Visualization of space competition and plume formation with complex potentials for multiple source flows: Some examples and novel application to Chao lava flow (Chile)

Abstract

AbstractFluid displacement in a continuum pressured by a variable constellation of source flows can be visualized as solutions of line integrals. The algorithms are based on complex potentials that provide exact solutions of the Navier‐Stokes equation and allow users to specify both the location and flux strength of multiple sources. If relative strength and positioning of the sources are varied, a wide range of flow patterns and particle paths can be traced. Time‐dependent variations in the strength of the sources can account for transient‐flow problems. A further expansion is superposition of a background flow, which displaces the particle paths issued from the sources into concentrated plumes. The outlined modeling technique for visualization of multiple plume displacements is potentially relevant for a wide spectrum of practical situations. Detailed applications are possible, such as time tracking of groundwater‐plume migration from a series of pollution sources, tracking of salt‐feeder‐stock flow and suture zone formation when salt issued from the stocks coalesces into a salt canopy, and designing of optimal spacing and relative pressure strength of multiple water injection wells in field‐development plans for hydrocarbon production. Further applications are highlighted in the main text, including a simulation of geometrical features exposed in the Chao coulee (Chilean Andes).