This paper describes a new model of internal hydraulic jumps in two-layer systems that places no restrictions (such as the Boussinesq approximation) on the densities of the two fluids. The model is based on that of Borden and Meiburg (J. Fluid Mech., vol. 276, 2013, R1) for Boussinesq jumps, and has the appropriate behaviour in various limits (single-layer, small amplitude, Boussinesq, infinite depth). The energy flux loss in each layer across the jump is positive for all realistic jumps, reaching a maximum for the jump with maximum speed. Larger-amplitude jumps are possible, with decreasing energy loss, down to the ‘conjugate state’ of zero energy loss. However, it is argued that such states may be difficult to realise in practice, and if formed, will tend to the jump with maximum speed. The energy loss is mostly in the contracting layer unless the density there is small. The two-layer model is extended to incorporate mixing between the layers within the jump, with mixing based on the Richardson number.

Using two-dimensional direct numerical simulations, we investigate the flow in a fluid of kinematic viscosity ${\it\nu}$ and density ${\it\rho}$ around elliptical foils of density ${\it\rho}_{s}$ with major axis $c$ and minor axis $b$ for three different aspect ratios: $AR=b/c=1$ (a circle); $AR=0.5$; and $AR=0.1$. The vertical location of these foils $y_{s}(t)=A\sin (2{\rm\pi}f_{0}t)$ oscillates with amplitude $A$ and frequency $f_{0}$ in two distinct ways: ‘pure’ oscillation, where the foils are constrained to remain in place; and ‘flying’ oscillation, where horizontal motion is allowed. We simulate the flow for a range of the two appropriate control parameters, the non-dimensional amplitude, or Keulegan–Carpenter number $KC=2{\rm\pi}A/c$, and the non-dimensional frequency, or Stokes number ${\it\beta}=f_{0}c^{2}/{\it\nu}$. We observe three distinct patterns of asymmetry, labelled ‘S-type’ for synchronous asymmetry, ‘$\text{QP}_{\text{H}}$-type’ and ‘$\text{QP}_{\text{L}}$-type’ for quasi-periodic asymmetry at sufficiently high and sufficiently low (i.e. $AR=0.1$) aspect ratios, respectively. These patterns are separated at the critical locus in $KC$–${\it\beta}$ space by a ‘freezing point’ where the two incommensurate frequencies of the QP-type flows combine, and we show that this freezing point tends to occur at smaller values of $KC$ as $AR$ decreases. We find for the smallest aspect ratio case ($AR=0.1$) that the transition to asymmetry, for all values of $KC$, occurs for a critical value of an ‘amplitude’ Stokes number ${\it\beta}_{A}={\it\beta}(KC)^{2}=4{\rm\pi}^{2}f_{0}A^{2}/{\it\nu}\simeq 3$. The $\text{QP}_{\text{L}}$-type asymmetry for $AR=0.1$ is qualitatively different in physical and mathematical structure from the $\text{QP}_{\text{H}}$-type asymmetry at higher aspect ratio. The flows at the two ends of the ellipse become essentially decoupled from each other for the $\text{QP}_{\text{L}}$-type asymmetry, the two frequencies in the horizontal force signature being close to the primary frequency, rather than twice the primary frequency as in the $\text{QP}_{\text{H}}$-type asymmetry. Furthermore, the associated coefficients arising from a Floquet stability analysis close to the critical thresholds are profoundly different for low aspect ratio foils. Freedom to move slightly suppresses the transition to S-type asymmetry, and for certain parameters, if a purely oscillating foil subject to S-type asymmetry is released to move, flow symmetry is rapidly recovered due to the negative feedback of small horizontal foil motion. Conversely, for the ‘higher’ aspect ratios, the transition to $\text{QP}_{\text{H}}$-type asymmetry is encouraged when the foil is allowed to move, with strong positive feedback occurring between the shed vortices from successive oscillation cycles. For $AR=0.1$, freedom to move significantly encourages the onset of asymmetry, but the newly observed ‘primary’ $\text{QP}_{\text{L}}$-type asymmetry found for pure oscillation no longer occurs when the foil flies, with S-type asymmetry leading ultimately to locomotion at a constant speed occurring all along the transition boundary for all values of $KC$ and ${\it\beta}$.

Rayleigh–Taylor instability experiments are performed using both immiscible and miscible incompressible liquid combinations having a relatively large Atwood number of $A\equiv ({\it\rho}_{2}-{\it\rho}_{1})/({\it\rho}_{2}+{\it\rho}_{1})=0.48$. The liquid-filled tank is attached to a test sled that is accelerated downwards along a vertical rail system using a system of weights and pulleys producing approximately $1g$ net acceleration. The tank is backlit and images are digitally recorded using a high-speed video camera. The experiments are either initiated with forced initial perturbations or are left unforced. The forced experiments have an initial perturbation imposed by vertically oscillating the liquid-filled tank to produce Faraday waves at the interface. The unforced experiments rely on random interfacial fluctuations, resulting from background noise, to seed the instability. The main focus of this study is to determine the effects of forced initial perturbations and the effects of miscibility on the growth parameter, ${\it\alpha}$. Measurements of the mixing-layer width, $h$, are acquired, from which ${\it\alpha}$ is determined. It is found that initial perturbations of the form used in this study do not affect measured ${\it\alpha}$ values. However, miscibility is observed to strongly affect ${\it\alpha}$, resulting in a factor of two reduction in its value, a finding not previously observed in past experiments. In addition, all measured ${\it\alpha}$ values are found to be smaller than those obtained in previous experimental studies.

A zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with $k^{+}\approx 11$ and a momentum-thickness Reynolds number of approximately 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number $Pr=0.71$ is simulated. The dynamic multiscale approach developed by Araya et al. (J. Fluid Mech., vol. 670, 2011, pp. 581–605) is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang & Castillo (J. Turbul., vol. 4, 2003, 006) inner/outer scaling. It is shown that the Reynolds analogy does not hold for $y^{+}<9$. In this region the value of the turbulent Prandtl number departs substantially from unity. Above this region the Reynolds analogy is only approximately valid, with the turbulent Prandtl number decreasing from 1 to 0.7 across the boundary layer for rough and smooth walls. In comparison with the smooth-wall case, the turbulent transport of heat per unit mass, $\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$, towards the wall is enhanced in the buffer layer, but the transport of $\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$ away from the wall is reduced in the outer layer for the rough case; similar behaviour is found for the vertical transport of turbulent momentum per unit mass, $\overline{v^{\prime }u^{\prime }v^{\prime }}$. Above the roughness sublayer (3$k$–5$k$) it is found that most of the temperature field statistics, including higher-order moments and conditional averages, are highly similar for the smooth and rough surface flow, showing that the Townsend’s Reynolds number similarity hypothesis applies for the thermal field as well as the velocity field for the Reynolds number and $k^{+}$ considered in this study.

A layered description of the structure of turbulent flame brushes is provided for situations featuring large but finite values of the Damköhler number, which correspond to the wrinkled flame regime of turbulent premixed combustion. One special focus of this study is placed on the description of the leading edge of the turbulent flame brush, the role of which is known to be essential with respect to propagation, transport and stabilization issues. On the basis of rather simple and well-identified working hypotheses, the influence of slight increases in the Karlovitz number values is revealed. The phenomenology and associated statistics are also investigated analytically, which leads to a mathematical description of the leading edge internal structure. With respect to the progress variable statistics, i.e. probability density function, this leading edge can indeed be thought of as the inner part of a boundary layer where the influence of the finite thickness of laminar flamelets can no longer be neglected. From the proposed description, standard fast-chemistry closures, which are currently used to perform the numerical simulation of turbulent combustion, may easily be generalized to account for the finite-rate chemistry effects occurring in this sublayer, thus emphasizing the interest of the present analysis for turbulent combustion theory and modelling.

We consider whether small-amplitude topography in a two-dimensional ocean may contain internal wave attractors. These are closed orbits formed by the characteristics (or wave beam paths) of the linear, inviscid, steady-state Boussinesq equations, and their existence may imply enhanced scattering and energy decay for the internal tide when dissipation is present. We develop a numerical code to detect attractors over arbitrary topography, and apply this to random, Gaussian topography with different covariance functions. The rate of attractors per length of topography increases with the fraction of supercritical topography, but surprisingly, it also increases as the amplitude of the topography is decreased, while the supercritical fraction is held constant. This can partly be understood by appealing to Rice’s formula for the rate of zero crossings of a stochastic process. We compute the rate of attractors for a covariance function typical of ocean bathymetry away from large features and find it is about 10 attractors per 1000 km. This could have implications for the overall energy budget of the ocean.

We performed numerical experiments on a one-dimensional elastic solid oscillating in a two-dimensional viscous incompressible fluid with the intent of discerning the interplay of vorticity and elastodynamics in flapping wing propulsion. Perhaps for the first time, we have established the role of foil deflection topology and its influence on vorticity generation, through spatially and temporally evolving foil slope and curvature. Though the frequency of oscillation of the foil has a definite role, it is the phase relation between foil slope and pressure that determines thrust or drag. Similarly, the phase difference between flapping velocity, and pressure and inertial forces, determine the power input to the foil, and in turn drives propulsive efficiency. At low frequencies of oscillation, the sympathetic slope and curvature of deformation of the foil allow generation of leading-edge vortices that do not separate; they cause substantial rise in pressure between the leading edge and mid-chord. The circulatory component of pressure is determined primarily by the leading-edge vortex and therefore thrust too is predominantly circulatory in origin at low frequencies. In the intermediate and high-frequency range, thrust and drag on the foil spatially alternate and non-circulatory forces dominate over circulatory and viscous forces. For the mass ratios we simulated, thrust due to flapping varies quadratically as a function of Strouhal number or trailing-edge flapping velocity; further, the trailing edge flapping velocities peak at the same set of frequencies where the thrust is also a maximum. Propulsive efficiency, on the other hand, is roughly a mirror image of the thrust variation with respect to Strouhal number. Given that most instances of flapping propulsion in nature are primarily through distributed muscular actuation that enables precise control of deformation shape, leading to high thrust and efficiency, the results presented here are pointers towards understanding some of the mechanisms that drive thrust and propulsive efficiency.

We investigate the motion of a gas–liquid interface in a test tube induced by a large acceleration via impulsive force. We conduct simple experiments in which the tube partially filled with a liquid falls under gravity and hits a rigid floor. A curved gas–liquid interface inside the tube reverses and eventually forms a so-called focused jet. In our experiments, there arises either vibration of the interface or an increment in the velocity of the liquid jet, accompanied by the onset of cavitation in the liquid column. These phenomena cannot be explained by a considering pressure impulse in a classical potential flow analysis, which does not account for finite speeds of sound or phase changes. Here we model such water-hammer events as a result of the one-dimensional propagation of a pressure wave and its interaction with boundaries through acoustic impedance mismatching. The method of characteristics is applied to describe pressure-wave interactions and the subsequent cavitation. The model proposed is found to be able to capture the time-dependent characteristics of the liquid jet.

We experimentally investigate the turbulent wall plume that forms next to a uniformly distributed source of buoyancy. Our experimental results are compared with the theoretical model and experiments of Cooper & Hunt (J. Fluid Mech., vol. 646, 2010, pp. 39–58). Our experiments give a top-hat entrainment coefficient of $0.048\pm 0.006$. We measure a maximum vertical plume velocity that follows the scaling predicted by Cooper & Hunt but is significantly smaller. Our measurements allow us to construct a turbulent plume model that predicts all plume properties at any height. We use this plume model to calculate plume widths, velocities and Reynolds numbers for typical dissolving icebergs and ice fronts and for a typical room with a heated or cooled vertical surface.

Defining a link between wind-tunnel settling chamber screens, flow quality and test section boundary-layer spanwise variation is necessary for accurate transition prediction. The aim of this work is to begin establishing this link. The computed, steady, laminar wake of a zither (screen model) with imperfect wire spacing is tracked through a contraction and into a model test section. The contraction converts the zither wake into streamwise vorticity which then creates spanwise variation (streaks) in the test-section boundary layer. The magnitude of the spanwise variation is sensitive to the zither open-area ratio and imperfections, but the observed wavelength is relatively insensitive to the zither wire spacing. Increased spanwise variation is attributed to large wavelength variation of drag across the zither, and not the coalescence of jets phenomena. The linear stability of the streaks is predicted using the parabolized stability equations with the $\text{e}^{N}$ method. A standard deviation of zither wire position error of 38.1 ${\rm\mu}$m (15 % of wire diameter) for a zither of 50 % open-area ratio is found to suppress Tollmien–Schlichting wave growth significantly.

Flow of a thin viscous film down a flat inclined plane becomes unstable to long-wave interfacial fluctuations when the Reynolds number based on the mean film thickness becomes larger than a critical value (this value decreases as the angle of inclination to the horizontal increases, and in particular becomes zero when the plate is vertical). Control of these interfacial instabilities is relevant to a wide range of industrial applications including coating processes and heat or mass transfer systems. This study considers the effect of blowing and suction through the substrate in order to construct from first principles physically realistic models that can be used for detailed passive and active control studies of direct relevance to possible experiments. Two different long-wave, thin-film equations are derived to describe this system; these include the imposed blowing/suction as well as inertia, surface tension, gravity and viscosity. The case of spatially periodic blowing and suction is considered in detail and the bifurcation structure of forced steady states is explored numerically to predict that steady states cease to exist for sufficiently large suction speeds since the film locally thins to zero thickness, giving way to dry patches on the substrate. The linear stability of the resulting non-uniform steady states is investigated for perturbations of arbitrary wavelength, and any instabilities are followed into the fully nonlinear regime using time-dependent computations. The case of small amplitude blowing/suction is studied analytically both for steady states and their stability. Finally, the transition between travelling waves and non-uniform steady states is explored as the amplitude of blowing and suction is increased.

We report on the enhancement of turbulent convective heat transport due to vapour-bubble nucleation at the bottom plate of a cylindrical Rayleigh–Bénard sample (aspect ratio 1.00, diameter 8.8 cm) filled with liquid. Microcavities acted as nucleation sites, allowing for well-controlled bubble nucleation. Only the central part of the bottom plate with a triangular array of microcavities (etched over an area with diameter of 2.5 cm) was heated. We studied the influence of the cavity density and of the superheat $T_{b}-T_{on}$ ($T_{b}$ is the bottom-plate temperature and $T_{on}$ is the value of $T_{b}$ below which no nucleation occurred). The effective thermal conductivity, as expressed by the Nusselt number $\mathit{Nu}$, was measured as a function of the superheat by varying $T_{b}$ and keeping a fixed difference $T_{b}-T_{t}\simeq 16$  K ($T_{t}$ is the top-plate temperature). Initially $T_{b}$ was much larger than $T_{on}$ (large superheat), and the cavities vigorously nucleated vapour bubbles, resulting in two-phase flow. Reducing $T_{b}$ in steps until it was below $T_{on}$ resulted in cavity deactivation, i.e. in one-phase flow. Once all cavities were inactive, $T_{b}$ was increased again, but they did not reactivate. This led to one-phase flow for positive superheat. The heat transport of both one- and two-phase flow under nominally the same thermal forcing and degree of superheat was measured. The Nusselt number of the two-phase flow was enhanced relative to the one-phase system by an amount that increased with increasing $T_{b}$. Varying the cavity density (69, 32, 3.2, 1.2 and $0.3~\text{mm}^{-2}$) had only a small effect on the global $\mathit{Nu}$ enhancement; it was found that $\mathit{Nu}$ per active site decreased as the cavity density increased. The heat-flux enhancement of an isolated nucleating site was found to be limited by the rate at which the cavity could generate bubbles. Local bulk temperatures of one- and two-phase flows were measured at two positions along the vertical centreline. Bubbles increased the liquid temperature (compared to one-phase flow) as they rose. The increase was correlated with the heat-flux enhancement. The temperature fluctuations, as well as local thermal gradients, were reduced (relative to one-phase flow) by the vapour bubbles. Blocking the large-scale circulation around the nucleating area, as well as increasing the effective buoyancy of the two-phase flow by thermally isolating the liquid column above the heated area, increased the heat-flux enhancement.

Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the momentum-balance equations by extending the recent depth-averaged ${\it\mu}(I)$-rheology for dense granular flows to two spatial dimensions, using the principle of material frame indifference or objectivity. Scaling the cross-slope coordinate on the width of the channel and the velocity on the one-dimensional steady uniform solution, we show that the steady two-dimensional downslope velocity profile is independent of scale. The only controlling parameters are the channel aspect ratio, the slope inclination angle and the frictional properties of the chute and the sidewalls. Solutions are constructed for both no-slip conditions and for a constant Coulomb friction at the walls. For narrow chutes, a pronounced parabolic-like depth-averaged downstream velocity profile develops. However, for very wide channels, the flow is almost uniform with narrow boundary layers close to the sidewalls. Both of these cases are in direct contrast to conventional inviscid avalanche models, which do not develop a cross-slope profile. Steady-state numerical solutions to the full three-dimensional ${\it\mu}(I)$-rheology are computed using the finite element method. It is shown that these solutions are also independent of scale. For sufficiently shallow channels, the depth-averaged velocity profile computed from the full solution is in excellent agreement with the results of the depth-averaged theory. The full downstream velocity can be reconstructed from the depth-averaged theory by assuming a Bagnold-like velocity profile with depth. For wide chutes, this is very close to the results of the full three-dimensional calculation. For experimental validation, a laser profilometer and balance are used to determine the relationship between the total mass flux in the chute and the flow thickness for a range of slope angles and channel widths, and particle image velocimetry (PIV) is used to record the corresponding surface velocity profiles. The measured values are in good quantitative agreement with reconstructed solutions to the new depth-averaged theory.

Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

The helical absolute equilibrium of a compressible adiabatic flow presents not only polarization between two purely helical modes of opposite chiralities but also that between vortical and acoustic modes, deviating from the equipartition predicted by Kraichnan (J. Acoust. Soc. Am., vol. 27, 1955, pp. 438–441). Owing to the existence of the acoustic mode, even if all the Fourier modes of one chiral sector in the sharpened Helmholtz decomposition (Moses, SIAM J. Appl. Maths, vol. 21, 1971, pp. 114–130) are thoroughly truncated, leaving the system with positive-definite helicity and energy, negative temperature and the corresponding large-scale concentration of vortical modes are not allowed, unlike in the incompressible case.

We consider here the effects of inertia on the instability of a flat liquid film under the effects of capillary and intermolecular forces (van der Waals interaction). Firstly, we perform a linear stability analysis within the long-wave approximation, which shows that the inclusion of inertia does not produce new regions of instability other than the one previously known from the usual lubrication case. The wavelength, ${\it\lambda}_{m}$, corresponding to the maximum growth, ${\it\omega}_{m}$ and the critical (marginal) wavelength do not change. The most affected feature of the instability under an increase of the Laplace number is the noticeable decrease of the growth rates of the unstable modes. In order to put in evidence the effects of the bidimensional aspects of the flow (neglected in the long-wave approximation), we also calculate the dispersion relation of the instability from the linearized version of the complete Navier–Stokes (N–S) equations. Unlike the long-wave approximation, the bidimensional model shows that ${\it\lambda}_{m}$ can vary significantly with inertia when the aspect ratio of the film is not sufficiently small. We also perform numerical simulations of the nonlinear N–S equations and analyse to which extent the linear predictions can be applied depending on both the amount of inertia involved and the aspect ratio of the film.

The purely conductive state in configurations such as the Rayleigh–Bénard one is linearly stable for yield stress fluids at all Rayleigh numbers, $Ra$. However, on changing to localized heater configurations the static background state exists only if the yield stress is sufficiently large. Otherwise, thermal plumes may be induced in a stationary viscoplastic fluid layer, as illustrated in the recent experimental study of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144–153). Here, we study an analogous problem both analytically and computationally, from the perspective of an ideal yield stress fluid (Bingham fluid) that is initially stationary in a locally heated rectangular tank. We show that for a non-zero yield stress the onset of flow waits for a start time $t_{s}$ that increases with the dimensionless ratio of yield stress to buoyancy stress, denoted $B$. We provide a precise mathematical definition of $t_{s}$ and approximately evaluate this for different values of $B$, using both computational and semianalytical methods. For sufficiently large $B\geqslant B_{cr}$, the fluid is unable to yield. For the flow studied, $B_{cr}\approx 0.00307$. The critical value $B_{cr}$ and the start time $t_{s}$, for $B<B_{cr}$, are wholly independent of $Ra$ and $Pr$. For $B<B_{cr}$, yielding starts at $t=t_{s}$. The flow develops into either a weakly or a strongly convective flow. In the former case the passage to a steady state is relatively smooth and monotone, resulting eventually in a steady convective plume above the heater, rising and impinging on the upper wall, then recirculating steadily around the tank. With strongly convecting flows, for progressively larger $Ra$ we observe an increasing number of distinct plume heads and a tendency for plumes to develop as short-lived pulses. Over a certain range of $(Ra,B)$ the flow becomes temporarily frozen between two consecutive pulses. Such characteristics are distinctly reminiscent of the experimental work of Davaille et al. (J. Non-Newtonian Fluid Mech., vol. 193, 2013, 144–153). The yield stress plays a multifaceted role here as it affects plume temperature, size and velocity through different mechanisms. On the one hand, increasing $B$ tends to increase the maximum temperature of the plume heads. On the other hand, for larger $B\rightarrow B_{cr}$, the plume never starts.

A series of direct numerical simulations of mass transfer across the air–water interface driven by buoyancy-induced convection have been carried out to elucidate the physical mechanisms that play a role in the transfer of heat and atmospheric gases. The buoyant instability is caused by the presence of a thin layer of cold water situated on top of a body of warm water. In time, heat and atmospheric gases diffuse into the uppermost part of the thermal boundary layer and are subsequently transported down into the bulk by falling sheets and plumes of cold water. Using a specifically designed numerical code for the discretization of scalar convection and diffusion, it was possible to accurately resolve this buoyant-instability-induced transport of atmospheric gases into the bulk at a realistic Prandtl number ($\mathit{Pr}=6$) and Schmidt numbers ranging from $\mathit{Sc}=20$ to $\mathit{Sc}=500$. The simulations presented here provided a detailed insight into instantaneous gas transfer processes. The falling plumes with highly gas-saturated fluid in their core were found to penetrate deep inside the bulk. With an initial temperature difference between the water surface and the bulk of slightly above $2$  K, peaks in the instantaneous heat flux in excess of $1600~\text{W}~\text{m}^{-2}$ were observed, proving the potential effectiveness of buoyant-convective heat and gas transfer. Furthermore, the validity of the scaling law for the ratio of gas and heat transfer velocities $K_{L}/H_{L}\propto (\mathit{Pr}/\mathit{Sc})^{0.5}$ for the entire range of Schmidt numbers considered was confirmed. A good time-accurate approximation of $K_{L}$ was found using surface information such as velocity fluctuations and convection cell size or surface divergence. A reasonable time accuracy for the $K_{L}$ estimation was obtained using the horizontal integral length scale and the root mean square of the horizontal velocity fluctuations in the upper part of the bulk.

In this paper, we report the results of an experimental sensitivity analysis on a thermoacoustic system – an electrically heated Rijke tube. We measure the change of the linear stability characteristics of the system, quantified as shifts in the growth rate and oscillation frequency, that is caused by the introduction of a passive control device. The control device is a mesh, which causes drag in the system. The rate of growth is slow, so the growth rate and frequency can be measured very accurately over many hundreds of cycles in the linear regime with and without control. These measurements agree qualitatively well with the theoretical predictions from adjoint-based methods of Magri & Juniper (J. Fluid Mech., vol. 719, 2013, pp. 183–202). This agreement supports the use of adjoint methods for the development and implementation of control strategies for more complex thermoacoustic systems.