Nonlinear dynamics at the interface of two-layer stratified flows over pronounced obstacles

TL;DR

This study investigates the flow regimes of two-layer stratified fluids over obstacles, identifying four flow types and analyzing the stability and transition conditions through experiments, simulations, and theoretical analysis.

Contribution

It provides a comprehensive analysis of flow regimes and stability transitions over obstacles in stratified flows, combining experimental, numerical, and theoretical approaches.

Findings

Four distinct flow regimes identified: sub-critical, hydraulic jump, Kelvin-Helmholtz, and billow shedding.

Critical Froude number depends on obstacle geometry and is predicted by hydraulic theory.

Kelvin-Helmholtz instability leads to billow shedding at high upstream velocities.

Abstract

The flow of a two--layer stratified fluid over an abrupt topographic obstacle, simulating relevant situations in oceanographic problems, is investigated numerically and experimentally in a simplified two--dimensional situation. Experimental results and numerical simulations are presented at low Froude numbers in a two-layer stratified flow and for two abrupt obstacles, semi--cylindrical and prismatic. We find four different regimes of the flow immediately past the obstacles: sub-critical (I), internal hydraulic jump (II), Kelvin-Helmholtz at the interface (III) and shedding of billows (IV). The critical condition for delimiting the experiments is obtained using the hydraulic theory. Moreover, the dependence of the critical Froude number on the geometry of the obstacle are investigated. The transition from regime III to regime IV is explained with a theoretical stability analysis. The results from the stability analysis are confirmed with the DPIV measurements. In regime (IV), when the velocity upstream is large enough, we find that Kelvin-Helmhotz instability of the jet produces shedding of billows. Important differences with flows like Von Karman's street are explained. Remarkable agreement between the experimental results and numerical simulations are obtained.