Experimental study on the origin of lobe-cleft structures in a sand storm

Abstract

Lobes and clefts are characteristic structures at the front of sand storms. In this paper, their original formation mechanism and geometric features are studied experimentally and theoretically. A rotatable lock-exchange tank is utilized to avoid the strong local disturbances existing in the conventional horizontal apparatus, and the original lobe size is selected as the dominant spanwise wavelength by a statistical method instead of the mean lobe size used in the literature. It is shown that at the initial formation stage, the measured lobe sizes for different tank geometries and density differences (or Atwood numbers) have a 1/3 scaling law with the Grashof number (Gr) as predicted by a Rayleigh–Taylor (RT) model, especially at moderate Gr range, and substantially depend on the diffusion effect represented by the Schmidt number. Furthermore, using turbulent Schmidt number and eddy viscosity for atmosphere in the RT model predicts large scale dominant lobes, whose sizes agree qualitatively with those observed in a real sand storm, revealing that the underlying control mechanism for these lobe and cleft structures is intrinsically related to the RT instability.

Graphic Abstract

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. 1.

    Simpson, J.E.: Gravity Currents: In the Environment and the Laboratory. Cambridge University Press, London (1999)

    Google Scholar 

  2. 2.

    Huppert, H.E.: Gravity currents: a personal perspective. J. Fluid Mech. 554, 299–322 (2006). https://doi.org/10.1017/S002211200600930X

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Meiburg, E., Kneller, B.: Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42, 135–156 (2010). https://doi.org/10.1146/annurev-fluid-121108-145618

    Article  MATH  Google Scholar 

  4. 4.

    Simpson, J.E.: Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 4, 759–768 (1972). https://doi.org/10.1017/S0022112072000461

    Article  Google Scholar 

  5. 5.

    Neufeld, J.: Lobe-cleft patterns in the leading edge of a Gravity Current. [Masters Thesis]. University of Toronto, Toronto (2002)

  6. 6.

    McElwaine, J.N., Patterson, M.D.: Lobe and cleft formation at the head of a gravity current. In: Proceedings of the XXI International Congress of Theoretical and Applied Mechanics, pp. 15–21 (2004)

  7. 7.

    Härtel, C., Carlsson, F., Thunblom, M.: Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2: The lobe-and-cleft instability. J. Fluid Mech. 418, 213–229 (2000). https://doi.org/10.1017/S0022112000001270

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Cantero, M.I., Lee, J.R., Balachandar, S., et al.: On the front velocity of gravity currents. J. Fluid Mech. 586, 1–39 (2007). https://doi.org/10.1017/S0022112007005769

    Article  MATH  Google Scholar 

  9. 9.

    Bonometti, T., Balachandar, S.: Effect of Schmidt number on the structure and propagation of density currents. Theor. Comput. Fluid Dyn. 22, 341 (2008). https://doi.org/10.1007/s00162-008-0085-2

    Article  MATH  Google Scholar 

  10. 10.

    Cantero, M.I., Balachandar, S., García, M.H., et al.: Turbulent structures in planar gravity currents and their influence on the flow dynamics. J. Geophys. Res.: Oceans 113, C08018 (2008). https://doi.org/10.1029/2007JC004645

    Article  Google Scholar 

  11. 11.

    Espath, L.F.R., Pinto, L.C., Laizet, S., Silvestrini, J.H.: High-fidelity simulations of the lobe-and-cleft structures and the deposition map in particle-driven gravity currents. Phys. Fluids 27, 056604 (2015). https://doi.org/10.1063/1.4921191

    Article  Google Scholar 

  12. 12.

    Xie, C.Y., Tao, J.J., Zhang, L.S.: Origin of lobe and cleft at the gravity current front. Phys. Rev. E 100, 031103 (2019). https://doi.org/10.1103/PhysRevE.100.031103

    Article  Google Scholar 

  13. 13.

    Simpson, J.E.: Gravity currents in the laboratory, atmosphere and ocean. Annu. Rev. Fluid Mech. 14, 213–234 (1982). https://doi.org/10.1146/annurev.fl.14.010182.001241

    Article  MATH  Google Scholar 

  14. 14.

    Daly, B.J., Pracht, W.E.: Numerical study of density-current surges. Phys. Fluids 11, 15–30 (1968). https://doi.org/10.1063/1.1691748

    Article  MATH  Google Scholar 

  15. 15.

    Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. 8, 679–698 (1986). https://doi.org/10.1109/TPAMI.1986.4767851

    Article  Google Scholar 

  16. 16.

    Tominaga, Y., Stathopoulos, T.: Turbulent Schmidt numbers for CFD analysis with various types of flow field. Atmos. Environ. 41, 8091–8099 (2007). https://doi.org/10.1016/j.atmosenv.2007.06.054

    Article  Google Scholar 

  17. 17.

    Constantin, A., Johnson, R.S.: Atmospheric Ekman flows with variable eddy viscosity. Bound. Layer Meteorol. 170, 395–414 (2019). https://doi.org/10.1007/s10546-018-0404-0

    Article  Google Scholar 

Download references

Acknowledgements

We thank Qining Wang and Jinsheng Liu for their technical assistance in the experiments. The simulation was performed on the TianHe-1(A). The support by the National Natural Science Foundation of China (Grants No. 91752203, 11490553) is acknowledged.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jian-Jun Tao.

Additional information

Executive Editor: Xuesong Wu

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, LS., Tao, JJ., Wang, GH. et al. Experimental study on the origin of lobe-cleft structures in a sand storm. Acta Mech. Sin. 37, 47–52 (2021). https://doi.org/10.1007/s10409-021-01053-7

Download citation

Keywords

  • Gravity current
  • Lobe-cleft formation
  • Rayleigh–Taylor instability
  • Sand storm
  • Diffusion effect