Characterizing Flows in Ahupua'a, a Native Hawai'ian Water Management System: Theory and Simulation Studies
Date
2023
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Abstract
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 ahupuaāa
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 ahupuaāa agricultural
systems to connect hydraulic engineering and Native Hawaiian traditional practices with scientific
visualization of flow patterns. Specifically, irrigation systems on ahupuaāa, such as that on
Limahula Garden & Preserve on Kauaāi, will be modeled through an OpenFOAM package for CFD
simulations that will mimic flow within the ahupuaāa 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 Ahupuaāa, and perform CFD simulations for a better understanding of loāi kalo flow patterns,
modeled as overflow in weirs in series. My final results will include mathematical, computational,
and cultural aspects of ahupuaāa 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.
Description
Keywords
Civil engineering, Hydraulic engineering, Mathematics, Agricultural Simulation, AhupuaŹ»a, Native Hawaiian Agriculture, Specific Energy, Weir Flow
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61 pages
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