Oceanic mesoscale currents (‘eddies’) can have significant effects on the distributions of passive tracers. The associated inhomogeneous and anisotropic eddy fluxes are traditionally parametrised using a transport tensor ($K$-tensor), which contains both diffusive and advective components. In this study, we analyse the eddy transport tensor in a quasigeostrophic double-gyre flow. First, the flow and passive tracer fields are decomposed into large- and small-scale (eddy) components by spatial filtering, and the resulting eddy forcing includes an eddy tracer flux representing advection by eddies and non-advective terms. Second, we use the flux-gradient relation between the eddy fluxes and the large-scale tracer gradient to estimate the associated $K$-tensors in their entire structural, spatial and temporal complexity, without making any additional assumptions or simplifications. The divergent components of the eddy tracer fluxes are extracted via the Helmholtz decomposition, which yields a divergent tensor. The remaining rotational flux does not affect the tracer evolution, but dominates the total tracer flux, affecting both its magnitude and spatial structure. However, in terms of estimating the eddy forcing, the transport tensor prevails over its divergent counterpart because of the significant numerical errors induced by the Helmholtz decomposition. Our analyses demonstrate that, in general, the $K$-tensor for the eddy forcing is not unique, that is, it is tracer-dependent. Our study raises serious questions on how to interpret and use various estimates of $K$-tensors obtained from either observations or eddy-resolving model solutions.

This paper presents an experimental investigation of the characteristics of laminar– turbulent transition occurring on a flat-plate boundary layer due to the interaction with a non-impinging aerofoil wake. Previous studies have tended to focus on transition induced by free-stream turbulence or by the wake of a circular cylinder, both of which exhibit different forcing characteristics to the present experimental arrangement. A tripped NACA 0014 aerofoil was used to generate a fully turbulent wake, upstream of and at various heights above a laminar, flat-plate boundary layer, in the UK National Low-turbulence Wind Tunnel at City, University of London. Hot-wire measurements conducted in the pre-transitional region reveal the wall-normal and spanwise structure of the disturbances induced within the boundary layer and the rate of growth of disturbance energy. Disturbance profiles generally (but not uniquely) follow the non-modal distribution obtained from transient growth theory, but energy growth rates are mainly exponential rather than algebraic. Energy spectra demonstrate the existence of mixed transitional features (both natural and bypass) in the boundary layer. Two-point spatial correlations reveal the presence of a streaky structure, but with spanwise scale much larger than the boundary layer thickness, in contrast to the trends seen in free-stream turbulence-induced bypass transition and cylinder wake-induced transition. The gap between aerofoil and flat plate affects both the evolution of non-modal disturbance profile and the appearance of the streaky structure; the spacing of the streaks was also found to scale with the vertical gap between aerofoil and flat plate. Overall, the combination of observed characteristics is quite different from the forced transition mechanisms previously reported in the literature.

We study the linear stability of a surfactant-laden shear-imposed fluid flowing down a compliant substrate. The aim is to extend the earlier and recent studies (Carpenter & Garrad, J. Fluid Mech., vol. 155, 1985, pp. 465–510; Alexander et al., J. Fluid Mech., vol. 900, 2020, A40) in the presence of insoluble surfactant when an external streamwise imposed shear stress acts at the fluid surface. In other words, the current study expands the earlier study (Wei, Phys. Fluids, vol. 17, 2005, 012103) in the presence of a flexible substrate. The Orr–Sommerfeld-type boundary value problem is derived and solved by using the long-wave series expansion as well as the Chebyshev spectral collocation method for disturbances of arbitrary wavenumbers. The long-wave result reveals the existence of two dominant temporal modes, the so-called surface mode and surfactant mode, where the surface mode propagates faster than the surfactant mode. It is found that the surface mode can be stabilized by introducing an insoluble surfactant at the fluid surface even though the spring stiffness $C_K$ keeps a lower value than its critical value $C_K^*$. But the imposed shear stress exhibits a dual role in the surface mode in two different regimes of spring stiffness $C_K$, i.e. a stabilizing effect when $C_K< C_K^*$ and a destabilizing effect when $C_K>C_K^*$. Further, the surfactant mode becomes more unstable with the increasing values of spring stiffness $C_K$ and damping coefficient $C_D$. On the other hand, the numerical result in the arbitrary wavenumber regime reveals the existence of subcritical instability induced by the surface mode. Furthermore, a different temporal mode, the so-called wall mode, appears in the finite wavenumber regime for special values of $C_K$ and $C_D$, which becomes weaker with increasing values of the wall parameters $C_K$, $C_D$, $C_B$ and $C_T$, but becomes stronger with increasing values of the inclination angle $\theta$ and wall parameter $C_I$. Moreover, the temporal growth rate associated with the wall mode enhances with the increasing value of the Marangoni number but attenuates with the increasing value of imposed shear stress. In addition, another temporal mode, the so-called shear mode, emerges in the finite wavenumber regime when the Reynolds number is high and the inclination angle is small. The unstable region generated by the shear mode magnifies with the increasing value of the imposed shear stress but decays with the increasing value of Marangoni number. Further, the shear mode becomes more unstable as soon as the spring stiffness $C_K$ and damping coefficient $C_D$ increase.

The interaction between the flow above and below a permeable wall is a central topic in the study of porous media. While previous investigations have provided compelling evidence of the strong coupling between the two regions, few studies have quantitatively measured the directionality, i.e. cause-and-effect relations, of this interaction. To shed light on the problem, interface-resolved direct numerical simulations of channel flow over a cylinder array for porosity $\varphi =0.4$–$0.9$ are performed, and the friction Reynolds number of the top smooth wall is controlled to be $Re_{\tau }\approx 180$. We use transfer entropy as a marker to evaluate the causal interaction between the free turbulent flow and the porous medium. Correlation analysis and linear coherence spectra are also leveraged to complete the study. Our results show that the permeability of the porous medium has a profound impact on the intensity, time scale and spatial extent of surface–subsurface interactions. The interaction of the free flow and porous medium is further decomposed into two coupling directions, namely, top-down and bottom-up. For low-porosity cases, top-down and bottom-up interactions are strongly asymmetric, the former being mostly influenced by small near-wall eddies, and the latter reflecting the onset of Kelvin–Helmholtz type instabilities due to the perturbation from the porous medium. As the porosity increases, both top-down and bottom-up interactions are dominated by shear-flow instabilities.

Gas volumes with an equivalent spherical diameter greater than that of the tube in which they rise by buoyancy – so-called Taylor bubbles – assume a characteristic bullet shape and ascend with a velocity that is dependent primarily on the tube diameter, and also on the physical properties of the liquid, but, remarkably, is mostly independent of the gas volume. The requirement of liquid volume conservation suggests a plausible explanation of this paradoxical feature in that the space vacated under the rising bubble must be replenished by the liquid film falling along the bubble surface. It is demonstrated by numerical means that, by limiting the bubble diameter, a cylindrical ‘cage’ of thin vertical rods coaxial with the tube permits the flow rate of this film to increase, with the result that the bubble is able to ascend with a significantly higher velocity than in an empty tube with the same diameter.

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of open-loop control on the linear stability properties of unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i.e. yields the largest first-order (linear) eigenvalue variation. In this study an adjoint method is proposed for computing a second-order (quadratic) sensitivity operator, and applied to the flow past a circular cylinder, controlled with a steady body force or a passive device model. Maps of second-order eigenvalue variations are obtained, without computing controlled base flows and eigenmodes. For finite control amplitudes, the second-order analysis improves the accuracy of the first-order prediction, and informs about its range of validity, and whether it underestimates or overestimates the actual eigenvalue variation. Regions are identified where control has little or no first-order effect but a second-order effect. In the cylinder wake, the effect of a control cylinder tends to be underestimated by the first-order sensitivity, and including second-order effects yields larger regions of flow restabilisation. Second-order effects can be decomposed into two mechanisms: second-order base flow modification, and interaction between first-order modifications of the base flow and eigenmode. Both contribute equally in general in sensitive regions of the cylinder wake. Exploiting the second-order sensitivity operator, the optimal control maximising the total second-order stabilisation is computed via a quadratic eigenvalue problem. The approach is applicable to other types of control (e.g. wall blowing/suction and shape deformation) and other eigenvalue problems (e.g. amplification of time-harmonic perturbations, or resolvent gain, in stable flows).

Thin, viscous liquid films subjected to impact events can deform. Here we investigate free-surface oil-film deformations that arise owing to the build up of air under the impacting and rebouncing of water drops. Using digital holographic microscopy, we measure the three-dimensional surface topography of the deformed film immediately after the drop rebound, with a resolution down to 20 nm. We first discuss how the film is initially deformed during impact, as a function of film thickness, film viscosity and drop impact speed. Subsequently, we describe the slow relaxation process of the deformed film after the rebound. Scaling laws for the broadening of the width and the decay of the amplitude of the perturbations are obtained experimentally and found to be in excellent agreement with the results from a lubrication analysis. We finally arrive at a detailed spatio–temporal description of the oil-film deformations that arise during the impact and rebouncing of water drops.

We calculate the steady acoustic flow – the steady drift of fluid mass or acoustic streaming appearing along the path of an acoustic stimulus – in porous media. In particular, we suggest a mechanism to explain acoustic contributions to mass transport in porous media at geological, unit operation and lab-on-a-chip length scales. We study several cases of steady acoustic flow for a planar acoustic wave whose wavelength is large compared with the pore size. We commence our analysis at the ideal limit of same acoustic properties in the solid and fluid. The effective flow may then be treated intuitively according to the Darcy equation for flow through porous media in addition to a correction for the average azimuth of the pores compared with the acoustic path. We further consider the framework of a rigid porous frame, where the presence of a flow forcing mechanism resulting from the viscous dissipation of the acoustic wave at the solid surface of the pores hinders the intuitive application of the Darcy equation. However, we show that the steady acoustic flow in this case may be written as a quasi-Darcy-type equation. The analysis is conducted by a detailed calculation of the transport of mass through cylindrical pores of similar size but arbitrary azimuth compared with the acoustic path. We consider large, medium and small pore diameter limits relative to the viscous penetration length of the acoustic wave near the pore surface.

We present an analytical study of two-dimensional flow in a wedge driven by a time-dependent surface heat flux as a model problem to understand buoyancy-induced cross-shore flow. Besides the turbulent Prandtl number and the relevant Rayleigh number, both assumed to be of order unity, the solution is seen to depend on the geometry through a parameter $\beta$, representing the bottom slope. An analytic solution is sought in the asymptotic limit $\beta \ll 1$ for a water layer bounded by an adiabatic bottom surface subject to a harmonic heat flux on the upper surface. The analysis reveals that the motion at leading order can be expressed as the sum of a harmonic component and a steady component, the latter driven by nonlinear advection. This steady-streaming motion includes a near-shore vortex with associated recirculating motion that can affect cross-shore transport and dispersion in coastal environments. The analytical solution is compared with numerical solutions of the complete conservation equations for small values of $\beta$. Excellent quantitative agreement is found for values of the Rayleigh number below a critical value at which the periodic solution undergoes a period-doubling bifurcation, leading to the establishment of thermal-instability cells that dominate the offshore flow dynamics, while the near-shore dynamics remains well described by the analytical solution. The analysis illustrates that a periodic heat input that leads to a vertically inhomogeneous temperature distribution can result in residual motion, net heat fluxes and persistent temperature structure in the cross-shore direction.

Turbulence is investigated in the lee of an open-cell metal foam layer. In contrast to canonical grids, metal foams are locally irregular but statistically isotropic. The solid matrix is characterised by two lengths, the ligament thickness $d_f$ and the pore diameter $d_p$. A direct numerical simulation is conducted on a realistic metal foam geometry for which $d_f/d_p = 0.14$ and the porous layer thickness is five times the pore diameter. The Reynolds number based on the pore size is ${\textit {Re}}_{d_p} = 4000$, corresponding to a Taylor-scale Reynolds number ${\textit {Re}}_\lambda \approx 80$. Closer to the foam than two pore diameters, the pressure and turbulent transports of turbulent kinetic energy are non-negligible. In the same region, ${\textit {Re}}_\lambda$ undergoes a steep decrease whereas the dissipation coefficient $C_{\epsilon }$ increases like ${\textit {Re}}_\lambda ^{-1}$. At larger distances from the porous layer, the classical grid turbulence situation is recovered, where the mean advection of turbulent kinetic energy equals dissipation. This entails a power-law decay of turbulent quantities and characteristic lengths. The decaying exponents of integral, Taylor and Kolmogorov scales are close to one-half, indicating that the turbulence simulated here differs from Saffman turbulence. Analysis of the scaling exponents of structure functions and the decorrelation length of dissipation reveals that small-scale fluctuations are weakly intermittent.

This study gives insights into the interfacial instability of water droplets through a combination of laboratory experiments, numerical simulations and analytical modelling. An experiment is conducted in a narrow gap between two plates to model the two-dimensional cylindrical geometry, and a pulsed laser beam is focused inside a water droplet to generate a cavitation bubble. Three distinct characteristics of droplet deformation can be observed: (i) splashing; (ii) ventilating; and (iii) a stable state. In addition, an analytical model considering the Rayleigh–Taylor instability and bubble oscillation is developed based on the assumption that fluid is inviscid and incompressible. The analytical model is solved to obtain a phase diagram describing three distinct phenomena. Two dimensionless parameters, $\hat {\eta }_{ins}$ and $\hat {\eta }_{sta}$, are used to determine the boundaries between different regimes. The parameter $\hat {\eta }_{ins}$ is defined by the ratio of the perturbation amplitude to the difference between the droplet and bubble radii, whereas the other parameter $\hat {\eta }_{sta}$ is defined by the ratio of the perturbation amplitude to the initial droplet radius. Interfacial instability is induced when the perturbed droplet surface penetrates the bubble boundary, namely, $\rvert \hat {\eta }_{ins} \rvert \geq 1$. Splashing and ventilating phenomena occur for $\hat {\eta }_{ins}\geq 1$ and $\hat {\eta }_{ins}\leq -1$, respectively. A stable state occurs when droplet fragmentation does not appear despite small-amplitude perturbations for $\hat {\eta }_{sta}\leq 0.1$. There is a transition zone between the ventilating and stable state, which is bounded by $\hat {\eta }_{ins} = -1$ and $\hat {\eta }_{sta} = 0.1$. Finally, the phase diagram is verified by the experimental and numerical results.

This paper documents and discusses the structure and Reynolds number scaling of the viscous sublayer in front of a cylinder–wall junction. The data were obtained by large-eddy simulation and particle-image velocimetry in an open channel at cylinder Reynolds numbers of $Re_D=20\ 000$, $39\ 000$ and $78\ 000$. We distinguish between outer and inner flow regions. The outer region covers the downflow, the horseshoe vortex and an upstream-directed near-wall jet in front of the cylinder. When normalized with the bulk velocity and the cylinder diameter, the dynamics of the outer flow depends only weakly on the Reynolds number in the investigated range. The inner region is the thin laminar sublayer developing along the bottom wall under the near-wall jet. In the region of the maximum wall shear stress, the amplitude of the friction coefficient and the inner layer thickness both scale with the inverse of the square root of the cylinder Reynolds number. The velocity profiles in the inner layer can be approximated well by Falkner–Skan profiles, scaled by the thickness of the inner layer and the velocity at the interface between the inner and outer layers. Even when the pressure gradient parameter of the Falkner–Skan profiles was estimated by outer flow variables, a good match between velocity profiles in the inner layer and the corresponding Falkner–Skan solutions is observed in the region of maximal wall shear stress. In the whole region of the upstream directed wall jet, the wall shear stress can be estimated from these Falkner–Skan profiles with an accuracy between $10\,\%$ and $20\,\%$.

We present a fully analytical solution for the natural oscillation of an inviscid sessile drop with small Bond number (surface tension dominates gravity) and a fixed contact line on a flat horizontal plate. The governing equations are expressed in terms of the toroidal coordinate system which yields solutions involving hypergeometric functions. Resonant frequencies are identified for zonal, sectoral and tesseral vibration modes. The predictions show excellent agreement with experimental data reported in the literature, particularly for flatter drops (lower $\theta _{c}$, but not so low as to incur significant viscous dissipation) and higher modes of vibration.

The stability of the boundary layer generated by the harmonic oscillations of a plate in its own plane in a fluid otherwise at rest (Stokes boundary layer) is investigated by considering the time development of perturbations of small amplitude and introducing a momentary criterion of instability. The temporal scale of the perturbations is assumed to be much smaller than the period of the plate oscillations because transition takes place at values of the Reynolds number much larger than one. The results confirm that the Stokes boundary layer is linearly unstable when the Reynolds number is larger than a first critical value $R_{\delta ,c1}$ equal to $85$, which is almost coincident with that determined by Von Kerczek & Davis (J. Fluid Mech., vol. 62, issue 4, 1974, 753–773) for a Stokes boundary layer in a fluid domain which is bounded by a second fixed plate at a distance $h^{*}$ from the oscillating one. For values of the Reynolds number close to $R_{\delta ,c1}$, the instability is restricted to phases close to the inversion of the plate velocity. When the Reynolds number becomes larger than a second threshold value $R_{\delta ,c2}$ close to $200$, the instability rapidly pervades a large part of the cycle. However, only when the Reynolds number becomes larger than a third critical value $R_{\delta ,c3}$ equal to $850$, is the instability present during the whole cycle. Heuristically, these three critical values of the Reynolds number can be associated with the transition from the laminar regime to the disturbed laminar, the intermittently turbulent and fully turbulent regimes.

Wall roughness induces extra drag in wall-bounded turbulent flows. Mapping any given roughness geometry to its fluid dynamic behaviour has been hampered by the lack of accurate and direct measurements of skin-friction drag. Here, the Taylor–Couette (TC) system provides an opportunity as it is a closed system and allows direct and reliable measurement of the skin-friction. However, the wall curvature potentially complicates the connection between the wall friction and the wall roughness. Here, we investigate a highly turbulent TC flow, with a hydrodynamically fully rough, rotating inner cylinder, while the outer cylinder is kept smooth and stationary. We carry out particle image velocimetry (PIV) measurements in the Twente Turbulent Taylor–Couette (T3C) facility with Reynolds numbers in the range of $4.6\times 10^5 < Re_i < 1.77\times 10^6$. From these we find, while taking into account the influence of the curved walls on the turbulence, that the observed effects of a hydrodynamically fully rough surface are similar for TC turbulence and flat-plate turbulent boundary layer flows (BL). Hence, the equivalent sand grain height ks, that characterizes the drag properties of a rough surface, is similar for both flow geometries. Next, we obtain the dependence of the torque (skin-friction drag) on the Reynolds number for a given wall roughness, characterized by ks, and find agreement with the same results derived from PIV measurements within $5\,\%$. Our findings demonstrate that global torque measurements in the TC facility could be well suited to reliably deduce wall-drag properties for any rough surface.

Effects of fast-propagating water waves on the overlying wind are investigated using simulation and theoretical analysis. By performing a large eddy simulation (LES) of turbulent wind over water waves with high wave age, we observe that the perturbation to wind velocity and pressure by the waves, or the wave-induced airflow, is mainly induced by the vertical movement of the wave surface. We perform scaling analysis to show that the turbulent stress effects on fast wave-induced airflow are negligible. Moreover, we find that the curvilinear model developed for opposing wave effects on wind by Cao et al. (J. Fluid Mech., vol. 901, 2020, p. A27) provides predictions that agree well with the present LES results of wind following fast waves. Our analyses of the results indicate that the fast wave-induced airflow is a quasilinear process. To elucidate the mechanisms for fast wave effects, we split the curvilinear model into two equations corresponding to wave kinematics and forcing by wave elevation, respectively. Using these equations, we illustrate that the vertical component of wave orbital velocity induces a strong airflow perturbation, which produces the dominant components of fast wave-induced airflow and determines its overall spatial structure. Furthermore, we discover that the weak components of fast wave-induced airflow are forced by the dominant components via viscous stress and by the forcing induced by wave elevation, and generate the form drag on the wave surface.

An analytic estimate of the lower bounds on zonal enstrophy has been studied for the beta-plane model of two-dimensional barotropic flow. The estimate provides exact lower bounds on the zonal enstrophy, which hence must be satisfied regardless of the dynamics. The energy, impulse, circulation as well as the total enstrophy are invoked as constraints for the minimization of the zonal enstrophy. The corresponding variational principle has an unusual mathematical structure (primarily because the target functional is not a coercive form), by which the constraints work out in an interesting way. A discrete set of zonal enstrophy levels is generated by the energy constraint; each level is specified by an eigenvalue that represents the meridional mode number of zonal flow. However, the value itself of the zonal enstrophy level is a function of only impulse and circulation, being independent of the energy (and total enstrophy). Instead, the energy works in selecting the ‘level’ (eigenvalue) of the relaxed state. The relaxation occurs by emitting small-scale wavy enstrophy, and continues as far as the nonlinear effect, scaled by the energy, can create wavy enstrophy. Comparison to numerical simulations shows that the theory gives a consistent estimate of the zonal enstrophy in the relaxed state.

Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter $C$, our direct numerical simulations show that shear-driven turbulence may either be completely laminarised or it transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, which in isothermal pipe flow has recently been linked to complete suppression of turbulence (Kühnen et al., Nat. Phys., vol. 14, 2018, pp. 386–390), and the flattened laminar base profile has enhanced nonlinear stability (Marensi et al., J. Fluid Mech., vol. 863, 2019, pp. 50–875). In agreement with these findings, the nonlinear lower-branch travelling-wave solution analysed here, which is believed to mediate transition to turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. A linear instability of the laminar base flow is responsible for the appearance of the relatively quiescent convection driven state for $C\gtrsim 4$ across the range of Reynolds numbers considered. In the suppression of turbulence, however, i.e. in the transition from turbulence, we find clearer association with the analysis of He et al. (J. Fluid Mech., vol. 809, 2016, pp. 31–71) than with the above dynamical systems approach, which describes better the transition to turbulence. The laminarisation criterion He et al. propose, based on an apparent Reynolds number of the flow as measured by its driving pressure gradient, is found to capture the critical $C=C_{cr}(Re)$ above which the flow will be laminarised or switch to the convection-driven type. Our analysis suggests that it is the weakened rolls, rather than the streaks, which appear to be critical for laminarisation.

We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameters are the Péclet number $Pe$, which quantifies the ratio of the solutal advection rate to the diffusion rate, and the Schmidt number $Sc$, which is the ratio of viscosity and diffusivity. First, we study the diffusiophoretic flow on a catalytic plane in two dimensions. From a linear stability analysis, we obtain that for $Pe$ larger than $8{\rm \pi}$ mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger $Pe$, nonlinear terms become important. For $Pe > 16{\rm \pi}$, multiple concentration plumes are emitted from the catalytic plane, which eventually merge into a single larger one. When $Pe$ is even larger ($Pe \gtrsim 603$ for Schmidt number $Sc=1$), there are continuous emissions and merging events of the concentration plumes. The newly found flow states have different flow structures for different $Sc$: for $Sc\geqslant 1$, we observe the chaotic emission of plumes, but the fluctuations of concentration are only present in the region near the catalytic plane. In contrast, for $Sc<1$, chaotic flow motion occurs also in the bulk. In the second part of the paper, we conduct three-dimensional simulations for spherical catalytic particles, and beyond a critical Péclet number again find continuous plume emission and plume merging, now leading to a chaotic motion of the phoretic particle. Our results thus help us to understand the experimentally observed chaotic motion of catalytic particles in the high $Pe$ regime.

This study is inspired by the velvety structures on an owl's upper wing surface. Anechoic wind tunnel experiments were conducted to study the effect of the velvety structures on trailing edge noise as well as the boundary layer flow of a flat plate model. The tests were conducted in The Hong Kong University of Science and Technology low-speed wind tunnel, ultra-quiet noise injection test and evaluation device (UNITED). It was found that the trailing edge noise spectra are significantly modified by the velvety structures. In general, the velvety structures increase the low-frequency noise below a cross-over Strouhal number $St_c$ but reduce the spectral level at higher frequencies. The velvety surface also changes the boundary layer characteristics in terms of the boundary layer thickness, non-dimensional velocity distribution and turbulence distribution. Vortex shedding is suppressed by the velvety coating despite the blunt trailing edge. An analytic model is proposed for the trailing edge noise of a flat plate, including the effect of finite trailing edge thickness and velvety structures on the flat plate surface. The model uses the near wake distribution of the mean and fluctuating velocities in the streamwise direction as the input. The predictions, which require no empirical corrections, match well with the experiments for both the baseline and velvet-coated configurations. With a detailed non-dimensional analysis, this study proposes a potential aeroacoustic function of velvet structures, i.e. noise control through manipulation of boundary layer statistics.