Free-Boundary Seepage from Asymmetric Soil Channels
We present an inverse method for the study of the seepage from soil channels without lining. We give integral representations of the complex potential, velocity field, stream lines, free phreatic lines, and contour of the channel by means of Levi-Civita's function 𝜔. For different values of the Taylor coefficients of 𝜔, we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the stream lines, and the equipotential lines. Examples are given for various symmetric or asymmetric channels, with smooth contours or with angular points.
A conformal mapping approach for investigating the free-boundary seepage from symmetric channels
We present a new method to investigate the two-dimensional free-boundary groundwater seepage from symmetric soil channels into a homogeneous isotropic porous medium. We use Levi–Civitá’s function to construct an integral representation for the conformal mapping of the complex potential domain onto the physical flow domain. A genetic algorithm (GA) is used to calculate the coefficients of the Maclaurin series expansion of Levi–Civitá’s function. The coordinates of the points from the channel contour, calculated by means of the integral representation, must satisfy the analytic equation of the contour. We use this condition to define the objective function of the genetic algorithm. Levi–Civitá’s function is afterwards used to calculate the seepage loss, the free lines, the streamlines, the equipotential lines, the isobars and the velocity field. Some examples illustrate the method.
The Inca Occupation of the South Coast of Peru
like the others, however; it forks into several nearly parallel ravines of which the largest are Huayuri, Rio Grande-Palpa, Ingenio (called Collao in ancient times), Nasca proper (the ancient Caxamarca), Taruga, and Poroma. Due to peculiarities of the local topography, the irrigated areas in Ica and the ravines of Nasca are located inland, at the foot of the mountains, rather than at the mouths of the rivers as is more usual in Peruvian coastal valleys. No sharp natural or cultural boundary separates the valley of Chincha from the valleys of Cafiete (ancient Huarco and Runahuana), Asia, and Mala, the next valleys going up the coast to the northwest. At the other end of the area we are considering, however, there is a sharp break; beyond Yauca the Andean foothills reach out to the sea, natural conditions are quite different, and there are important differences in the archaeological picture as well. The historical sources which mention the south coast are not particularly helpful, except in so far as they provide us with a few dates. To begin with, no chronicler gives an explicit account of the political organization of the south coast at the time it came into contact with the Incas. It can, perhaps, be inferred from Cabello Balboa's statements about common policy toward the Inca invaders that there was some sort of political connection between the valleys of Mala, Cafiete, and Chincha, but the connection need have been no more than a temporary military alliance. Cabello makes no mention at all of Pisco. The valleys of Ica, Nasca, and 125