### NEW BOUSSINESQ SYSTEM FOR NONLINEAR WATER WAVES

#### Abstract

#### Keywords

#### References

Peregrine, D.H., Long waves on a beach, J. Fluid Mech., vol. 27, 4, 815-827.

Madsen, P.A., Murray, R., and Sorensen, O.R. (1991). A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 1. Coastal Eng., 15, 371-388.

Madsen, P. A., and Sorensen, O. R. (1992). A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly varying bathymetry, Coastal Eng., 18, 183-204.

Nwogu, O. (1993). Alternative form of Boussinesq equations for nearshore wave propagation, J. Waterway, Port, Coastal and Ocean Engrng., 119, 618-638.

Wei, G., Kirby, J. T., Grilli, S. T., Subramanya, R. (1995). A fully nonlinear Boussinesq model for surface waves. I. Highly nonlinear, unsteady waves, J. Fluid Mech., 294, 71-92.

Madsen, P. A., Schaer, H. A. (1998). Higher order Boussinesq-type equations for surface gravity waves - derivation and analysis,Phil. Trans. Roy. Soc. A, 356, 1-59.

Kennedy, A.B., Kirby, J.T., Chen, Q., and Dalrymple, R.A. (2001). Boussinesq-type equations with improved nonlinear performance. Wave Motion, 33, 225-243.

Gobbi, M.F. and Kirby, J.T. (1999). Wave evolution over submerged sills: Tests of a high-order Boussinesq model, Coastal Eng. 37, 57-96, and erratum, Coastal Eng. 40, 277.

Gobbi, M.F.G., Kirby, J.T., Wei, G. (2000). A fully nonlinear Boussinesq model for surface waves. II. Extension to O(4). J. Fluid Mech., 405, 181-210.

Schaer, H.A., and Madsen, P.A. (1993). A Boussinesq model for waves breaking in shallow water. Coastal Eng., 20, 185-202.

Sorensen, O.R., Schaer, H.A., and Madsen, P.A. (1998). Surf zone dynamics simulated by a Boussinesq type model. III Wave-induced horizontal circulations. Coastal Eng., 33, 155-176.

Chen, Q., Kirby, J.T., Dalrymple, R.A., Kennedy, A.B., and Chawla, A. (2000). Boussinesq modeling of wave transformation, breaking, and runup. II: 2D. J. Waterway, Port, Coastal and Ocean Engrng., 126, 48-56.

Kennedy, A.B., Chen, Q., Kirby, J.T., and Dalrymple, R.A. (2000a). Boussinesq modeling of wave transformation, breaking, and runup. I: 1D. J. Waterway, Port, Coastal and Ocean Engrng., 126, 39-47.

Kennedy, A.B., Dalrymple, R.A., Kirby, J.T., and Chen, Q. (2000b). Determination of inverse depths using direct Boussinesq modeling. J. Waterway, Port, Coastal and Ocean Engrng., 126, 206-214.

Lynett, P.J., Wu T. R. and Liu, P.L.-F., Modeling wave runup with depth-integrated equations,Coastal Eng.,46, 89-107.

Nwogu, O., and Demirbilek, Z. (2010). Infragravity wave motions and runup over shallow fringing reefs. J. Waterway, Port, Coastal and Ocean Engrng., 136, 295-305.

Bonneton, P., Barthelemy, E., Chazel, F., Cienfuegos, R., Lannes, D., Marche, F., and Tissier, M. (2011a). Recent advances in Serre-Green Naghdi modelling for wave transformation, breaking, and runup.Eur. J, Mech. B-Fluids, 30, 589-597.

Madsen, P.A., and Agnon, Y. (2003). Accuracy and convergence of velocity formulations for water waves in the framework of Boussinesq theory. J. Fluid Mech., 477, 285-319.

Kennedy, A.B., and Kirby, J.T. (2002). Simpliﬁed higher-order Boussinesq equations - 1. Linear simpliﬁ- cations. Coastal. Eng., 44, 205-229.

Lynett, P.J., and Liu, P.L.-F. (2004). A two-layer approach to wave modelling.Proc. Roy. Soc. B, 460, 2637-2669.

Schaer, H.A. (2009). A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH. Coastal Eng., 56, 517-533.

Shields, J.J., and Webster, W.C. (1988). On direct methods in water-wave theory, J. Fluid Mech., 197, 171-199.

Green, A.E., and Naghdi, P.M. (1976). A derivation of equations for wave propagation in water of variable depth. J. Fluid Mech. 78, 237-246.

This work is licensed under a Creative Commons Attribution 3.0 License.