Shallow Water Turbulent Surface Wave Striking an Adverse Slope

• Autorzy: Bose S. K.

Identyfikatory

DOI

10.1515/acgeo-2015-0023

• Języki publikacji: EN

Abstrakty

EN

The problem of a sinusoidal wave crest striking an adverse slope due to gradual elevation of the bed is relevant for coastal sea waves. Turbulence based RANS equations are used here under turbulence closure assumptions. Depth-averaging the equations of continuity and momentum, yield two differential equations for the surface elevation and the average forward velocity. After nondimensionalization, the two equations are converted in terms of elevation over the inclined bed and the discharge, where the latter is a function of the former satisfying a first order differential equation, while the elevation is given by a first order evolution equation which is treated by Lax-Wendroff discretization. Starting initially with a single sinusoidal crest, it is shown that as time progresses, the crest leans forwards, causing a jump in the crest upfront resulting in its roll over as a jet. Three cases show that jump becomes more prominent with increasing bed inclination.

Słowa kluczowe

EN

surface waves; shallow water waves; inclined bed; turbulence; unsteady flow; breaking waves

PL

fale powierzchniowe; fale płytkie; turbulencja; przepływ niestacjonarny; fale rozbijające

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2015
• Tom: Vol. 63, no. 4
• Strony: 1090--1102
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Bose S. K.

• S.N. Bose National Centre for Basic Sciences, Kolkata 700064, India

Bibliografia

• [1] Abbott, H.B. (1979), Computational Hydraulics: Elements of the Theory of Free Surface Flows, Pitman Publ., London.
• [2] Basco, D.R. (1987), Computation of rapidly varied, unsteady, free-surface flow,Water- Resources Investigations Report 83-4284, U.S. Geological Survey, Reston, Virginia, U.S.A.
• [3] 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.
• [4] Bose, S.K. (2009), Numeric Programming in Fortran, Narosa, New Delhi.
• [5] 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).
• [6] 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.
• [7] Bose, S.K., and S. Dey (2013), Turbulent unsteady flow profiles over an adverse slope, Acta Geopys. 61, 1, 84-97, DOI:10.2478/s11600-012-0080-2.
• [8] Bose, S.K., and S. Dey (2014), Gravity waves on turbulent shear flow: Reynolds averaged approach, J. Hydraul. Eng. 140, 3, 340-346, DOI:10.1061/(ASCE)HY. 1943-7900.0000820.
• [9] Casulli, V., and R.T. Cheng (1992), Semi-implicit finite difference methods for threedimensional shallow water flow, Int. J. Num. Meth. Fluids 15, 6, 629-648, DOI:10.1002/fld.1650150602.
• [10] Casulli, V., and G.S. Stelling (1998), Numerical simulation of 3D quasihydrostatic, free-surface flows, J. Hydraul. Eng. 124, 7, 678-686, DOI:10.1061/(ASCE)0733-9429(1998)124:7(678).
• [11] 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.
• [12] Chow, V.T. (1959), Open Channel Hydraulics, McGraw-Hill, New York.
• [13] Cunge, J.A., F.M. Holly, and A. Verwey (1980), Practical Aspects of Computational River Hydraulics, Pitman Publ., London.
• [14] Fennema, R.J., and M.H. Chaudhry (1990), Explicit methods for 2-D transient free-surface flows, J. Hydraul. Eng. 116, 8, 1013-1034, DOI:10.1061/(ASCE)0733-9429(1990)116:8(1013).
• [15] 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).
• [16] Katopodes, N.D (1984), A dissipative Galerkin scheme for open-channel flow, J. Hydraul. Eng. 110, 4, 450-466, DOI:10.1061/(ASCE)0733-9429 (1984)110:4(450) .
• [17] Kundu, A. (ed.) (2007), Tsunami and Nonlinear Waves, Springer, Berlin.
• [18] Lamb, H. (1932), Hydrodynamics, Cambridge Univ. Press, Cambridge.
• [19] Mader, C.L. (2004), Numerical Modeling of Water Waves, CRC Press, Boca Raton.
• [20] Namin, M.M., B. Lin, and R.A. Falconer (2001), An implicit numerical algorithm for solving non-hydrstatic free-surface flow problems, Int. J. Num. Meth. Fluids 35, 341-356.
• [21] 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.
• [22] Radespiel, R., and N. Kroll (1995), Accurate flux vector splitting for shocks and shear layers, J. Comput. Phys. 121, 1, 66-78, DOI:10.1006/jcph.1995.1179.
• [23] Schlichting, H., and K. Gersten (2000), Boundary Layer Theory, 8th ed., Springer- Verlag, Berlin.
• [24] Stoker, J.J. (1957), Water Waves, Interscience, New York.
• [25] Strelkoff, T. (1969), One-dimensional equations of open-channel flow, J. Hydraul. Div. 95, 3, 861-876.
• [26] Xing, Y., and C.-W. Shu (2005), High order finite difference WENO schemes with the exact conservation property for the shallow water equations, J. Comput. Phys. 208, 1, 206-227, DOI:10.1016/j.jcp.2005.02.
• [27] Yen, B.C. (1973), Open-channel flow equations revisited, J. Eng. Mech. Div. 99, 5, 979-1009.