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Experimental and Theoretical Study on Interfacial Instabilities of Turbidity Currents

Khavasi, Ehsan | 2013

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45790 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Firoozabadi, Bahar; Afshin, Hossein
  7. Abstract:
  8. Turbidity currents are one of the more frequently observed types of stratified flows. In these currents, the density difference is created as a result of particles. Hydrodynamic instabilities at the interface of these currents could occur in various modes and have an important role in the mixing process. The main goal of this study is to investigate the interfacial stability of turbidity current, theoretical and experimentally. The linear stability analysis in temporal and spatial framework are used for studying the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters such as bed slope, viscosity, and particle size on the stability is also considered. The pseudospectral collocation method employed Chebyshev polynomials is used for solving two coupled eigenvalue equations. Based on the results, there are some differences in the stability characteristics of the two density profiles. In the case of R=1 (R is the ratio of the shear layer thickness to the density layer thickness), the stability boundary in smooth profile is the transition from the unstable flow (where the dominant unstable mode is Kelvin-Helmholtz) to the stable one where in piecewise linear profile this boundary is the transition from Kelvin-Helmholtz to Holmboe mode. It is also shown that the unstable region increases with the bed slope and unstable modes amplify as the bed slope increases. For R = 5 the flow does not become stable by increasing the stratification in non-zero bed slope, and in some wavenumbers the Kelvin-Helmholtz and Holmboe modes co-exist. In addition, by increasing the bed slope the growth rate of the Holmboe mode and the range of its existence decreases. As expected, the viscosity makes the current more stable, and for the large values of the viscosity (small Reynolds number) the flow becomes stable at long waves (small wave numbers) for all bulk Richardson numbers. Existence of small particles does not change the instability characteristics so much, however, large particles make the flow more unstable. In the experimental investigation, experiments are performed in the existence of a triangle obstacle. Both Kelvin-Helmholtz and (asymmetric) Holmboe instabilities occur during the experiments; the first one was downstream and the second one was upstream of the obstacle. Kelvin-Helmholtz instability is observed by approximately zero (phase) speed with respect to the mean flow. With the aim of measuring spectral distribution of velocity fluctuations, the effects of some parameters are studied on interfacial waves; Kelvin-Helmholtz waves weaken as: the local Richardson number (J),an increase in inlet Froude number (Fin) or a reduction in obstacle height (H). The one-sided (asymmetry) Holmboe instability is detected moving to the upstream. This one-sidedness is as a result of asymmetry existence in velocity and density profiles in this research. Train of asymmetric Holmboe waves is observed while ejecting dense fluid into upper layer. The ejecting process happens randomly. Furthermore, Secondary circulations behind these waves are perceived. Mentioned parameters (J, Fin, H) do not show meaningful effect on Holmboe waves. Phase speed of these waves increases with local Richardson number. The measured average wavelength of these waves is about 17 cm. The wavelength of one-sided Holmboe waves decreases as local Richardson number increases. The unstable region of one-sided Holmboe waves is obtained and is compared with linear stability’s prediction
  9. Keywords:
  10. Richardson Number ; Linear Stability ; Turbidity Current ; Interfacial Instability ; Stratified Shear Flow

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