Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

Abstract

This study focuses on the investigation of stratified Taylor–Couette flow (STCF) using non-modal analysis, which has received relatively limited attention compared to other shear flows. The dynamics of perturbations under different temperature conditions are explored, and their patterns of amplification are analyzed. The study highlights the correlation between flow configurations, emphasizing the similarity in transient dynamics despite different speed ratios. The subcritical effects of thermal stratification on disturbance dynamics are examined, considering the interplay between viscous and buoyancy effects counteracted by strong centrifugal forces. It is found that increasing the wall temperature beyond a critical value leads to buoyancy forces dominating, resulting in a linear increase in the amplification factor. The research reveals significant deviations from previous results, indicating the significant role of temperature stratification.

Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

“…These values are chosen for illustrative purposes to show that the energy quantities oscillate between the cylinders before and after the turning points. For a more detailed discussion of these turning points please see figure 4 in Godwin et al [19].…”

“…The primary goal of this study is to explore the physical processes responsible for triggering transient bifurcation, with specific objectives outlined as follows: developing a linear model for STCF and conducting a numerical evaluation using the Chebyshev collocation method, determining the least stable eigenvalue for each configuration, identifying the maximum amplification factor and optimal perturbation for the least stable mode, and ultimately deriving and evaluating the energy budget quantities associated with the optimal perturbation. This paper primarily focuses on the last objective, as the other aspects have already been satisfactorily addressed in previous work [19].…”

“…A recent work by Godwin et al [19] focussed specifically on the short-time instability of STCF. To explore the short-time instability of STCF, the authors conducted a detailed numerical investigation employing transient growth analysis techniques.…”

Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

“…A recent work by Godwin et al [28] focused specifically on the short-time instability of STCF. To explore the short-time instability of STCF, the authors conducted a detailed numerical investigation employing transient growth analysis techniques.…”

“…The study sheds light on the transient instability induced by buoyancy in counter-rotating STCF within the bounds of the linear regime considered, but it does not capture the physical mechanism that triggers the transient bifurcation phenomena at Grashof number Gr ≈ Gr c . As in [28], the critical value Gr c is the value of Gr when the amplification factor reaches a local minimum.…”