrode conductivity probes (up to four probes for salinity fluctuations) which are towed at the same speed as the obstacle. The velocity and salinity signals are recorded on magnetic tapes. A portion of these signals is processed directly-on-line with a digital computer.

From these shadowgraphs and probe measurements, we observe that

• (i) Far downstream of the obstacle where the turbulence has already subsided, the stratified fluid always has a layered structure. This layered structure persists for a long time, and is a result of the convection of turbulently mixed layers by the mean flow. These results indicate that in the regions of a stably stratified atmosphere and ocean where the turbulence has subsided, one could often find layered structure.

• (ii) There are spectral peaks and valleys in the measured velocity and salinity autospectra when the stratifications are sufficiently strong. Under certain conditions, these spectral peaks tend to lift up the spectral curves to show substantialf ^−5/3 subranges, although the turbulence Reynolds numbers are too low for the flows to have recognizable inertial subranges. This anomalousf ^−5/3 subrange demonstrates the pitfalls of using spectral measurements in thef ^−5/3 subrange to predict the turbulent energy dissipation rate through the Kolmogorov hypothesis.

• (iii) A diagnostic method is developed for distinguishing internal waves from turbulence, utilizing their phase characteristics. The phase characteristics can be conveniently examined from the cospectra and quadrature spectra measurements of: (a), two vertically separated velocity probes; (b), two vertically separated density probes; and (c), a velocity probe and a density probe. This method is demonstrated to be useful in the laboratory and can be applied directly to atmospheric and oceanic measurements to distinguish internal waves from turbulence.

• (iv) From the coherency measurements, it is found that the entire turbulent stratified wake is actually whipping up and down at a frequency corresponding to the Brunt-Väisälä frequency. This indicates that similar stratified shear flows in the atmosphere and in the ocean, such as the jet streams in the atmosphere and the Cromwell current in the ocean, may oscillate vertically, which in turn can induce horizontal oscillation and meandering.