[1] Karst aquifers exhibit highly conductive features caused from rock dissolution processes. Flow within these structures can become turbulent and therefore can be expressed by nonlinear gradient functions. One way to account for these effects is by coupling a continuum model with a conduit network. Alternatively, turbulent flow can be considered by adapting the hydraulic conductivity within the continuum model. Consequently, the significance of turbulent flow on the dynamic behavior of karst springs is investigated by an enhanced single-continuum model that results in conduit-type flow in continuum cells (CTFC). The single-continuum approach CTFC represents laminar and turbulent flow as well as more complex hybrid models that require additional programming and numerical efforts. A parameter study is conducted to investigate the effects of turbulent flow on the response of karst springs to recharge events using the new CTFC approach, existing hybrid models, and MODFLOW-2005. Results reflect the importance of representing (1) turbulent flow in karst conduits and (2) the exchange between conduits and continuum cells. More specifically, laminar models overestimate maximum spring discharge and underestimate hydraulic gradients within the conduit. It follows that aquifer properties inferred from spring hydrographs are potentially impaired by ignoring flow effects due to turbulence. The exchange factor used for hybrid models is necessary to account for the scale dependency between hydraulic properties of the matrix continuum and conduits. This functionality, which is not included in CTFC, can be mimicked by appropriate use of the Horizontal Flow Barrier package for MODFLOW.

As a result of rock dissolution processes, karst aquifers exhibit highly conductive features such as caves and conduits. Within these structures, groundwater flow can become turbulent and therefore be described by nonlinear gradient functions. Some numerical groundwater flow models explicitly account for pipe hydraulics by coupling the continuum model with a pipe network that represents the conduit system. In contrast, the Conduit Flow Process Mode 2 (CFPM2) for MODFLOW-2005 approximates turbulent flow by reducing the hydraulic conductivity within the existing linear head gradient of the MODFLOW continuum model. This approach reduces the practical as well as numerical efforts for simulating turbulence. The original formulation was for large pore aquifers where the onset of turbulence is at low Reynolds numbers (1 to 100) and not for conduits or pipes. In addition, the existing code requires multiple time steps for convergence due to iterative adjustment of the hydraulic conductivity. Modifications to the existing CFPM2 were made by implementing a generalized power function with a user-defined exponent. This allows for matching turbulence in porous media or pipes and eliminates the time steps required for iterative adjustment of hydraulic conductivity. The modified CFPM2 successfully replicated simple benchmark test problems.

[1] To examine the interrelation between hydrogeological environment and conduit development in deep-seated settings, a conceptual model is tested by numerical modeling. Based on field observations, simplified model settings are designed and crucial parameters are varied. A coupled continuum-pipe flow model is employed for simulating conduit development within the soluble unit of a multilayer aquifer system. In agreement with field observations, the evolving cave patterns are characterized by pronounced horizontal passages and multiple vertical conduits at the bottom of the soluble unit but only few at the top. The frequency distribution of conduit diameters is found to be bimodal if the permeability of the rock formation is sufficiently high to allow competitive conduit development governed by the feedback between increasing flow and dissolution rates. This feedback, however, is suppressed in low-permeability formations. As a consequence, conduit development is uniform rather than competitive.Citation: Rehrl, C., S. Birk, and A. B. Klimchouk (2008), Conduit evolution in deep-seated settings: Conceptual and numerical models based on field observations, Water Resour. Res., 44, W11425,

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