Experiments were performed to examine the generation of internal waves by a barotropic tide forcing a continuously stratified fluid over idealized continental shelf/slope topography. A range of responses was observed, including the generation of both internal wave beams and boundary layer boluses, primarily dependent on the values of both the Reynolds number and the topographic steepness parameter. The formation of beams required a critical bottom slope, whilst for bolus formation a large vertical fluid excursion was necessary. A bolus formed when the non-dimensional vertical excursion parameter ΔhN/W0 > 3.2. Here Δh is the vertical excursion, N is the buoyancy frequency and W0 is the near-bottom vertical velocity associated with the local depth-averaged velocity. We simplified the classification of the observed flow regimes using a generation parameter G, defined as the ratio of a Reynolds number to the topographic steepness parameter. The estimated flow regime boundaries were: for G < 3 only a beam was observed, for 3 < G < 50 there was a transitional regime with both a beam and a bolus observed, for 50 < G < 400 there was another transitional regime with no beam but a bolus observed, and finally for the regime with G > 400 there was no bolus observed. We estimated that approximately 4% of the barotropic energy was converted to baroclinic energy when beams were generated.

Numerical simulations were conducted to investigate the effects of surface suction and injection on the global behaviour of linear disturbances in the rotating-disk boundary layer. This extends earlier work, which considered the case with no mass transfer. For disturbances in the genuine base flow, where radially inhomogeneity is retained, mass injection at the disk surface led to behaviour that remained qualitatively similar to that which was found when there was no mass transfer. The initial development of disturbances within the absolutely unstable region involved temporal growth and upstream propagation, as should be anticipated for an absolute instability. However, this did not persist indefinitely. Just as for the case without mass transfer, the simulation results suggested that convective behaviour would eventually dominate, for all the Reynolds numbers investigated. In marked contrast, the results obtained for flows with mass suction indicate a destabilization due to the effects of the base-flow radial inhomogeneity. It was possible to identify disturbances excited within the absolutely unstable region that grew continually, with a temporal growth rate that increased as the disturbance evolved. The strong locally stabilizing effect of suction on the absolute instability, which gives rise to large increases in critical Reynolds numbers, appears to be obtainable only at the expense of introducing a new form of global instability. Analogous forms of global behaviour can be found in impulse solutions of the linearized complex Ginzburg–Landau equation. These solutions were deployed to interpret and make comparisons with the numerical simulation results. They illustrate how the long-term behaviour of a disturbance can be determined by the precise balance between radial increases in temporal growth rates, corresponding shifts in temporal frequencies and diffusion/dispersion effects. This balance provides some insight into why disturbances that are absolutely unstable, for the homogenized version of the rotating-disk boundary-layer flow, may become, in the genuine radially inhomogeneous flow, either globally stable or globally unstable, depending on the level of mass transfer that is applied at the disk surface.

Flow velocities of a dilute gas–solid two-phase flow in a vertical sudden expansion were measured using phase Doppler anemometry to study the behaviour of the turbulence modulation for the stronger shear for various particle mass loadings, inlet Reynolds numbers and particle diameters. The measurements show that the particles changed the gas turbulence by elongation of the entire gas flow field in the downstream direction, which displaced the axial profile of the section-averaged fluctuation velocity in comparison with that of the single-phase flow, and by either the particle inertia reducing the local turbulence or the wake eddy effects enhancing the turbulence. Both mechanisms resulted in an apparent turbulence modulation, which has not been referred to in the related literature, and have led to an ambiguous understanding of turbulence modulation. The elongation and inlet effects should be eliminated to estimate whether the gas turbulence was really modified. The linear relationship between the gas mean velocity gradient and the root-mean-square fluctuation velocity, which was found to be similar to that in single-phase flows, gradually disappeared as the flow developed and the shear intensity reduced. The linear relationship also varied with different conditions. Specifically, the turbulence modulation was enhanced by higher particle mass loadings and the linear relationship disappeared with increasing particle mass loading. This linearity can perhaps be regarded as a criterion for determining the effect of stronger turbulence modulation.

In this paper, the wave propagation on a plane dry bottom after a dam break is analysed. Two mathematical models have been used and compared with each other for simulating such a dam-break scenario. First, the fully three-dimensional Navier–Stokes equations for a weakly compressible fluid have been solved using the new smooth particle hydrodynamics formulation, recently proposed by Ferrari et al. (Comput. Fluids, vol. 38, 2009, p. 1203). Second, the two-dimensional shallow water equations (SWEs) are solved using a third-order weighted essentially non-oscillatory finite-volume scheme. The numerical results are critically compared against the laboratory measurements provided by Fraccarollo & Toro (J. Hydraul. Res., vol. 33, 1995, p. 843). The experimental data provide the temporal evolution of the pressure field, the water depth and the vertical velocity profile at 40 gauges, located in the reservoir and in front of the gate. Our analysis reveals the shortcomings of SWEs in the initial stages of the dam-break phenomenon in reproducing many important flow features of the unsteady free-surface flow: the shallow water model predicts a complex wave structure and a wavy evolution of local free-surface elevations in the reservoir that can be clearly identified to be only model artefacts. However, the quasi-incompressible Navier–Stokes model reproduces well the high gradients in the flow field and predicts the cycles of simultaneous rapid decreasing and frozen stages of the free surface in the tank along with the velocity oscillations. Asymptotically, i.e. for ‘large times’, the shallow water model and the weakly compressible Navier–Stokes model agree well with the experimental data, since the classical SWE assumptions are satisfied only at large times.

The influence of a geostrophically balanced or potential vorticity (PV) containing background flow on the propagation of a coherent gravity wave is examined in a rotating shallow-water model. Over inertial time scales, we find that the gravity wave energy is scattered into other modes of similar wavelength, but with different directions of propagation. We attribute this response to nonlinear resonant interactions between the PV and gravity wave modes, despite the absence of any exchange of energy between the two, and show that the response is consistent with resonant triad theory. We first consider the scattering of a gravity wave mode due to a single PV mode, and compare the theoretical response to numerical solutions. This is followed by consideration of the propagation of a coherent gravity mode through a turbulent PV background. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.

Round jets originating from a pipe nozzle are computed by large-eddy simulations (LES) to investigate the effects of the nozzle-exit conditions on the flow and sound fields of initially laminar jets. The jets are at Mach number 0.9 and Reynolds number 105, and exhibit exit boundary layers characterized by Blasius velocity profiles, maximum root-mean-square (r.m.s.) axial velocity fluctuations between 0.2 and 1.9% of the jet velocity, and momentum thicknesses varying from 0.003 to 0.023 times the jet radius. The far-field noise is determined from the LES data on a cylindrical surface by solving the acoustic equations. Jets with a thinner boundary layer develop earlier but at a slower rate, yielding longer potential cores and lower centreline turbulent intensities. Adding random pressure disturbances of low magnitude in the nozzle also increases the potential core length and reduces peak r.m.s. radial velocity fluctuations in the shear layer. In all the jets, the shear-layer transition is dominated by vortex rolling-ups and pairings, which generate strong additional acoustic components, but also amplify the downstream-dominant low-frequency noise component when the exit boundary layer is thick. The introduction of inlet noise however results in weaker pairings, thus spectacularly reducing their contributions to the sound field. This high sensitivity to the initial conditions is in good agreement with experimental observations.