Taylor's problem and morphodynamics

Abstract

In the fundamental process of reflection of Kelvin waves in a rectangular semi-enclosed basin, known as Taylor Problem, the generation of Poincare waves and sandbank formation are investigated applying a two-dimensional, vertically integrated numerical model. The Taylor problem separates clearly areas where Kelvin and Poincare waves exist. Without consideration of morphodynamics, the calculated pattern of currents agrees with previous solutions of Taylor Problem. If morphodynamics is allowed in the numerical modeling of the Taylor problem, sandbank-like bed forms appear at the closed boundary on the side where the incident Kelvin wave transforms into Poincare waves. The presence of sandbanks modifies the wavelength of Poincare waves generated in the vicinity of the closed boundary in relation to those produced in the calculation without consideration of morphodynamics. The Poincare waves are evanescent in both cases. The presence of sandbanks influences the generation of Poincare waves whereas the formation of sandbanks itself is initiated by Poincare waves. Using calculated wavelengths of Poincare waves and wavelengths of sandbanks, we show that sandbanks could be generated through a nonlinear interaction where friction and advection terms seem to play a relevant role. Numerical experiments reveal that a bay, located in the neighborhood of the closed boundary, diffracts the incident Kelvin wave producing also evanescent Poincare waves and modifying the generation of bed forms. A bay, located far away of the closed boundary generates Poincare waves which propagate in all directions. Trapped Poincare waves seem to favor the development of bed forms.