Yih-Ho Pao


A towing tank system was used to study the structure of turbulence in stably stratified fluids. Turbulence is generated by moving an obstacle (a grid or a cylinder) in a tank of stratified salt water. Recent improved shadowgraph pictures of these laboratory generated stratified flows are shown in this paper. They give further support to Pao's observation that (i) internal waves and turbulence coexist in turbulent stratified flows, with internal waves at the large scales and turbulence at the small scales; (ii) turbulence decays much more rapidly than internal waves; and (iii) the turbulent-nonturbulent interfaces are not necessarily sharp, and the transition region may consist of mostly internal waves.

Velocity and concentration fluctuations in the wake of the obstacle are measured respectively with quartz-coated hot-film probes and single electrode conductivity probes which are towed at the same speed as the obstacle. The velocity and concentration signals are processed with a digital computer utilizing a fast Fourier transform technique to obtain spectra, correlations, rms values, etc. Our probe measurement methods and data processing techniques will be discussed in detail in this paper.

The velocity auto-spectra measured behind the stratified wake of a cylinder are proportional to f-5/3 for a decade of frequency range while the turbulence Reynolds numbers of the flows are too low to have an inertial subrange. The reason for this anomalous inertial subrange is discussed in the context of a unified spectral model proposed by Pao. The measured concentration auto-spectra have a substantial range of frequencies behaving like f-5/3; the f-5/3 range of the concentration auto-spectra extend to higher frequencies than those of the velocity auto-spectra measured in the same position.

Diagnostic methods to distinguish internal waves from turbulence with two probe measurements are proposed. This can be accomplished by comparing the co-spectra and the quadrature-spectra or the coherencies of (i) two vertically separated velocity probes, or (ii) two vertically separated salinity (or temperature) probes, or (iii) a velocity probe and a salinity (or temperature) probe. These methods developed in the laboratory can be applied directly to atmospheric and oceanic measurements to distinguish internal waves from turbulence.

Meeting Name

Symposium on Turbulence Measurements in Liquids (1969: Sep., Rolla, MO)


Chemical and Biochemical Engineering

Document Type

Article - Conference proceedings

Presentation Type

Invited Lecturer


Turbulence Measurements in Modified Fluids

Document Version

Final Version

File Type





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