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Flow laminarization and acceleration by suspended particles. (English) Zbl 1323.76028

Summary: In [Prikl. Mat. Mekh. 17, 261–274 (1953; Zbl 0053.15302)], G. I. Barenblatt presents a model for partial laminarization and acceleration of shear flows by the presence of suspended particles of different sizes, and provides a formal asymptotic analysis of the resulting velocity equation. In the present paper, we revisit the model. In particular, we allow for a continuum of particle sizes, rewrite the velocity equation in a form which involves the Laplace transform of a given function or measure, and provide several rigorous asymptotic expansions for the velocity. The model contributes to a better insight to the extreme velocities in hurricanes, fire storms, and dust storms, and the analysis confirms Barenblatt’s conclusion that often the smallest suspended particles are responsible for the extreme flow acceleration at large altitudes.

MSC:

76F05 Isotropic turbulence; homogeneous turbulence
76F10 Shear flows and turbulence
76F25 Turbulent transport, mixing
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics

Citations:

Zbl 0053.15302
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Full Text: DOI

References:

[1] V. Vanoni, {\it Transportation of suspended sediment by water}, Trans. Amer. Soc. Civil Eng., 111 (1946), pp. 67-133.
[2] G.I. Barenblatt, {\it On the motion of suspended particles in a turbulent flow}, Prikl. Mat. Mekh., 17 (1953), pp. 261-274. · Zbl 0053.15302
[3] A.N. Kolmogorov, {\it On a new version of the gravitational theory of motion of suspended sediment}, Vestnik MGU, 3 (1954), pp. 41-45.
[4] G.I. Barenblatt, {\it On the motion of suspended particles in a turbulent flow occupying a half-space or a plane open channel of finite depth}, Prikl. Mat. Mekh., 19 (1955), pp. 61-88.
[5] A.S. Monin and A.M. Yaglom, {\it Statistical Fluid Mechanics. Mechanics of Turbulence}, Vol. 1, MIT Press, Cambridge, 1971.
[6] G.I. Barenblatt and G.S. Golitsyn, {\it Local structure of mature dust storms}, J. Atmos. Sci., 31 (1974), pp. 1917-1933.
[7] M.R. Maxey, {\it The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields}, J. Fluid Mech., 174 (1987), pp. 441-465. · Zbl 0617.76058
[8] C. Wamser and V.N. Lykossov, {\it On the friction velocity during blowing snow}, Beitr. Phys. Atmos., 68 (1995), pp. 85-94.
[9] G.I. Barenblatt, {\it Scaling, Self-Similarity, and Intermediate Asymptotics}, Cambridge University Press, Cambridge, 1996. · Zbl 0907.76002
[10] J. Lighthill, {\it Ocean spray and the thermodynamics of tropical cyclones}, J. Engrg. Math., 35 (1999), pp. 11-42. · Zbl 0936.76090
[11] J. Guo and P.Y. Julien, {\it Turbulent velocity profiles in sediment-laden flows}, J. Hydraulic Res., 39 (2001), pp. 11-23.
[12] G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, {\it A note concerning the Lighthill “sandwich model” of tropical cyclones}, Proc. Natl. Acad. Sci. USA, 102 (2005), pp. 11148-11150.
[13] B.S. Mazumber and K. Ghoshal, {\it Velocity and concentration profiles in uniform sediment-laden flow}, Appl. Math. Model., 30 (2006), pp. 164-176. · Zbl 1163.76376
[14] G.I. Barenblatt, {\it Shear flow laminarization and acceleration by heavy suspended particles: A mathematical model and geophysical applications}, Comm. Appl. Math. Comput. Sci., 4 (2009), pp. 153-175. · Zbl 1187.76668
[15] S. Balachandar and J.K. Eaton, {\it Turbulent dispersed multiphase phase flow}, Annu. Rev. Fluid Mech., 42 (2010), pp. 111-133. · Zbl 1345.76106
[16] Y. Rastigejev, S.A. Suslov, and Y.-H. Lin, {\it Effect of ocean spray on vertical momentum transport under high-wind conditions}, Bound. Layer Meteorol., 141 (2011), pp. 1-20.
[17] Y. Rastigejev and S.A. Suslov, {\it \(E-ε\) Model of spray-laden near-sea atmospheric layer in high wind conditions}, J. Phys. Oceanogr., 44 (2014), pp. 742-763.
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