We investigate a turbulent stratified plane Poiseuille flow using linear models and nonlinear simulations. We propose the first complete explanation for the prolific and coherent backward (BWs)- and forward-propagating waves (FWs), which have been observed in these flows. We demonstrate a significant presence of oblique waves in the channel core, particularly for the FWs. Critically, we show that neglect of spanwise structure leads to a distorted dispersion relation due to its strong dependence on the angle of obliquity. Interestingly, solutions to the Taylor–Goldstein equations show that wave dynamics is strongly dependent on shear, with only a weak dependence on buoyancy for the BWs at low and order-one wavenumbers, when the wavenumber is scaled by the channel half-height. As the wavenumber increases, waves transition from a shear-dominated regime to a buoyancy-dominated regime, with their dispersion relation tending towards that of idealised internal waves subject to a shear-free and constant-buoyancy-gradient flow, with a characteristic velocity and buoyancy frequency corresponding to respective centreline values in the channel. Finally, we show that the dominance of the BWs arises due to the external forcing of the system, whereby turbulent fluid ejected into the core has a lower momentum when compared with the local flow, therefore preferentially generating BWs in the channel. Qualitatively, channel-core dynamics can be reproduced with low-momentum forcing to a velocity profile with a velocity maximum and a corresponding negative second derivative intersecting a region of strong buoyancy gradient. This structure is inherent to a wide variety of jet-like environmental, atmospheric and industrial flows, suggesting that BWs are a critical control on dynamics of such flows.

We present the results of a combined experimental and theoretical investigation of different fluid sheet structures formed during the impingement of a laminar liquid jet on a vial, with a slightly larger diameter than the jet and filled with the same liquid. The present set-up produces all diverse fluid sheet structures, unlike previous experiments that required a deflector disk resulting in no-slip and no-penetration boundary conditions. The water sheet structures are classified into four regimes; regime I: pre-sheet; regime II: puffing, characterized by the periodic formation and destruction of the upward-rising water sheet, an interesting observation not reported earlier; regime III, steady upward, inverted umbrella-like sheet structures; and regime IV, the formation of downward, umbrella-like sheet structures, which can be either open or closed, classically referred to as ‘water bells’. The water sheet structures observed are governed by the non-dimensional parameters: the ratio of vial diameter to the jet diameter at impact ($X$), the capillary number ($Ca$), the Weber number ($We$) and the Froude number ($Fr$). The parametric spaces $X-Ca$, $X-We$ and $X-Fr$ exhibit the demarcation of the four regimes. A semi-empirical expression for the ejection angle of the liquid sheet, primarily responsible for different shapes, is derived in a control volume that provides a theoretical basis for the identified regime diagrams. The puffing water bells in regime II are found to be quasi-steady as the experimental trajectories are in good agreement with the steady-state theory. The rise time of puffing water bells that determines the puffing frequency has been modelled.

We report the dynamics of a droplet levitated in a multi-emitter, single-axis acoustic levitator. The deformation and atomisation behaviour of the droplet in the acoustic field displays myriad complex phenomena, in a series of events. These include the primary breakup of the droplet, wherein it exhibits stable levitation, deformation, sheet formation and equatorial atomisation, followed by its secondary breakup, which could be of various types such as umbrella, bag, bubble or multi-stage breakup. A large number of tiny atomised droplets, formed as a result of the primary and secondary breakup, can remain levitated in the acoustic levitator and exhibit aggregation and coalescence. The visualisation of the interfacial instabilities on the surface of the liquid sheet using both side- and top-view imaging is presented. An approximate size distribution of the atomised droplets is also provided. The stable levitation of the droplet is due to a balance of acoustic and gravitational forces while the resulting ellipsoidal shape of the droplet is a consequence of the balance of the deforming acoustic force and the restoring capillary force. Stronger acoustic forces can no longer be balanced by capillary forces, resulting in a highly flattened droplet, with a thin liquid sheet at the edge (equatorial region). The thinning of the sheet is caused by the differential acceleration induced by the increasing pressure difference between the poles and the equator as the sheet deforms. When the sheet thickness reduces to of the order of a few microns, Faraday waves develop at the thinnest region (preceding the rim), which causes the generation of tiny-sized droplets that are ejected perpendicular to the sheet. The corresponding hole formation results in a perforated sheet that causes the detachment of the annular rim, which breaks due to Rayleigh–Plateau (RP) instability. The radial ligaments generated in the sheet, possibly due to Rayleigh–Taylor (RT) instability, break into droplets of different sizes. The secondary breakup exhibits Weber number dependency and includes umbrella, bag, bubble or multi-stage types, ultimately resulting in the complete atomisation of the droplets. Both the primary and the secondary breakup of the droplet involve interfacial instabilities such as Faraday, Kelvin–Helmholtz, RT and RP and are well supported by visual evidence.

Bounds on heat transfer have been the subject of previous studies concerning convection in the Boussinesq approximation: in the Rayleigh–Bénard configuration, the first result obtained by Howard (J. Fluid Mech., vol. 17, issue 3, 1963, pp. 405–432) states that the dimensionless heat flux $\textit {Nu}$ carried out by convection is such that $\textit {Nu} < (3/64 \ Ra)^{1/2}$ for large values of the Rayleigh number $Ra$, independently of the Prandtl number $Pr$. This is still the best-known upper bound, only with the prefactor improved to $\textit {Nu} -1 < 0.02634 \ Ra^{1/2}$ by Plasting & Kerswell (J. Fluid Mech., vol. 477, 2003, pp. 363–379). In the present paper, this result is extended to compressible convection. An upper bound is obtained for the anelastic liquid approximation, which is similar to an anelastic model used in astrophysics based on a turbulent diffusivity for entropy. The anelastic bound is still scaling as $Ra^{1/2}$, independently of $Pr$, but depends on the dissipation number $\mathcal {D}$ and on the equation of state. For monatomic gases and large Rayleigh numbers, the bound is $\textit {Nu} < 25.8\, Ra^{{1}/{2}} / (1-\mathcal {D}/2 )^{{5}/{2}}$.

Flows over a disc are studied in a wind tunnel over incidence angles between $0^\circ \text { and }36^\circ$, a Reynolds number of $2.7 \times 10^4$ and rotational speed ratios of $0\unicode{x2013}10$. Smoke-wire visualization, particle image velocimetry and hot-film anemometry are employed. Two vortex shedding modes originating from the upstream surface of the disc are observed. The first is dominant at incidence angles up to ${\sim }21^\circ$. Beyond $21^\circ$, the second mode dominates. It appears as a soliton on the vortices and has a shedding frequency nearly twice that of the first at the highest incidence angle. The Strouhal number monotonically increases with incidence angle from approximately 0.2 to 0.4. Spectral analysis of the hot-film measurements confirms the findings from flow visualization experiments. Flows over the spinning disc generally mimic the stationary disc flows; however, centrifugal forces lead to cross-stream instability features that may be attributed to spiral wave instabilities intrinsic to the boundary layers in rotating flows. Velocity measurements are used to construct streamline patterns to compare with the smoke streaklines. The unsteadiness of the flows results in large variances. Mean strain rates are extracted from velocity data, where the fixed disc case at normal incidence compares well with theoretical predictions. The unsteady boundary layer thickness over the fixed disc, however, is approximately twice that predicted by theory for steady flow, stemming from the dominance of large unsteady vortices. Limited comparisons are made of the Strouhal numbers from experiments and numerical calculations in the literature.