Paralelos en la decoración en cuerda seca total

The literature indicates foremost that an assessment of indirect recharge from infiltrating ephemeral river flow should be rooted in a sound and physically-based (i.e., hydrodynamic) description of the flow processes. Attributable to potentially high transmission losses, process variables can span a wide range of magnitudes under changing dynamics. It was briefly discussed that such conditions can counteract the application of typical numerical solution procedures for the governing flow equations. Chapter 4 reviews and discusses the applicable solution procedures for the flow models in more depth after the hydrodynamic theory is presented in the following Chapter 3. Consequently, in Chapter 5, this thesis presents an analytical zero-inertia model for advancing surge flow in initially dry non-prismatic channels with a significant effect of infiltration on the mass and momentum balance, as well as under potentially weak process dynamics. One further objective of this thesis is the development and testing of an exact analytical solution of the zero-inertia equations for runoff phenomena on hillslopes under time-varying rainfall.

Chapter 3

Principles of Physically-Based

Modeling of Infiltrating Free

Surface Flows

This chapter presents the basic theoretical background of hydrodynamic flow routing in ephemeral channels. Moreover, the presented approaches can be applied for any kind of free surface flows, i.e., also for overland flow modeling. The dynamics of an infiltrating flow event are first discussed with regard to different governing conditions, for example, for furrow irrigation or infiltrating wadi flow. Consecutively, coming from the full hydrodynamic shallow-water equations for the one- dimensional case (the Saint-Venant equations), the zero-inertia and kinematic wave approximations are discussed. The physically-based models are then extended in order to account for losses or inflows and, consecutively, the consideration of two-dimensional flow geometries in a one-dimensional model is outlined. The chapter closes with a discussion on the applicability of the hydrodynamic modeling approaches under the specific conditions of ephemeral river routing and overland flow routing. The discussion is supplemented with a brief outline of the kinematic shock phenomenon, which can play a role, particularly for flash flood events.

3.1

Hydraulic Phases of an Infiltrating Flow Event

In furrow irrigation modeling (Walker and Humpherys, 1983; W¨ohling, 2005), an infiltrating flow event on a permeable bed can be divided in four phases, namely, the advance phase, storage phase, depletion phase, and recession phase (Fig. 3.1a). Flow advance starts if there is an inflow into the furrow and persists until the flow reaches the lower end of the furrow. More water is applied during the storage phase which ends when the inflow is decreased. The depletion phase begins when water moves further down the furrow as the water depth at the inlet decreases. If the inflow ceases, the recession phase begins, which lasts until all water has infiltrated or left the furrow at the lowermost end.

Furrow irrigation is mostly carried out by applying surges of water, i.e., the inlet is opened, the inflow rapidly reaches a quasiconstant value, and is then swiftly cut off after a certain time. Together with the comparably short length of an irrigation furrow, this methodology usually leads

x (kilometers) t (hours)

Advance phase

Front-end recession phase

1. Inflow starts 2. Infiltration

equals inflow 3. Inflow ends

Wetted wadi reach

(b)

x (meters) t (minutes)

Advance phase

Rear-end recession phase

1. Inflow starts 2. Flow reaches furrow’s end 3. Furrow is dry Furrow length (a) x (kilometers) t (days)

Front-end recession phase

1. Inflow starts 3. Inflow ends Upstream reach (c) Storage phase 2. Inflow reduces Depletion phase 2. Inflow ceases Downstream reach Advance phase 2. Inf. = inflow Flow advance weakens due to transmission losses Recession in the upstream section

Figure 3.1: Hydraulic phases of a flow event (a) in a field furrow; (b) in a natural wadi channel; and (c) downstream of a recharge dam.

3.1 Hydraulic Phases of an Infiltrating Flow Event

Table 3.1: Main properties of the flow upstream and downstream of a recharge dam under normal operational conditions (no spillway operation).

Upstream reach Downstream Reach Event duration Hours Days

Process dynamics Pronounced Typically weak Gradients of the dependent variables Steep Smoothed Typical flow rates (m3_{· s}−1_{) 10}2 ₁₀0_–101

Transmission loss quotas Low–intermediate Intermediate–high Initial wadi bed state Dry Dry

to a rear-end recession, which means that upper portions of the furrow fall dry when the body of water in the furrow still moves downwards. If infiltration is pronounced and/or furrow slope is mild, a front-end recession can occur when the inflow reduces, leading to a ceasing flow, beginning from the wave tip and moving in the upstream direction (Walker and Humpherys, 1983). Nevertheless, this front-end recession is of minor interest in furrow irrigation theory and modeling.

Compared to wadi flow, furrow irrigation events are of a short duration; the inflow is cut off relatively fast, and flow lengths are limited. In contrast, the natural flood inflow to a wadi reach is highly transient, with a steep rising limb of the hydrograph and a comparably mild recession (cf. Fig. 1.3a). This leads to a fast advance of the flow and an extended recession phase, mainly established by front-end recession (Fig. 3.1b). Typically during recession, inflow rates and, therefore, flow momentum are small. Assuming a free lower boundary and a limited inflow volume, the flow advance coercively ends if total infiltration exceeds the flow rate, which may be the case a certain time after the inflow peak has entered the wadi. The recession phase directly follows the advance phase. Although front-end recession is assumed to be dominant, rear-end recession can occur as well, which would be observable as a decline in the wetting and traveling flow domain from the lower and the upper end. Moreover, certain constellations of inflow dynamics, infiltration properties, and wadi morphology could even lead to a dispartment of one infiltrating flow domains into two or more. Figure 3.1c shows the advance and recession dynamics in a natural wadi, influenced by dam operation for an event significantly smaller than the design flood; in other words, all water infiltrates in the reach downstream of the dam, and the outflow of the dam is not influenced by spillway operation. Dam operation leads to a weakening of process dynamics downstream of the dam and the flow event may be prolonged from some hours in the upstream reach to some days in the downstream reach. Maximum dam outflow and the maximum extent of the infiltrating flow domain more or less

coincide1 and the downstream advance finally ceases during a prolonged dam release. Nevertheless,

infiltration and the connected loss of mass and momentum also impact the advance dynamics of the downstream flow domain in a transient and nonlinear manner. Hence, a hydrodynamic modeling concept with included infiltration losses is envisaged for the simulation of wadi flow under dam operation to estimate potential recharge. Finally, Table 3.1 summarizes main properties of the flow upstream and downstream of a recharge dam.

1 _{More precisely, the point in time where recession starts is not directly dependent on the transit of an inflow peak,}

but on the relationship of inflow rates and infiltration. The distinction between flow advance and flow recession cannot, therefore, be provided a priori.