Optimality and self-organization in subsurface flow processes

地下的流动模式在所有尺度上都受强烈的非均质性支配。这种非均质性既影响地下作为水储存的性质，也影响溶质的运输。尽管这种多尺度非均质性的重要性毋庸置疑，但将其整合到地下水流的数值模型中仍然是一个主要的挑战。首先，人们对非均质性的空间结构及其与地质条件的关系知之甚少，其次，所需的范围将导致不合理的数值计算。在过去的几十年里，从最优化原则(这里，最小能量耗散)推导流型的统计特性已经成为一种成功的方法，至少对于地球表面的河流网络和心血管系统这两个系统来说是如此。最近，申请者发表了一个从最小能量耗散原理推导多孔介质中流动的孔隙度和水力传导性空间模式的理论框架。然而，相关研究仍停留在理论概念的层面上，主要包括孔隙度、电导率和磁通密度(达西速度)之间的关系。验证这一概念，将其进一步发展应用于实际场景，并将其转化为集总参数模型，是本项目的主要目标。验证将包括与自然界中发现的泉水大小分布和个别泉水流量曲线有关的集水区大小的统计分布。原始通用模型的扩展将包含Boussinesq近似的水平和倾斜无承压含水层以及真正的3D模式。集总参数模型将从分布式模型的所有版本中导出，以便使它们可在数值上处理。

Flow patterns in the subsurface are governed by a strong heterogeneity at all scales. This heterogeneity affects both the properties of the subsurface as a water storage and the transport of solutes. Despite the undoubted importance of this multi-scale heterogeneity, integrating it in numerical models of subsurface flow is still a major challenge. First, little is known about the spatial structure of the heterogeneity and its relationship to the geological conditions, and second the required range would result in an unreasonable numerical effort.In the last decades, deriving statistical properties of flow patterns from principles of optimality (here, minimum energy dissipation) has turned to be a successful approach atleast for two systems -- river networks at Earth's surface and the cardiovascular system.Recently a theoretical framework for deriving spatial patterns of porosity and hydraulic conductivity for flow in porous media from the principle of minimum energy dissipation was published by the applicant. However, the related research is still on the level of a theoretical concept mainly consisting of relations between porosity, conductivity and flux densitiy (Darcy velocity).Validating this concept, developing it further for application to realistic scenarios, and transferring it to lumped parameter models are the main goals of the proposed project. Validation will cover the statistical distribution of catchment sizes in relation to spring-size distributions found in nature and individual spring discharge curves. Extensions of the original generic model will contain horizontal and sloping unconfined aquifers in Boussinesq approximation and genuine 3D patterns. Lumped parameter models will be derived from all versions of the distributed models in order to make them numerically treatable.