Experimental study on the interfacial instability of particle-laden stratified shear flows

Abstract

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 suspended particles. The interfacial instability of turbidity current is studied experimentally in the present research. Both Kelvin-Helmholtz and (asymmetric) Holmboe instabilities are observed 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 (F in) 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, F in , 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 onesided Holmboe waves is obtained and is compared with linear stability's prediction.

Presence of Holmboe waves in particle-laden intrusive gravity current

“…12 c shows that the phase speed initially augments and then reduces with the decrease of IGC density, without exhibiting a discernible pattern. This outcome is in agreement with the experiments of Khavasi and Firoozabadi and Zhou and Lawrence, while the results of linear stability theory indicate that the Holmboe wave phase speed is always proportional to the Richardson number 13 , 26 , 47 , 48 . The addition of particles to the IGC reduces its speed, thereby decreasing the distance it travels, which in turn results in a decrease in the speed of the LGC due to the deposition of particles.…”

“…As evidenced, with the increase of the IGC density (decrease in the density difference), the value of the J diminishes in both cases and the R parameter increases, which is consistent with the findings of Khavasi and Firoozabadi 26 , 47 , 48 . According to the linear stability theory and furthermore laboratory experiments, it is postulated that J augments as the density difference grows 26 , 47 , 48 . The occurrence of Holmboe waves is resultant from this trend.…”

“…As the inter-layer gradient of density intensifies, the speed difference between the two layers amplifies, thus creating a greater difference in the phase speed of the two crests, and consequently, a larger wavelength. This conclusion has been corroborated in both laboratory experiments by Khavasi and Firoozabadi and Zhou and Lawrence 13 , 26 .…”

“…By disregarding the z -coordinate in the governing equations, it can be ascertained that Holmboe waves are two-dimensional since they move along the length of the channel, increasing or decreasing in height. This two-dimensional nature of the Holmboe instability was theoretically demonstrated by Haigh and Lawrence and experimentally verified by Khavasi and Firoozabadi 14 , 26 . However, Smyth postulated that at very low Reynolds numbers, ranging from 200 to 400, three-dimensional instability is observed 27 .…”

“…Specifically, the most frequent Holmboe waves appear at roughly and . Khavasi and Firoozabadi identified asymmetric Holmboe waves in their experiments when , though their calculations indicate that Holmboe waves require 26 . At and , Kelvin–Helmholtz waves are seen (with the exception of two cases).…”