Oscillatory Flows and Wave Propagation in Porous Media (Partially Saturated and Free Surface Hydraulics) Y. WANG, R. ABABOU & M. MARCOUX Institut de Mécanique des Fluides de Toulouse (IMFT), Allée du Professeur Camille Soula, 31400 Toulouse, France. e-mail: ababou@imft.fr Abstract In this paper, we investigate the response of water tables in porous media, due to sudden changes or periodic oscillations of water levels in adjacent open water bodies. This concerns the effects of tides, swells and waves in beaches, estuaries, and ports, in interaction with porous or macroporous structures like dykes, moles, breakwaters, reservoirs and river banks. The phenomena of interest are the transmission and dissipation of waves through these porous media, with or without capillary effects. We use three types of approaches: (a) experimental (wetting front propagation in a sandbox, oscillations through sand in a wave canal); (b) analytical (Dupuit- Boussinesq 2D plane flow); and (c) numerical (2D plane flow and 3D variably saturated flow). The plane flow model is used to analyze wave dissipation and transmission of water table fluctuations in (x,y,t) neglecting vertical velocities and capillary effects. The second model accounts for variable saturation and is fully ‘3D’; it takes into account capillary effects in the unsaturated zone, and is able to represent multiple free surface dynamics in (x,y,z,t). This model, based on Richards’ equation, is further extended to account for fast flow in macroporous media (quadratic head losses). Internal seepage, perched water, and other complex infiltration/exfiltration phenomena can then be modelled (Ababou & Trégarot 2002). Results from these three approaches are compared in order to validate the analytical and numerical solutions, and to study the characteristics of the porous structures and their influence on wave propagation and oscillation processes. Key words Groundwater, water table, porous media, macroporous, interfaces, fluctuations, decay, dissipation, dispersion, water waves, capillary, infiltration, Darcy, Forchheimer, Dupuit- Boussinesq, Richards, coastal hydrodynamics, wave propagation, oscillations, free surfaces. INTRODUCTION AND OBJECTIVES In hydrology and hydrogeology, water levels undergo oscillations or abrupt changes in time. This can occur in aquifers, reservoirs, lakes, rivers, embankments, estuaries, ports, and coastal zones. In many cases, oscillations of free surfaces take place in open water bodies, and then, propagate into adjacent porous media (beaches, coastal aquifers, river banks, dykes, breakwaters, and so on). We focus here on the effects on natural variations and oscillations of water levels in environmental contexts, such as: - subsurface effects of tides and swells (beach, coastal and estuarial hydraulics); - transmission/dissipation of tides and swells through dykes, or breakwaters (harbours) - large variations of water levels in rivers and reservoirs, e.g. due to dam operations, - effect of river floods on groundwater via stream-aquifer interactions (hydrology). We investigate here, in particular, the response of a ‘free surface’ porous medium water system (e.g. a phreatic aquifer with a so-called ‘groundwater table’) to varying water levels in adjacent open water bodies. Two main types of dynamics are - Wang Y., R. Ababou, M. Marcoux, 2008: “Oscillatory Flows and Wave Propagation in Porous Media : Partially Saturated Free Surface Hydraulics”. Proceedings, International Conference IAHR-GW 2008, International Association of Hydraulics Research _ Ground Water, Istambul, Turkey, June 2008, 9 pp. www.iahr-gw2008.net Erratum: Fig.3 has been corrected in this version.