Turbulent unsteady flow profiles over an adverse slope
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
When an unsteady free surface flow encounters an adverse slope, it results in a decelerating flow up the adverse slope. The time dependent turbulent flow is treated here by appropriately reducing the two-dimensional Reynolds averaged Navier-Stokes equation along with the equation of continuity considering turbulence closure. With suitable choice of parameters, the resulting differential equations are numerically solved to compute free surface and streamwise velocity profiles with time. It is found that initially the advancing free surface is convex upwards for a short time, followed by a jump of the free surface with a negative streamwise velocity that is a backwater rolling breaker due to deceleration of flow. At later time, however, the velocity becomes positive, that is, the breakers roll forward. This dual feature of motion, that is a surge followed by rolling breakers, is repeated for sometime before the jumps stop. The theoretical analysis presented here is motivated by tidal bores propagating upstream in an estuarine river.
- Abbott, H.B. (1979), Computational Hydraulics: Elements of the Theory of Free Surface Flows, Pitman, London.
- Basco, D.R. (1987), Computation of rapidly varied, unsteady, free-surface flow, Water-Resources Investigations Report 83-4284, U.S. Geological Survey, Reston, Virginia, USA.
- Benqué, J.P., J.A. Cunge, J. Feuillet, A. Hauguel, and F.M. Holly, Jr. (1982), New method for tidal current computation, J. Waterw. Port Coast. Ocean Div. ASCE 108,3, 396–417.
- Bose, S.K. (2009), Numeric Computing in Fortran, Narosa, New Delhi.
- Bose, S.K., and S. Dey (2007), Curvilinear flow profiles based on Reynolds averaging, J. Hydraul. Eng. 133,9, 1074–1079, DOI: 10.1061/(ASCE) 0733-9429(2007)133:9(1074). CrossRef
- Bose, S.K., and S. Dey (2009), Reynolds averaged theory of turbulent shear flows over undulating beds and formation of sand waves, Phys. Rev. E 80,3, 036304, DOI: 10.1103/PhysRevE.80.036304. CrossRef
- Casulli, V., and R.T. Cheng (1992), Semi-implicit finite difference methods for three-dimensional shallow water flow, Int. J. Num. Meth. Fluids 15,6, 629–648, DOI: 10.1002/fld.1650150602. CrossRef
- Casulli, V., and G.S. Stelling (1998), Numerical simulation of 3D quasi-hydrostatic, free-surface flows, J. Hydraul. Eng. 124,7, 678–686, DOI: 10.1061/(ASCE)0733-9429(1998)124:7(678). CrossRef
- Chaudhry, M.H. (1994), Open Channel Flow, Prentice-Hall of India, New Delhi.
- Chen, X.J. (2003), A free-surface correction method for simulating shallow water flows, J. Comput. Phys. 189,2, 557–578, DOI: 10.1016/S0021-9991(03)00234-1. CrossRef
- Chow, V.T. (1959), Open Channel Hydraulics, McGraw-Hill, New York, 680 pp.
- Cunge, J.A., F.M. Holly, and A. Verwey (1980), Practical Aspects of Computational River Hydraulics, Pitman, London, 420 pp.
- Dey, S. (1998), End depth in circular channels, J. Hydraul. Eng. 124,8, 856–863, DOI: 10.1061/(ASCE)0733-9429(1998)124:8(856). CrossRef
- Dey, S. (2002), Free overfall in open channels: State-of-the-art review, Flow Meas. Instrum. 13,5–6, 247–264, DOI: 10.1016/S0955-5986 (02)00055-9. CrossRef
- Dey, S., and M.F. Lambert (2005), Reynolds stress and bed shear in nonuniform unsteady open-channel flow, J. Hydraul. Eng. 131,7, 610–614, DOI: 10.1061/(ASCE)0733-9429(2005)131:7(610). CrossRef
- Fennema, R.J., and M.H. Chaudhry (1990), Explicit methods for 2-D transient freesurface flows, J. Hydraul. Eng. 116,8, 1013–1034, DOI: 10.1061/(ASCE) 0733-9429(1990)116:8(1013). CrossRef
- Garcia-Navarro, P., F. Alcrudo, and J.M. Savirón (1992), 1-D open-channel flow simulation using TVD-McCormack scheme, J. Hydraul. Eng. 118,10, 1359–1372, DOI: 10.1061/(ASCE)0733-9429(1992)118:10(1359). CrossRef
- Garcia-Navarro, P., M.E. Hubbard, and A. Priestley (1995), Accurate flux vector splitting for shocks and shear layers, J. Comput. Phys. 121,1, 79–93, DOI: 10.1006/jcph.1995.1180. CrossRef
- Gill, M.A. (1976), Exact solution of gradually varied flow, J. Hydraul. Div. ASCE 102,9, 1353–1364.
- Henderson, F.M. (1966), Open Channel Flow, MacMillan, New York.
- Katopodes, N.D. (1984), A dissipative Galerkin scheme for open-channel flow, J. Hydraul. Eng. ASCE 110,4, 450–466, DOI: 10.1061/(ASCE)0733-9429(1984)110:4(450). CrossRef
- Kumar, A. (1978), Integral solutions of the gradually varied equation for rectangular and triangular channels, ICE Proc. 65,3, 509–515, DOI: 10.1680/iicep.1978.2802. CrossRef
- Kumar, A. (1979), Gradually varied surface profiles in horizontal and adversely sloping channels, ICE Proc. 67,2, 435–452, DOI: 10.1680/iicep.1979.2467. CrossRef
- Molinas, A., and C.T. Yang (1985), Generalised water surface profile computations, J. Hydraul. Eng. 111,3, 381–397, DOI: 10.1061/(ASCE)0733-9429(1985)111:3(381). CrossRef
- Namin, M.M., B. Lin, and R.A. Falconer (2001), An implicit numerical algorithm for solving non-hydrostatic free-surface flow problems, Int. J. Num. Meth. Fluids 35,3, 341–356, DOI: 10.1002/1097-0363(20010215)35:3〈341::AIDFLD96〉3.0.CO;2-R. CrossRef
- Prasad, R. (1970), Numerical method of computing flow profiles, J. Hydraul. Div. 96,1, 75–86.
- Quecedo, M., and M. Pastor (2003), Finite element modelling of free surface flows on inclined and curved beds, J. Comput. Phys. 189,1, 45–62, DOI: 10.1016/S0021-9991(03)00200-6. CrossRef
- Schlichting, H., and K. Gersten (2000), Boundary Layer Theory, 8 ed., Springer-Verlag, Berlin.
- Strelkoff, T. (1969), One-dimensional equations of open-channel flow, J. Hydraul. Div. 95,3, 861–866.
- Yen, B.C. (1973), Open-channel flow equations revisited, J. Eng. Mech. Div. 99,5, 979–1009.
- Turbulent unsteady flow profiles over an adverse slope
Volume 61, Issue 1 , pp 84-97
- Cover Date
- Print ISSN
- Online ISSN
- SP Versita
- Additional Links
- flow characteristics
- flow profiles
- free surface profile
- turbulent flow
- unsteady flow
- Industry Sectors