# Experiments on a jet in a crossflow in the low-velocity-ratio regime

## TL;DR

This paper experimentally investigates the hairpin instability of a jet in a crossflow at low velocity ratios, characterizing its dynamics and thresholds using spectral analysis and the Landau model.

## Contribution

It provides the first detailed spectral and dynamical analysis of hairpin instability in low-velocity-ratio jets in crossflow, applying the Landau model to determine bifurcation thresholds.

## Key findings

- Hairpin instability occurs via Hopf bifurcation.
- The Landau model accurately describes the instability dynamics.
- Threshold values for hairpin shedding are precisely determined.

## Abstract

The hairpin instability of a jet in a crossflow (JICF) for a low jet-to-crossflow velocity ratio is investigated experimentally for a velocity ratio range of $R\in(0.14,0.75)$ and crossflow Reynolds numbers $Re_D\in(260,640)$. From spectral analysis we characterize the Strouhal number and amplitude of the hairpin instability as a function of $R$ and $Re_D$. We demonstrate that the dynamics of the hairpins is well described by the Landau model, and, hence, that the instability occurs through Hopf bifurcation, similarly to other hydrodynamical oscillators such as wake behind different bluff bodies. Using the Landau model, we determine the precise threshold values of hairpin shedding. We also study the spatial dependence of this hydrodynamical instability, which shows a global behaviour.