Dilute gravity flows: A phenomenological model in thin layer theory |
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| Institution: | 1. University of Rome ‘Niccolò Cusano’, Via don Carlo Gnocchi 3, Rome 00166, Italy;2. University of Tuscia, Largo dell’Università snc, Viterbo 01100, Italy;3. University of Rome ‘Tor Vergata’, Via del Politecnico 1, Rome 00133, Italy;4. Istituto Applicazioni Calcolo, CNR, Via dei Taurini 19, Rome 00185, Italy;1. Laboratory of Pediatric Oncology, Radboud Institute for Molecular Life Sciences, Radboud University Medical Centre, Nijmegen, P.O.Box 9101, 6500 HB Nijmegen, The Netherlands;2. Division of Cell Biology, The Netherlands Cancer Institute NKI-AVL, Plesmanlaan 121, 1066 CX Amsterdam, The Netherlands |
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| Abstract: | We present a simple model for the equations of the motion of turbidity flows. The flow is treated as a deformable geometrical object, parametrized by four characteristic quantities linked to the flow: U, the mean motion velocity of the flow object; l, its length; h, its height; φ, the particles' volumetric concentration. To characterise their temporal evolution, we assume that the gravity flow of a finite volume of particulate mixture reflects the balance between the driving gravity force, the turbulent friction, the spreading due to pressure forces, the incorporation of the ambient fluid, and the deposition and/or the erosion of particles. Special emphasis is placed on the search for analytical solutions over long periods. The study shows the evolution of solutions for three physical cases and includes comparison with numerical and analogical experiments. |
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