The dominant feature of the compressible starting jet is the interaction between the emerging vortex ring and the trailing jet. There are two types of interaction: the shock–shear layer–vortex interaction and the shear layer–vortex interaction. The former is clearly not present in the incompressible case, since there are no shocks. The shear layer–vortex interaction has been reported in the literature in the incompressible case and it was found that compressibility reduces the critical Reynolds number for the interaction. Four governing parameters describe the compressible starting jet: the non-dimensional mass supply, the Reynolds number, the reservoir to unbounded chamber temperature ratio and the reservoir to unbounded chamber pressure ratio. The latter parameter does not exist in the incompressible case. For large Reynolds numbers, the vortex pinch-off takes place in a multiple way. We studied the compressible starting jet numerically and found that the interaction strongly links the vortex ring and the trailing jet. The shear layer–vortex interaction leads to a rapid breakdown of the head vortex ring when the flow impacted by the Kelvin–Helmholtz instabilities is ingested into the head vortex ring. The shock–shear layer–vortex interaction is similar to the noise generation mechanism of broadband shock noise in a continuously blowing jet and results in similar sound pressure amplitudes in the far field.

Flow-induced oscillations of a flexibly mounted triangular prism allowed to oscillate in the cross-flow direction are studied experimentally, covering the entire range of possible angles of attack. For angles of attack smaller than $\unicode[STIX]{x1D6FC}=25^{\circ }$ (where $0^{\circ }$ corresponds to the case where one of the vertices is facing the incoming flow), no oscillation is observed in the entire reduced velocity range tested. At larger angles of attack of $\unicode[STIX]{x1D6FC}=30^{\circ }$ and $\unicode[STIX]{x1D6FC}=35^{\circ }$ , there exists a limited range of reduced velocities where the prism experiences vortex-induced vibration (VIV). In this range, the frequency of oscillations locks into the natural frequency twice: once approaching from the Strouhal frequencies and once from half the Strouhal frequencies. Once the lock-in is lost, there is a range with almost-zero-amplitude oscillations, followed by another range of non-zero-amplitude response. The oscillations in this range are triggered when the Strouhal frequency reaches a value three times the natural frequency of the system. Large-amplitude low-frequency galloping-type oscillations are observed in this range. At angles of attack larger than $\unicode[STIX]{x1D6FC}=35^{\circ }$ , once the oscillations start, their amplitude increases continuously with increasing reduced velocity. At these angles of attack, the initial VIV-type response gives way to a galloping-type response at higher reduced velocities. High-frequency vortex shedding is observed in the wake of the prism for the ranges with a galloping-type response, suggesting that the structure’s oscillations are at a lower frequency compared with the shedding frequency and its amplitude is larger than the typical VIV-type amplitudes, when galloping-type response is observed.

Known structures and self-sustaining mechanisms of wall turbulence are reviewed and explored in the context of the scale interactions implied by the nonlinear advective term in the Navier–Stokes equations. The viewpoint is shaped by the systems approach provided by the resolvent framework for wall turbulence proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in which the nonlinearity is interpreted as providing the forcing to the linear Navier–Stokes operator (the resolvent). Elements of the structure of wall turbulence that can be uncovered as the treatment of the nonlinearity ranges from data-informed approximation to analysis of exact solutions of the Navier–Stokes equations (so-called exact coherent states) are discussed. The article concludes with an outline of the feasibility of extending this kind of approach to high-Reynolds-number wall turbulence in canonical flows and beyond.

The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times 10^{9}\leqslant Ra_{F}\leqslant 1.8\times 10^{11}$ and cylindrical cells in the range $1.4\times 10^{10}\leqslant Ra_{F}\leqslant 1.2\times 10^{12}$ with the Prandtl number $Pr$ fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading-order level, the magnitude of temperature fluctuations in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function in the bulk is essentially invariant with respect to both the insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed $Ra_{F}$ , the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas an asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical velocity.

The present work considers the low-Reynolds-number wake flow behind a squareback Ahmed body, in close proximity to a ground. At low Reynolds numbers such wakes are known to undergo a series of bifurcations to a state that breaks reflectional symmetry. The symmetry breaking of the wake also persists at turbulent high Reynolds numbers, where it manifests as bi-modal behaviour with random switching between the asymmetric states. Thus far, it has only been possible to study the low-Reynolds-number sequence of bifurcations experimentally and mathematically. The present work presents the first numerical simulations capturing the sequence of symmetry breaking bifurcations that occur. A study of how the wake topology changes throughout suggests that interaction between the closer top/bottom pair of parallel shear layers can only dominate once there is sufficient underbody flow. When this occurs, the two main vortex structures in the wake switch from being horizontally to vertically aligned. A linear feedback control strategy, designed to attenuate base pressure force fluctuations, is then implemented. This causes an accompanying reduction in drag and re-symmetrisation of the wake. Analysis using the dynamic mode decomposition confirms that the wake shedding mode is re-symmetrised. This work motivates future attempts to capture wake symmetry breaking and bi-modality in numerical simulations, and application of a promising feedback control strategy at higher, turbulent Reynolds numbers.

By extracting unstable invariant solutions directly from body-forced three-dimensional turbulence, we study the dynamical processes at play when the forcing is large scale and unidirectional in either the momentum or the vorticity equations. In the former case, the dynamical processes familiar from recent work on linearly stable shear flows – variously called the self-sustaining process (Waleffe, Phys. Fluids, vol. 9 (4), 1997, pp. 883–900) or vortex–wave interaction (Hall & Smith, J. Fluid Mech., vol. 227, 1991, pp. 641–666; Hall & Sherwin, J. Fluid Mech., vol. 661, 2010, pp. 178–205) – are important even when the base flow is linearly unstable. In the latter case, where the forcing drives Taylor–Green vortices, a number of mechanisms are observed from the various types of periodic orbits isolated. In particular, two different transient growth mechanisms are discussed to explain the more complex states found.