Mahato Rajesh K, Dey Subhasish, Ali Sk Zeeshan
Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, West Bengal, India.
Department of Civil Engineering, Indian Institute of Technology Hyderabad, Hyderabad 502284, Telangana, India.
Proc Math Phys Eng Sci. 2022 Jul;478(2263):20220137. doi: 10.1098/rspa.2022.0137. Epub 2022 Jul 13.
In this article, we explore the submarine channel formation driven by the interaction of turbidity currents with an erodible bed. The theoretical analysis considers the three-dimensional continuity and momentum equations of the fluid phase, and the advection-diffusion and Exner equations of the solid phase. The governing equations are linearized by imposing periodic perturbations on the base flow. We study the response of both the base flow (profiles of velocity and suspended sediment concentration) and perturbations (growth rate and perturbation fields) to changes in key parameters related to the flow and sediment transport. The growth rate and the critical wavenumber are examined for a given quintet formed by the gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer, Rouse number and erosion coefficient. The critical wavenumber reduces with an increase in gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer and erosion coefficient, while it increases with the Rouse number. For the submarine channel formation, we identify the upper threshold values for the gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer and erosion coefficient and the lower threshold value for the Rouse number.
在本文中，我们探讨了浊流与易侵蚀河床相互作用驱动下的海底峡谷形成过程。理论分析考虑了流体相的三维连续性和动量方程，以及固相的平流扩散方程和埃克斯纳方程。通过对基本流施加周期性扰动，将控制方程线性化。我们研究了基本流（速度和悬浮泥沙浓度剖面）和扰动（增长率和扰动场）对与水流和泥沙输运相关的关键参数变化的响应。对于由重力参数、纵向河床坡度、驱动层边缘的泥沙浓度、劳斯数和侵蚀系数组成的给定五元组，研究了增长率和临界波数。临界波数随着重力参数、纵向河床坡度、驱动层边缘的泥沙浓度和侵蚀系数的增加而减小，而随着劳斯数的增加而增大。对于海底峡谷的形成，我们确定了重力参数、纵向河床坡度、驱动层边缘的泥沙浓度和侵蚀系数的上限阈值以及劳斯数的下限阈值。
