Characterizing Flows in Ahupua'a, a Native Hawai'ian Water Management System: Theory and Simulation Studies

Acorda, Isaiah Kawena
Kim, Albert S.
Civil Engineering
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The concepts of specific energy and momentum have been fundamental to understanding hydraulicengineering for more than a century in modern times. The importance of water in Native Hawaiian culture was exposed through religion, language, and land. Such examples include the ahupua‘a system, where water was the primary indicator of dividing land and other resources. To have an in-depth understanding of ancient Native Hawaiian agricultural practices, computational fluid dynamics simulations will be performed for the Native Hawaiian ahupua‘a agricultural systems to connect hydraulic engineering and Native Hawaiian traditional practices with scientific visualization of flow patterns. Specifically, irrigation systems on ahupua‘a, such as that on Limahula Garden & Preserve on Kaua‘i, will be modeled through an OpenFOAM package for CFD simulations that will mimic flow within the ahupua‘a as slow overflows in a series of weirs. The model displays water flowing through three terraces in order to observe streamlines and overall flow. For the first part of the thesis, I will review the literature on the historical and cultural aspects of Ahupua’a, and perform CFD simulations for a better understanding of lo‘i kalo flow patterns, modeled as overflow in weirs in series. My final results will include mathematical, computational, and cultural aspects of ahupua‘a flows. For the second topic of this research, the specific energy and specific momentum will be mathematically re-investigated for quasi-rectangular channels with irregular bottoms. For open channel flow passing through wide rectangular channels, specific energy and momentum are used to find subcritical and supercritical water depths for various hydraulics applications, such as, but not limited to, sluice gates and hydraulic jumps. Historically, sequent or alternate depths and Froude number analyses were utilized to find solutions for flow depths using symbolic software. This thesis will include detailed mathematical derivations leading to the analytic solutions in the literature and will discuss the similarity and reciprocal relationship between the fundamental specific energy and momentum equations. These similarities of derivations can be extended to quasi-rectangular channels where the specific energy and specific momentum can be easily calculated. The main part of the mathematical work will inspect the depreciated cubic equations of specific energy and specific momentum and apply these equations for cases of quasi-rectnagular channels with a few examples. This thesis will include analyses of specific momentum and energy and physical analyses of the mathematical solutions in accordance with previous studies available in the literature.
Civil engineering, Hydraulic engineering, Mathematics, Agricultural Simulation, Ahupuaʻa, Native Hawaiian Agriculture, Specific Energy, Weir Flow
61 pages
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