Natural convection is omnipresent on Earth. A basic and well-studied model for it is Rayleigh–Bénard convection, the fluid flow in a layer heated from below and cooled from above. Most explorations of Rayleigh–Bénard convection focus on spatially uniform, perfectly conducting thermal boundary conditions, but many important geophysical phenomena are characterized by boundary conditions which are a mixture of conducting and adiabatic materials. For example, the differences in thermal conductivity between continental and oceanic lithospheres are believed to play an important role in plate tectonics. To study this, Wang et al. (J. Fluid Mech., vol. 817, 2017, R1), measure the effect of mixed adiabatic–conducting boundary conditions on turbulent Rayleigh–Bénard convection, finding experimental proof that even if the total heat transfer is primarily affected by the adiabatic fraction, the arrangement of adiabatic and conducting plates is crucial in determining the large-scale flow dynamics.

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.

A mathematical model of rhythmic motion of a charged droplet between two parallel electrodes is developed in this study. The work is motivated by recent experimental findings that report oscillatory behaviour of water in oil droplets under a direct current electric field. The model considers the presence of a charged droplet placed in a dielectric medium. The droplet is immediately attracted to the electrode with the opposite polarity. When approaching the electrode, the electric charge is electrochemically reversed within the droplet, which is then repelled to the other electrode. The entire process can periodically repeat. The model is able to track a deformable liquid–liquid interface, the dynamics of the wetting process at the electrodes and the dynamics of electrochemical charge transfer between the droplet and the electrodes. The dependences of the oscillation frequency, charge acquired by the droplet and charging time on several model parameters (surface charge density on electrodes, kinetic parameter of charging, droplet–electrode contact angle, droplet size, liquid permittivity) are examined. Qualitative agreement of the model predictions with available experimental data is obtained, e.g. the oscillation frequency increases with growing electric field strength or droplet size. Our model represents the first successful attempt to predict oscillatory motion of aqueous droplets by a pseudo-three-dimensional two-phase approach. Our model also strongly supports the theory that the oscillatory motion relies on the combination of electrochemical charge injection at the electrodes and electrostatic attraction/repulsion processes.

We consider the full three-dimensional dynamics of a thin falling liquid film on a flat plate inclined at some non-zero angle to the horizontal. In addition to gravitational effects, the flow is driven by an electric field which is normal to the substrate far from the flow. This extends the work of Tseluiko & Papageorgiou (J. Fluid Mech., vol. 556, 2006b, pp. 361–386) by including transverse dynamics. We study both the cases of overlying and hanging films, where the liquid lies above or below the substrate, respectively. Starting with the Navier–Stokes equations coupled with electrostatics, a fully nonlinear two-dimensional Benney equation for the interfacial dynamics is derived, valid for waves that are long compared to the film thickness. The weakly nonlinear evolution is governed by a Kuramoto–Sivashinsky equation with a non-local term due to the electric field effect. The electric field term is linearly destabilising and produces growth rates proportional to $|\unicode[STIX]{x1D743}|^{3}$, where $\unicode[STIX]{x1D743}$ is the wavenumber vector of the perturbations. It is found that transverse gravitational instabilities are always present for hanging films, and this leads to unboundedness of nonlinear solutions even in the absence of electric fields – this is due to the anisotropy of the nonlinearity. For overlying films and a restriction on the strength of the electric field, the equation is well-posed in the sense that it possesses bounded solutions. This two-dimensional equation is studied numerically for the case of periodic boundary conditions in order to assess the effects of inertia, electric field strength and the size of the periodic domain. Rich dynamical behaviours are observed and reported. For subcritical Reynolds number flows, a sufficiently strong electric field can promote non-trivial dynamics for some choices of domain size, leading to fully two-dimensional evolutions of the interface. We also observe two-dimensional spatiotemporal chaos on sufficiently large domains. For supercritical flows, such two-dimensional chaotic dynamics emerges in the absence of a field, and its presence enhances the amplitude of the fluctuations and broadens their spectrum.

The stability of the Taylor–Couette flow is analysed when there is a stable density stratification along the axial direction and when the flow is centrifugally unstable, i.e. in the Rayleigh-unstable regime. It is shown that not only the centrifugal instability but also the strato-rotational instability can occur. These two instabilities can be explained and well described by means of a Wentzel–Kramers–Brillouin–Jeffreys asymptotic analysis for large axial wavenumbers in inviscid and non-diffusive limits. In the presence of viscosity and diffusion, numerical results reveal that the strato-rotational instability becomes dominant over the centrifugal instability at the onset of instability when the axial density stratification is sufficiently strong. Linear transient energy growth is next investigated for counter-rotating cylinders in the stable regime of the Froude number–Reynolds number parameter space. We show that there exist two types of transient growth mechanism analogous to the lift up and the Orr mechanisms in homogeneous fluids but with the additional effect of density perturbations. The dominant mechanism depends on the stratification: when the stratification is strong, non-axisymmetric three-dimensional perturbations achieve the optimal energy growth through the Orr mechanism while for moderate stratification, axisymmetric perturbations lead to the optimal transient growth by a lift-up mechanism involving internal waves.

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

Faltinsen et al. (J. Fluid Mech., vol. 487, 2003, pp. 1–42) (henceforth, Part 1) examined an undamped nonlinear resonant steady-state sloshing in a square-base tank by developing an approximate (asymptotic) Narimanov–Moiseev-type multimodal theory. The focus was on longitudinal and diagonal harmonic tank excitations. Neglecting the linear viscous boundary-layer damping was justified for model tanks with breadths of the order of metres. However, nonlinear sloshing in clean tanks of smaller size (count in centimetres) may be affected by damping in finite depth conditions. Qualitative and quantitative properties of the damped resonant steady-state sloshing in a square-base tank are now studied by using the modal theory from Part 1 equipped with the linear damping terms. The tank harmonically oscillates along an arbitrary horizontal (oblique) direction. An analytical asymptotic steady-state undamped solution is derived and the corresponding response curves are analysed versus the forcing direction. When the tank width $=$ breadth $=$ $L\sim 10$  cm, the surface tension effect on the free-surface dynamics can be neglected but the linear viscous damping should be included into the Narimanov–Moiseev nonlinear asymptotic modal theory. We analytically show that the steady-state damped sloshing possesses a series of distinguishing features so that, e.g. the square-like standing wave regime fully disappears and becomes replaced by swirling. Typical response curves of the damped steady-state resonant sloshing are studied for the liquid depth-to-width ratio exceeding 0.5. The computational results of the steady-state resonant response amplitudes are in a satisfactory agreement with observations and measurements by Ikeda et al. (J. Fluid Mech., vol. 700, 2012, pp. 304–328), which were conducted with a relatively small laboratory container.

Linear stability of a viscoelastic liquid on an oscillating plane is studied for disturbances of arbitrary wavenumbers. The main aim is to extend the earlier study of Dandapat & Gupta (J. Fluid Mech., vol. 72, 1975, pp. 425–432) to the finite wavenumber regime, which has not been attempted so far in the literature. The Orr–Sommerfeld boundary value problem is formulated for an unsteady base flow, and it is resolved numerically based on the Chebyshev spectral collocation method along with the Floquet theory. The analytical solution predicts that U-shaped unstable regions appear in the separated bandwidths of the imposed frequency, and the dominant mode of the long-wave instability intensifies in the presence of the viscoelastic parameter. The numerical solution shows that oblique neutral curves come out from the branch points of the U-shaped neutral curves at finite wavenumber and continue with the imposed frequency until the curves cross the next U-shaped neutral curve. As a consequence, in the finite wavenumber regime, no stable bandwidth of the imposed frequency is predicted by the long-wavelength analysis. Further, in some frequency ranges, the finite wavenumber instability is more dangerous than the long-wave instability.

Spanwise flow field measurements are carried out for turbulent flows in channels with permeable bottom walls by particle image velocimetry (PIV) to understand the effects of the wall permeability on turbulence structure near porous walls. The porous media used are three kinds of foamed ceramics which have the same porosities (0.8) but different permeabilities. The turbulent flow fields in spanwise planes are discussed using instantaneous and statistical measurement data. At a small permeability Reynolds number ($Re_{K}$), low-speed and high-speed streaks, which are similar to those of solid-wall turbulence, are observed near the walls while at a large $Re_{K}$ the observed structure is very different from that of the solid-wall turbulence. It is found that the obtained spanwise scales of the structure can be reasonably correlated with the wall normal distance plus the zero-plane displacement which is estimated from the mean velocity profile. With the distribution profiles of the spanwise streak spacing and integral length scales, the transitional change of the turbulence structure over permeable walls is discussed.

We develop a general regularized thin-fibre (string) model to predict the properties of non-Newtonian fluid fibres generated by centrifugal spinning. In this process the fibre emerges from a nozzle of a spinneret that rotates rapidly around its axis of symmetry, in the presence of centrifugal, Coriolis, inertial, viscous/shear-thinning, surface tension and gravitational forces. We analyse the effects of five important dimensionless groups, namely, the Rossby number ($Rb$), the Reynolds number ($Re$), the Weber number ($We$), the Froude number ($Fr$) and a power-law index ($m$), on the steady state trajectory and thinning of fibre radius. In particular, we find that the gravitational force mainly affects the fibre vertical angle at small arc lengths as well as the fibre trajectory. We show that for small $Rb$, which is the regime of nanofibre formation in centrifugal spinning methods, rapid thinning of the fibre radius occurs over small arc lengths, which becomes more pronounced as $Re$ increases or $m$ decreases. At larger arc lengths, a relatively large $We$ results in a spiral trajectory regime, where the fibre eventually recovers a corresponding inviscid limit with a slow thinning of the fibre radius as a function of the arc length. Viscous forces do not prevent the fibre from approaching the inviscid limit, but very strong surface tension forces may do so as they could even result in a circular trajectory with an almost constant fibre radius. We divide the spiral and circular trajectories into zones of no thinning, intense thinning and slow or ceased thinning, and for each zone we provide simple expressions for the fibre radius as a function of the arc length.

The oscillatory flow around a spherical object lying on a rough bottom is investigated by means of direct numerical simulations of the continuity and Navier–Stokes equations. The rough bottom is simulated by a layer/multiple layers of spherical particles, the size of which is much smaller that the size of the object. The period and amplitude of the velocity oscillations of the free stream are chosen to mimic the flow at the bottom of sea waves and the size of the small spherical particles falls in the range of coarse sand/very fine gravel. Even though the computational costs allow only the simulation of moderate values of the Reynolds number characterizing the bottom boundary layer, the results show that the coherent vortex structures, shed by the spherical object, can break up and generate turbulence, if the Reynolds number of the object is sufficiently large. The knowledge of the velocity field allows the dynamics of the large-scale coherent vortices shed by the object to be determined and turbulence characteristics to be evaluated. Moreover, the forces and torques acting on both the large spherical object and the small particles, simulating sediment grains, can be determined and analysed, thus laying the groundwork for the investigation of sediment dynamics and scour developments.

The flow in a rectangular channel with walls made of polyacrylamide gel is experimentally studied to examine the effect of soft walls on transition and turbulence. The bottom wall is fixed to a substrate and the top wall is unrestrained. As the Reynolds number increases, two different flow regimes are observed. The first is the ‘soft-wall turbulence’ (Srinivas & Kumaran, J. Fluid Mech., vol. 780, 2015, pp. 649–686). There is a large increase in the magnitudes of the velocity fluctuations after transition and the fluid velocity fluctuations appear to be non-zero at the soft walls, although higher resolution measurements are required to establish the nature of the boundary dynamics. The fluid velocity fluctuations are symmetric about the centreline of the channel, and they show relatively little downstream variation. The wall displacement measurements indicate that there is no observable motion perpendicular to the surface to within the experimental resolution, but displacement fluctuations parallel to the surface are observed after transition. As the Reynolds number is further increased, there is a second ‘wall-flutter’ transition, which involves visible downstream travelling waves in the top (unrestrained) wall alone. Wall displacement fluctuations of frequency less than approximately $500~\text{rad}~\text{s}^{-1}$ are observed both parallel and perpendicular to the wall. The mean velocity profiles and turbulence intensities are asymmetric, with much larger turbulence intensities near the top wall. The transitions are observed in sequence from a laminar flow at Reynolds number less than 1000 for a channel of height 0.6 mm and from a turbulent flow at a Reynolds number greater than 1000 for a channel of height 1.8 mm.

Integral expressions for the first-order correction to the effective slip length for longitudinal flows over a unidirectional superhydrophobic surface with rectangular grooves are determined under the assumptions that the meniscus curvature is small and the viscosity contrast between the groove-trapped subphase gas and the working fluid is significant. Both pressure-driven channel flows and semi-infinite shear flows are considered. Reciprocity ideas, based on use of Green’s second identity, provide the integral expressions with integrands dependent on known flat-meniscus solutions found by Philip (Z. Angew. Math. Phys., vol. 23, 1972, pp. 353–372). The results extend earlier work by Sbragaglia & Prosperetti (Phys. Fluids, vol. 19, 2007, 043603) on how weak meniscus curvature affects hydrodynamic slip. In particular, we derive a new integral expression for the first-order slip length correction due to weak meniscus curvature.

We describe a simple model for turbulence in a marginally unstable, forced, stratified shear flow. The model illustrates the essential physics of marginally unstable turbulence, in particular the tendency of the mean flow to fluctuate about the marginally unstable state. Fluctuations are modelled as an oscillatory interaction between the mean shear and the turbulence. The interaction is made quantitative using empirically established properties of stratified turbulence. The model also suggests a practical way to estimate both the mean kinetic energy of the turbulence and its viscous dissipation rate. Solutions compare favourably with observations of fluctuating ‘deep cycle’ turbulence in the equatorial oceans.

A general formulation is proposed to control the integral amplification factor of harmonic disturbances in weakly non-parallel amplifier flows. The sensitivity of the local spatial stability spectrum to a base-flow modification is first determined, generalizing the results of Bottaro et al. (J. Fluid Mech., vol. 476, 2003, pp. 293–302). This result is then used to evaluate the sensitivity of the overall spatial growth to a modification of the inlet flow condition. This formalism is applied to a non-parallel Batchelor vortex, which is a well-known model for trailing vortices generated by a lifting wing. The resulting sensitivity map indicates the optimal modification of the inlet flow condition enabling the stabilization of the helical modes. It is shown that the control, formulated using a single linearization of the flow dynamics carried out on the uncontrolled configuration, successfully reduces the total spatial amplification of all convectively unstable disturbances.

We investigate a model of thin layer turbulence that follows the evolution of the two-dimensional motions $\boldsymbol{u}_{2D}(x,y)$ along the horizontal directions $(x,y)$ coupled to a single Fourier mode along the vertical direction ( $z$ ) of the form $\boldsymbol{u}_{q}(x,y,z)=[v_{x}(x,y)\sin (qz),v_{y}(x,y)\sin (qz),v_{z}(x,y)\cos (qz)]$ , reducing thus the system to two coupled, two-dimensional equations. The model, despite its simplicity and ad hoc construction, displays a rich behaviour. Its reduced dimensionality allows a thorough investigation of the transition from a forward to an inverse cascade of energy as the thickness of the layer $H=\unicode[STIX]{x03C0}/q$ is varied. Starting from a thick layer and reducing its thickness it is shown that two critical heights are met: (i) one for which the forward unidirectional cascade (similar to three-dimensional turbulence) transitions to a bidirectional cascade transferring energy to both small and large scales and (ii) one for which the bidirectional cascade transitions to a unidirectional inverse cascade when the layer becomes very thin (similar to two-dimensional turbulence). The two critical heights are shown to have different properties close to criticality that we are able to analyse with numerical simulations for a wide range of Reynolds numbers and aspect ratios.

Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on swimming aquatic animals.

The apparent gas permeability of a porous medium is an important parameter in the prediction of unconventional gas production, which was first investigated systematically by Klinkenberg in 1941 and found to increase with the reciprocal mean gas pressure (or equivalently, the Knudsen number). Although the underlying rarefaction effects are well known, the reason that the correction factor in Klinkenberg’s famous equation decreases when the Knudsen number increases has not been fully understood. Most of the studies idealize the porous medium as a bundle of straight cylindrical tubes; however, according to the gas kinetic theory, this only results in an increase of the correction factor with the Knudsen number, which clearly contradicts Klinkenberg’s experimental observations. Here, by solving the Bhatnagar–Gross–Krook equation in simplified (but not simple) porous media, we identify, for the first time, two key factors that can explain Klinkenberg’s experimental results: the tortuous flow path and the non-unitary tangential momentum accommodation coefficient for the gas–surface interaction. Moreover, we find that Klinkenberg’s results can only be observed when the ratio between the apparent and intrinsic permeabilities is ${\lesssim}30$; at large ratios (or Knudsen numbers) the correction factor increases with the Knudsen number. Our numerical results could also serve as benchmarking cases to assess the accuracy of macroscopic models and/or numerical schemes for the modelling/simulation of rarefied gas flows in complex geometries over a wide range of gas rarefaction. Specifically, we point out that the Navier–Stokes equations with the first-order velocity-slip boundary condition are often misused to predict the apparent gas permeability of the porous medium; that is, any nonlinear dependence of the apparent gas permeability with the Knudsen number, predicted from the Navier–Stokes equations, is not reliable. Worse still, for some types of gas–surface interactions, even the ‘filtered’ linear dependence of the apparent gas permeability with the Knudsen number is of no practical use since, compared to the numerical solution of the Bhatnagar–Gross–Krook equation, it is only accurate when the ratio between the apparent and intrinsic permeabilities is ${\lesssim}1.5$.

This paper discusses the evolution of coastal currents by considering, relative to a rotating frame, the flow development when buoyant fluid is injected into a quiescent fluid bounded by a solid wall. The initial rapid response is determined by the Coriolis force–pressure gradient balance with a Kelvin wave propagating rapidly, at the long-wave speed, with the bounding wall to its right (for positive rotation). However fluid columns can stretch or squash on ejection from coastal outflows so that the ejected fluid gains positive or negative relative vorticity. Depending on its sign, the image in the solid wall of this vorticity can reinforce or oppose the zero potential-vorticity-anomaly (PVa) current set up by the Kelvin wave (KW). This paper presents a simple, fully nonlinear, dispersive, quasi-geostrophic model to discuss the form of coastal outflows as the relative strength of vortex to KW driving is varied. The model retains sufficient physics to capture both effects at finite amplitude and thus the essential nonlinearity of the flow, but is sufficiently simple so as to allow highly accurate numerical integration of the full problem and also explicit, fully nonlinear solutions for the evolution of a uniform PVa outflow in the hydraulic limit. Outflow evolutions are shown to depend strongly on the sign of the PVa of the expelled fluid, which determines whether the vortex and KW driving are reinforcing or opposing, and on the ratio of the internal Rossby radius to the vortex-source scale, $|V_{0}/D^{2}\unicode[STIX]{x1D6F1}_{0}|^{1/2}$, of the flow (where $D$ measures the outflow depth, $\unicode[STIX]{x1D6F1}_{0}$ the PVa of the outflow and $V_{0}$ the volume flux of the outflow), which measures the relative strengths of the two drivers. Comparison of the explicit hydraulic solutions with the numerical integrations shows that the analytical solutions predict the flow development well with differences ascribable to dispersive Rossby waves on the current boundary and changes in the source region captured by the full equations but not present in the hydraulic solutions.

We investigate the influence of abrupt changes on boundary-layer instability and transition. Such changes can take different forms including a local porous wall, suction/injection and surface roughness as well as junctions between rigid and porous walls. They may modify the boundary conditions and/or the mean flow, and their effects on transition have usually been assessed by performing stability analysis for the modified base flow and/or boundary conditions. However, such a conventional local linear stability theory (LST) becomes invalid if the change occurs over a relatively short scale comparable with, or even shorter than, the characteristic wavelength of the instability. In this case, the influence on transition is through scattering with the abrupt change acting as a local scatter, that is, an instability mode propagating through the region of abrupt change is scattered by the strong streamwise inhomogeneity to acquire a different amplitude. A local scattering approach (LSA) should be formulated instead, in which a transmission coefficient, defined as the ratio of the amplitude of the instability wave after the scatter to that before, is introduced to characterize the effect on instability and transition. In the present study, we present a finite-Reynolds-number formulation of LSA for isolated changes including a rigid plate interspersed by a local porous panel and a wall suction through a narrow slot. When the weak non-parallelism of the unperturbed base flow is ignored, the local scattering problem can be cast as an eigenvalue problem, in which the transmission coefficient appears as the eigenvalue. We also improved the method to take into account the non-parallelism of the unperturbed base flow, where it is found that the weak non-parallelism has a rather minor effect. The general formulation is specialized to two-dimensional Tollmien–Schlichting (T–S) waves. The resulting eigenvalue problem is solved, and full direct numerical simulations (DNS) are performed to verify some of the predictions by LSA. A parametric study indicates that conventional LST is valid only when the change is sufficiently gradual, and becomes either inaccurate or invalid when the scale of the local distortion is short. A local porous panel enhances T–S waves, while a local suction with a moderate mass flux significantly inhibits T–S waves. In the latter case, a comprehensive comparison is made between the theoretical predictions and experimental data, and a satisfactory quantitative agreement was observed.