The utility of piston theory as a means of solving insentropic two-dimensional aerodynamic problems has been aptly demonstrated by many writers in recent years. The present treatment removes the restriction of isentropic flows, extending the applicability of piston theory to flows with strong shocks. Sample calculations for a thin biconvex airfoil are carried out in which the local flow is assumed to be isentropic and non-isentropic. Comparison of the result is made with that of the shock expansion theory of Cole, Gazley & Williams (1956).

The present work focuses on the geometrical features of a zero-pressure-gradient turbulent boundary layer based on vectorline segment analysis. In a turbulent vector field, tracing from any non-singular point, along either the vector or the inverse direction, one will reach a local extremum of the vector magnitude. The vectorline between the two local extrema is defined as the vectorline segment corresponding to the given spatial point. Specifically the vectorline segment can be the streamline segment for the velocity vector case, or the vorticity line segment for the vorticity vector case. Such a quantitatively defined and space-filling vectorline segment structure reflects the natural vectorial topology. Because of inhomogeneity in the wall-normal direction, vectorline segments corresponding to the grid points at specified wall-normal distances are sampled for statistics. For streamline segments, the probability density function (p.d.f.) of the normalized segment length in different flow regions matches a model solution, and for vorticity line segments such a p.d.f. in the log-law region and beyond matches the same model solution, which indicates some universality of different flow regions and different vector field structures. Typically the joint p.d.f. of the characteristic parameters of streamline segments presents clear asymmetry, which is closely related to the skewness of the velocity derivative. Moreover, the orientation statistics of vectorline segments, characterized by the coordinate difference between the segment starting point and ending point, have been provided to quantify the flow anisotropy.

This article presents a framework for building analytical solutions for coupled flow in two interacting multiphase domains. The coupled system consists of a multiphase sphere embedded in a multiphase substrate. Each of these domains consists of an interconnected, load-bearing, creeping matrix phase and an inviscid, interstitial fluid phase. This article outlines techniques for building analytical solutions for velocity, pressure and compaction within each domain, subject to boundary conditions of continuity of matrix velocity, normal traction, normal pressure gradient, and compaction at the interface between the two domains. The solutions, valid over a short period of time in the limit of small fluid fraction, are strongly dependent on the ratio of shear viscosities between the matrix phase in the sphere and the matrix phase in the substrate. Compaction and pressure drop across the interface, evaluated at the poles and the equator, are strongly dependent on the ratio of matrix shear viscosities in the two domains. When deformed under a pure shear deformation, the magnitude of flow within the sphere rapidly decreases with an increase in this ratio until it reaches a value of ${\sim}80$, after which the velocity within the sphere becomes relatively insensitive to the increase in the viscosity ratio.

In this paper, results of laboratory experiments simulating buoyancy-driven coastal currents produced by estuarine discharges into the ocean, are discussed. The responses of the propagation speeds of the currents to increases and decreases of the volumetric discharge rate at the source are investigated. For increasing discharge rate, we find that the mean speed of the current head displays a sharp rise some time after the source discharge condition has changed. In contrast, a decrease of the current speed following a decreasing discharge rate proceeds gradually. The current speed after acceleration or deceleration is found to be equal to the speed that would be expected had the discharge been at the higher or lower rate from the start of the experiment. The relative speed at which the information of the changed discharge condition at the source approaches the advancing current head from upstream, for both increasing and decreasing discharge rates, is found to be approximately one to three times the mean speed of the current. Further, we find that this transmission speed is 0.82±0.20 times the propagation speed of a linear, long interfacial Kelvin wave.

Using experimental transverse velocity data for very high-Reynolds-number turbulence, we suggest a model describing both the formation of intermittency and asymmetry of turbulence. The model, called the ‘bump model’, is a modification of the ramp model suggested previously. The connection between asymmetry and intermittency makes it possible to study the latter with relatively low moments.

We present an extension of Thomson’s (J. Fluid Mech., vol. 210, 1990, pp. 113–153) two-particle Lagrangian stochastic model that is constructed to be consistent with the $4/5$ law of turbulence. The rate of separation in the new model is reduced relative to the original model with zero skewness in the Eulerian longitudinal relative velocity distribution and is close to recent measurements from direct numerical simulations of homogeneous isotropic turbulence. The rate of separation in the equivalent backwards dispersion model is approximately a factor of 2.9 larger than the forwards dispersion model, a result that is consistent with previous work.

Motivated by work on tilted convection (Sheremet, J. Fluid Mech., vol. 506, 2004, p. 217), a set of experiments is presented here using the same set-up of a tilted tank attached to a rotating centrifuge with a 2.5 m arm. Within the tank small, almost neutrally buoyant, spheres are released, and their trajectories are recorded. Thus the forces acting on a sphere can be analysed in the case of misalignment between the buoyancy force and the axis of rotation.

The angles of descent characterizing the trajectory are compared with inviscid linear theory developed by Stewartson (Q. J. Math. Appl. Mech., vol. 6, 1953, p. 141), and the agreement is found to be good. The angles should be independent of the density anomaly of the spheres compared to their environment. Using the descent velocity from non-rotating experiments, the density of the spheres is estimated and used to determine the drag acting on them in the rotating experiments. It is found that the drag is up to 50% larger than expected from Stewartson's theory. The agreement is best, not for infinitesimal, but for small Rossby numbers. The results are consistent with observations recorded by Maxworthy (J. Fluid Mech., vol. 40, 1970, p. 453).

We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows.

Vorticity distributions in axisymmetric vortex rings produced by a piston–pipe apparatus are numerically studied over a range of Reynolds numbers, $Re$, and stroke-to-diameter ratios, $L/D$. It is found that a state of advective balance, such that $\unicode[STIX]{x1D701}\equiv \unicode[STIX]{x1D714}_{\unicode[STIX]{x1D719}}/r\approx F(\unicode[STIX]{x1D713},t)$, is achieved within the region (called the vortex ring bubble) enclosed by the dividing streamline. Here $\unicode[STIX]{x1D701}\equiv \unicode[STIX]{x1D714}_{\unicode[STIX]{x1D719}}/r$ is the ratio of azimuthal vorticity to cylindrical radius, and $\unicode[STIX]{x1D713}$ is the Stokes streamfunction in the frame of the ring. Some, but not all, of the $Re$ dependence in the time evolution of $F(\unicode[STIX]{x1D713},t)$ can be captured by introducing a scaled time $\unicode[STIX]{x1D70F}=\unicode[STIX]{x1D708}t$, where $\unicode[STIX]{x1D708}$ is the kinematic viscosity. When $\unicode[STIX]{x1D708}t/D^{2}\gtrsim 0.02$, the shape of $F(\unicode[STIX]{x1D713})$ is dominated by the linear-in-$\unicode[STIX]{x1D713}$ component, the coefficient of the quadratic term being an order of magnitude smaller. An important feature is that, as the dividing streamline ($\unicode[STIX]{x1D713}=0$) is approached, $F(\unicode[STIX]{x1D713})$ tends to a non-zero intercept which exhibits an extra $Re$ dependence. This and other features are explained by a simple toy model consisting of the one-dimensional cylindrical diffusion equation. The key ingredient in the model responsible for the extra $Re$ dependence is a Robin-type boundary condition, similar to Newton’s law of cooling, that accounts for the edge layer at the dividing streamline.

Theoretical investigation of acoustic wave interactions with turbulent premixed flames was conducted to evaluate the acoustic energy amplification and/or damping due to the interaction of low-frequency acoustic waves with turbulent flames in three-dimensional space. Such amplified or damped acoustic energy is either coherent or incoherent as wrinkled flames cause coherent energy of a monochromatic acoustic wave to be damped into incoherent energy of spatially diffused and spectrally broadened acoustic waves. Small perturbation method (SPM) up to the second order was utilized to analyse net coherent and incoherent acoustic energies of the reflected and transmitted waves scattered from a weakly wrinkled turbulent flame surface in random motion. General formulations for net coherent and incoherent energy budget of the scattered fields were derived that can be applied to any type of flame height statistics. Production and/or damping of acoustic energy scattered from a turbulent flame is attributed to two effects: one is the acoustic velocity jump due to flame's unsteady heat release and the other is the flame's wrinkling due to its unsteady motion. Dimensionless parameters that govern net acoustic energy budget were derived in case of Gaussian statistics of flame surface behaviour: the r.m.s. and correlation length of flame height, the frequency ratio of the incidence frequency to the flame's correlation frequency, the time ratio of the flame's diffusion to correlation time and the incidence angle. The results of the scattered acoustic energy budget showed that noticeable amplification of acoustic energy was obtained either for a small frequency ratio (≪1) at the critical incidence angle or for a large frequency ratio and time ratio (≫1), while damping was obtained for a small frequency ratio at off-critical incidence angles. The relative importance of unsteady heat release (the jump effect) and unsteady motion (the wrinkling effect) to net acoustic energy is controlled mainly by the frequency ratio: The unsteady heat release effect dominates the wrinkling effect at a large frequency ratio, and vice versa at a small frequency ratio. The energy transfer from coherent to incoherent energy is due to flame surface wrinkling and is enhanced with the square of the flame's r.m.s. height.