Author(s): Man Yue Lam; Andrejs A. Kolyshkin; Mohamed S. Ghidaoui

Linked Author(s): Man Yue Lam

Keywords: Shallow turbulent flows; Coherent structures; Shear instability; Froude number; Wave radiation

Abstract: Shallow turbulent water flows are characterized by having horizontal lengthscales far exceeding vertical lengthscales. Such flows are omnipresent in natural and man-made hydrosystems, e.g. river confluences, longshore currents along the coast and compound and composite channels. A striking feature of shallow turbulent flows is the presence of vortical two-dimensional coherent structures (2DCSs). The onset of 2DCSs is believed to be a result of linear instability of horizontal shear layers. The instability adds energy into the perturbations naturally present in the flows, while bed friction dissipates the perturbation energy. If the energy added is greater than the energy dissipated by bed friction, 2DCSs form. Such 2DCSs govern mass, momentum and constituent transport and the understanding of 2DCSs is important for water quality modeling and flow conveyance capacity in compound and composite channels. Froude number is shown by both linear and nonlinear models to stabilize horizontal shear layers. The stabilization process is governed by gravitational waves. Thus, the convective Froude number (Frc), which is defined by the velocity difference across a shear layer, is considered the key governing parameter of such stabilization effect. Previous work suggests that the stabilization mechanism is due to wave radiation in which energy is radiated from the shear layer and become unavailable for 2DCSs to develop. The 2DCSs formed under the high convective Froude numbers are also more elongated, i.e. the alongstream lengthscale of the 2DCSs is greater relative to the cross-stream lengthscale. However, the initial dynamics responsible for wave radiation has not been well elucidated. Normal-mode linear stability analysis gives eigenfunctions merely stating the fact that waves are radiated. Previous nonlinear modeling focuses on confirming linear stability results and characterizing the structure of radiating waves. In both cases, the process through wave radiation initiates is not studied. This work explains the initial dynamics responsible for wave radiation by linear initial value stability problem (IVP) and nonlinear simulations. The linear and nonlinear simulations will be conducted under initial conditions with unperturbed water depth. Initial nonlinear result shows that the initial growth rate of the perturbed mode is the same for simulations with Frc=0.4 and Frc=1.2. Wave radiation in the Frc=1.2 simulation develops only after the initial growth phase. The initial dynamics for Frc=0.4 in the nonlinear model are consistent with IVP results. An understanding of the initial dynamics for wave radiation is important for interpreting linear stability results, which usually consists of different modes of instabilities. For instance, linear stability results under high convective Froude number is likely to contain unstable modes corresponding to (i) wave radiation, (ii) roll wave (for streamwise Fr>2) and (iii) the interaction of the two in shallow shear layers. The understanding guides attribution of computed unstable modes to the corresponding physical processes.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022541

Year: 2022