Abstract
The balance of material momentum is applied to the motion of an ideal, incompressible fluid with special emphasis on water waves. To this end, the fluid flow is represented by its material or Lagrangian description. A variational approach using Hamilton’s principle is employed, with the incompressibility condition incorporated into the Lagrangian by means of a Lagrange multiplier. The balance of material momentum is obtained in its standard form known from nonlinear elasticity, however with the peculiarity that the dynamic Eshelby stress becomes hydrostatic and its divergence reduces to the (negative) gradient of an “Eshelby pressure”. The balance is applied to Gerstner’s nonlinear theory of water waves.
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Braun, M. (2018). The Balance of Material Momentum Applied to Water Waves. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_7
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DOI: https://doi.org/10.1007/978-3-319-72440-9_7
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