The extreme heat fluxes characteristic of hypersonic flows significantly limit the flight envelope of hypersonic vehicles. The role of hydrodynamic instability and the onset of laminar-to-turbulent boundary layer transition is of notable importance. The effect of streaks on the suppression of planar (second Mack mode) instabilities has been previously investigated, but a potentially passive and non-intrusive control method has not been established yet. Recent work shows that streaks can be generated through a spanwise variation in surface temperature. This method exploits the aerothermodynamic characteristics of the flow, and therefore promises to be robust. This work uses direct numerical simulations to determine and quantify the effectiveness of this novel control method in the suppression of second Mack mode instability for a hypersonic boundary layer over a flat plate. The computational analyses cover a range of Mach numbers, 4.8–6, and wall temperature ratios representative of both wind tunnel testing and flight scenarios. Among the range of configurations investigated, the energy of the second Mack mode is reduced by up to approximately 60 % by the steady streaks. The streak wavelength parameter plays a significant role in the stabilisation benefits. For a Mach 6 configuration, for the most linearly amplified second Mack mode disturbance frequency, nearly optimum performance is achieved for a spanwise wavelength of approximately 8–10 times the local boundary layer thickness. These findings open new avenues for controlling hypersonic boundary layers and offer valuable guidance for future experimental campaigns aimed at validating this novel control strategy.

We consider the response of a flexibly mounted square prism placed in inertial-viscoelastic fluid flow with one degree-of-freedom in the cross-flow direction. Under these flow conditions, both inertia and elastic effects are significant. We model the system numerically using a two-way coupling scheme to simulate the interaction between the fluid and the spring–mass system at a Reynolds number of $\textit{Re}=200$ for two mass ratios of $m^* = 2$ and 20, and a Weissenberg number of $\textit{Wi}=2$, across a range of reduced velocities. We demonstrate that introducing fluid elasticity suppresses vortex-induced vibrations of square prisms, consistent with prior findings for circular bluff bodies. However, we find that fluid elasticity amplifies the galloping response in comparison with the response in a Newtonian fluid, leading to larger oscillation amplitudes and the onset of galloping at lower reduced velocities. The predicted enhancement in galloping is significant, particularly at low mass ratios, where no galloping is observed over the wide reduced velocity range tested for Newtonian fluids. We show that this enhancement of galloping is likely the result of the observation that the addition of viscoelasticity increases the magnitude of the rate of change of the transverse flow-induced force on the prism with increasing angle of attack of the incoming flow.

We perform direct numerical simulations of continuously growing broadband surface waves forced by a turbulent atmospheric boundary layer coupled with a developing underwater current. We resolve and analyse the multiscale space–time evolution of the waves by considering the wave spectrum in frequency and wavenumber space and describe the kinematics of nonlinear gravity–capillary waves under a current initially described by a viscous boundary layer and transitioning to turbulence at later times under the wind-wave forcing. The wave speed experiences a scale-dependent Doppler shift, with shorter waves shifted by currents closer to the surface, in agreement with the framework from Stewart & Joy (1974 Deep Sea Res. Oceanogr. Abstracts 21(12), 1039–1049). At low wave slopes, the wave energy concentrates along the linear dispersion relation. When the wave slope is high enough, we observe wave energy located in multiple branches associated with nonlinear bound harmonics travelling at the speed of a carrier mode. These nonlinear branches are well described by a generalized nonlinear dispersion relation that links each harmonic to the effective velocity of the carrier mode to which they are bound, and are found to be Doppler shifted with the carrier mode. The generalized Doppler-shifted nonlinear dispersion relation remains valid as the underwater current becomes turbulent, and the depth-varying mean current profile can be systematically reconstructed from the measured phase velocities from waves at different scales.

We investigate thermal boundary layer (BL) asymmetry in turbulent Rayleigh–Bénard convection (RBC) under both spherical and annular geometries using different BL theories. Unlike planar RBC, the spherical and annular configurations exhibit asymmetric thermal BLs near the inner and outer boundaries due to boundary curvature and non-uniform radial gravity. We generalise three BL frameworks – the Prandtl–Blasius BL model, the steady free-convective model and the fluctuating BL model – and apply them to both geometries. Direct numerical simulations (DNSs), based on the Oberbeck–Boussinesq equations, are performed in three-dimensional spherical RBC and three-dimensional annular RBC for various radius ratios ($\eta$), gravity profiles and also Prandtl numbers ($ \textit{Pr}$), to compare with the predictions of the extended BL models. We find that the BL asymmetries predicted by both the extended steady free-convective BL and the fluctuating BL agree well with DNS results, with the fluctuating BL model providing the best agreement for the mean temperature profiles. A force-balance analysis further shows that this better performance is consistent with the DNS observation that, in the wall-normal direction within the thermal BL, buoyancy is balanced primarily by the pressure-gradient force. This is consistent with the assumption underlying the steady free-convective and fluctuating BL models. Moreover, the fluctuating BL model explicitly accounts for the contribution of turbulent fluctuations to the heat flux, which further improves its agreement with the DNS mean temperature profiles. We derive analytical expressions for the bulk temperature and the thermal BL thickness ratio as functions of the radius ratio and gravity profile across different Prandtl-number regimes. These expressions are obtained by integrating the similarity thermal equation for both the inner and outer BLs using an approximate similarity streamfunction, and by closing the solutions through a heat-flux matching condition. The resulting leading-order expressions obtained from both the steady free-convective and fluctuating BL models are shown to be the same, and they agree well with DNS data. This analytical result provides a robust and practical tool for quantifying BL asymmetry in curved RBC systems.

We consider free-surface flows driven by turbulence beneath the surface, particularly the strong free-surface turbulence (FST) regime, characterised by large Froude number ${\textit {Fr}}^2_T=\varepsilon /u_{\textit{rms}} {g}\,\gtrsim 0.1$. We study the surface layer, where air and water are highly mixed and turbulence modelling is challenging. We develop a definition of the surface-layer thickness $\delta _s$ based on the vertical derivative of intermittency $\gamma$ at the mean free surface $\bar {\eta }$, which, unlike previous definitions, is independent of the tail behaviour of $\gamma$. From direct numerical simulation (DNS) of statistically stationary, horizontally homogeneous strong FST, we show that scaling by $z^* = (z-\bar {\eta })/\delta _s$ collapses $\gamma$ across a wide range of ${\textit {Fr}}^2_T\in [0.03,0.3]$. The distribution more closely follows logistic rather than Gaussian behaviour. From the near-surface turbulence obtained from DNS, we make two general observations. First, we show that for strong FST there is minimal direct effect of the free surface on the isotropy, turbulence kinetic energy $\tilde {k}$ or dissipation rate $\varepsilon$ beneath the surface layer ($z^*\lt -0.5$). Instead, turbulence is only indirectly affected through the flux of kinetic energy into the surface layer. Second, we show that many relevant metrics within the surface layer ($z^*\in [-0.5, 0.5]$) collapse when appropriately scaled by $u_{\textit{rms}}^2=2\tilde {k}/3$ and $\varepsilon$ measured at $z^*=-0.5$. These observations suggest the possibility of a turbulence closure model which avoids direct modelling of $\tilde {k}$ and $\varepsilon$ in the surface layer. Towards this, we show that, across a wide range of ${\textit {Fr}}_T^2$, surface-layer thickness can be predicted by $\delta _s \approx 11.1 \,u_{\textit{rms}}^2 {g}^{-1}$ and energy flux into the surface layer by $W \approx 0.41 \,\varepsilon \delta _s$.

This work employs structured input–output analysis (SIOA) augmented by an eddy viscosity model (SIOA-e) to investigate turbulent flows over rigid and compliant walls. The SIOA-e framework demonstrates the capability in identifying both streamwise and spanwise dominant characteristic wavelengths for rigid wall turbulence. For compliant walls, the SIOA-e method predicts optimal compliant wall parameters associated with positive damping coefficients when minimizing input–output gain for near-wall cycle and very large-scale motions, respectively. The reduction of input–output gain due to the compliant wall is achieved by wall displacement resembling blowing and suction opposite to the wall-normal velocity of dominant streamwise vortices. However, optimized compliant wall parameters based on specific wavenumber–frequency combinations may amplify flow structures for other wavenumber–frequency pairs, potentially leading to an overall drag increase. For example, compliant wall parameters tuned for suppressing large-scale structures can affect both large- and small-scale structures. We also employ input–output analysis to predict convective velocity of wall displacement and pressure for turbulent flow over the compliant wall, and the predicted convective velocity of wall displacement is 0.53 times centreline velocity, which aligns well with recent experimental measurements.