Print Email Facebook Twitter A linear approach for the evolution of coherent structures in shallow mixing layers Title A linear approach for the evolution of coherent structures in shallow mixing layers Author Van Prooijen, B.C. Uijttewaal, W.S.J. Faculty Civil Engineering and Geosciences Department Hydraulic Engineering Date 2002-10-18 Abstract The development of large coherent structures in a shallow mixing layer is analyzed. The results are validated with experimental data obtained from particle tracking velocimetry. The mean flow field is modeled using the self-similarity of the velocity profiles. The characteristic features of the down-stream development of a shallow mixing layer flow, like the decrease of the velocity difference over the mixing layer, the decreasing growth of the mixing layer width, and the transverse shift of the center of the mixing layer layer are fairly well represented. It turned out that the entrainment coefficient could be taken constant, equal to a value obtained for unbounded mixing layers: ? = 0.085. Linearization of the shallow water equations leads to a modified Orr–Sommerfeld equation, with turbulence viscosity and bottom friction as dissipative terms. Growth rates are obtained for each position downstream, using the model for the mean flow field. For a given energy density spectrum at the inflow boundary, integration of the growth rates along the downstream direction yields the spectra at various downstream positions. These spectra provide a measure for the intensity and the length scale of the coherent structures (the dominant mode). The length scales found are in good agreement with the measured ones. The length scale of the most unstable mode appears much larger than the length scale of the dominant mode. Obviously, the longevity of the coherent structures plays a significant role. Three growth regimes can be distinguished: in the first regime the dominant mode is growing, in the second regime the dominant mode is dissipating, but other modes are still growing, and in the third regime all modes are dissipating. It is concluded that the development of the coherent structures in a shallow mixing layer can fairly well be described and interpreted by the proposed linear analysis. Subject riverschannel flowmixingturbulenceflow instabilityflow visualisationhydrologyfractals To reference this document use: http://resolver.tudelft.nl/uuid:115c96a3-6c4e-48c1-a698-f831829d184c DOI https://doi.org/10.1063/1.1514660 Publisher American Institute of Physics ISSN 1070-6631 Source http://link.aip.org/link/PHFLE6/v14/i12/p4105/s1 Source Physics of Fluids, 14 (12), 2002 Part of collection Institutional Repository Document type journal article Rights (c) 2002 Van Prooijen, B.C.; Uijttewaal, W.S.J.; American Institute of Physics Files PDF vanProoijen_2002.pdf 338.36 KB Close viewer /islandora/object/uuid:115c96a3-6c4e-48c1-a698-f831829d184c/datastream/OBJ/view