Um módulo analítico-numérico para cálculo de perfis verticais de velocidade em escoamentos com superfície livre

Abstract

Analytical-numerical equations capable of simulating three-dimensional hydrodynamic flows (x, y, z, t) from horizontal two-dimensional information (x, y, t) are of great value. This work presents a set of equations capable of doing so in such a way that it calculates vertical variations on both magnitude and direction of the flow, presenting a strong potential for being used as an operational tool to monitor phenomena such as salt water intrusion, coastal erosion, and flooding. These equations are valid for natural water bodies of free surface and shallow waters, fresh or salt, as long as these bodies are vertically homogeneous (even if laterally stratified) and whose pressure is hydrostatic. A refined turbulent viscosity profile of parabolic shape is presented. It analytically satisfies both bottom and surface dynamic boundary conditions. From it, a preliminary velocity profile of logarithmic shape is deduced, valid for steady and uniform flows. Then, from this preliminary velocity profile, an adjusted velocity profile is deduced, which represents the most relevant terms of the Navier-Stokes equation for geophysical flows, including the nonlinear advective accelerations. Such adjusted velocity profile can be fully deduced from variables that do not depend on the vertical dimension (independents of z). Such profile is then put to test under two numerical modelling scenarios: (1) a straight channel with a slope (2D model) and (2) a curvilinear channel with horizontal bottom (3D model). The proposed set of equations proves to be potentially capable of successfully simulating both scenarios, having even simulated a secondary helical flow in the second scenario.