Symmetry breaking in the wake of a streamwise oscillating cylinder in density stratified fluid flows

The wake dynamics of a circular cylinder oscillating in the streamwise direction within a stably (density) stratified fluid is investigated using two-dimensional numerical simulations: Floquet stability analysis and dynamic mode decomposition. At a fixed Reynolds number ( Re=175 ) and forcing frequency ratio ( fd/fSt=1.6 ), we examine the effects of the oscillation amplitude ( 0.1 AD 0.6 ) and the stratification strength ( 1 Fr ∞ ) on the wake structure and its symmetry breaking. In unstratified (homogeneous) flow ( Fr = ∞ ), the wake transitions from an asymmetric vortex street at low amplitudes to a symmetric state at higher amplitudes. This transition occurs via a Neimark–Sacker bifurcation, with Floquet analysis identifying a critical amplitude of AD = 0.455 . In stratified flow, buoyancy forces improve symmetry and suppress vortex shedding for AD=0 . At Fr = 1 , symmetry breaking first occurs at a threshold of AD = 0.246 , associated with a period-doubling bifurcation and subharmonic antisymmetric vortex shedding, and persists only within a finite amplitude window ( 0.246 < AD < 0.560 ), beyond which the wake restabilises into a symmetric pattern. At a fixed small amplitude ( AD = 0.1 ), a secondary critical transition is observed at Fr = 1.52 , marked by quasiperiodic antisymmetric shedding through a near-resonant Neimark–Sacker bifurcation. Stratification also influences force production: moderate stratification ( Fr ≈ 2 ) minimises drag through enhanced pressure recovery and suppressed wake asymmetry. These results highlight the dual role of stratification in promoting or delaying symmetry-breaking instabilities and modifying wake dynamics. Critical transition thresholds are established, providing insight into buoyancy-modulated flow control strategies relevant to geophysical and engineering applications involving oscillating bodies in stratified environments.