Wall-resolved large-eddy simulations of flow over an axisymmetric body of revolution (DARPA SUBOFF bare model) at $ \it{Re}_L=1.1\times 10^6$ are performed to investigate wall pressure fluctuations under the combined effects of transverse curvature and varying pressure gradients. Due to the coexistence of convex and concave streamwise curvatures, the flow in the stern region features alternating zones of favourable and adverse pressure gradients (APGs). The simulation validates experimental findings by Balantrapu et al. (2023, J. Fluid Mech., vol. 960, A28), confirming that in APG-dominant axisymmetric boundary layers without streamwise curvatures, the root mean square wall pressure fluctuations ($p_{w,rms}$) decrease downstream alongside the wall shear stress ($\tau _w$), maintaining a constant ratio $p_{w,rms}/\tau _{w}$. This study further finds that when streamwise curvatures and strong streamwise pressure gradient variations present, this relationship breaks down, suggesting that $\tau _w$ is not the dominant contributor to wall pressure fluctuations. Instead, the local maximum Reynolds shear stress $-\rho \langle u_su_n\rangle _{max }$ emerges as a more robust pressure scaling parameter. Normalising the wall pressure spectra by $-\rho \langle u_su_n\rangle _{max }$ yields better collapse across the entire stern region compared to conventional inner or mixed scaling methods. The magnitude and location of $-\rho \langle u_su_n\rangle _{max }$ significantly influence the spectral levels of wall pressure fluctuations across different frequency bands. As the turbulence intensity and $-\rho \langle u_su_n\rangle _{max }$ shift away from the wall, outer-layer structures – with larger spatial and temporal scales – dominate the coherence of wall pressure fluctuations. This mechanism drives sustained attenuation of high-frequency pressure fluctuations and a simultaneous increase in both the streamwise and transverse correlation lengths of wall pressure fluctuations over the stern region.

Recently, Nagib et al. (Phys. Fluids, vol. 36, no. 7, 2024, 075145) used indicator functions of streamwise normal stress profiles to identify the valid wall-distance and Reynolds number ranges for two models in direct numerical sumulation (DNS) of channel and pipe flows. Since such functions are challenging to construct from experimental data, we propose a simpler, more robust method better suited to experiments. Applied to the two leading models – logarithmic and power-law – for normal stresses in the ‘fitting region’ of wall-bounded flows, this method is tested on prominent experimental data sets in zero-pressure-gradient (ZPG) boundary layers and pipe flows across a wide Reynolds number range ($Re_\tau$). Valid regions for the models appear only for $Re_\tau \gtrapprox 10{\,}000$, with a lower bound $y^+_{in} \sim (Re_\tau )^{0.5}$ and $y^+_{in} \gtrapprox 400$. The upper bound is a fixed fraction of the boundary layer thickness or pipe radius, independent of $Re_\tau$. The power-law model is found to hold over a broader range, up to $Y \approx 0.4$ in ZPG and $Y \approx 0.5$ in pipe flows, compared with the logarithmic trend, which is formulated to be coincident with the classical logarithmic region for the mean flow ($Y \lessapprox 0.15$). A slightly higher exponent ($0.28$) than that of Chen & Sreenivasan (J. Fluid Mech. vol. 933, 2022, A20; J. Fluid Mech. vol. 976, 2023, A21) extends the power-law model’s validity and correcting for outer intermittency in ZPG flows further broadens it. Projections to the near-wall region of both models yield nearly identical predictions of near-wall peak stress across the highest available $Re_\tau$. These findings, alongside results from Monkewitz & Nagib (J. Fluid Mech. vol. 967, 2023, A15) and Baxerras et al. (J. Fluid Mech. vol. 987, 2024, R8), highlight the importance of nonlinear eddy growth and residual viscous effects in wall-bounded flow modelling, informing potential refinements to the logarithmic model, such as those proposed by Deshpande et al. (J. Fluid Mech. vol. 914, 2021, A5).

Rayleigh–Taylor instability (RTI) caused by rarefaction waves not only features variable acceleration but also incorporates time-dependent density, which introduces great challenges in predicting the finger growth behaviours. In this work, we propose a model for predicting the single-mode finger behaviours by extending the Layzer potential-flow framework to account for time-dependent acceleration and density. Relative to the previous models, the present model can evaluate the effect of time-dependent density on finger growth, and can describe the growth behaviours of both bubbles and spikes in rarefaction-driven RTI flows. In addition, the time-dependent curvature of the finger tip as it evolves from its initial value to the quasi-steady value is quantified. To validate the model, rarefaction-tube experiments and numerical simulations are conducted across a wide range of initial conditions. The results show that the present model can accurately capture the amplitude growth and curvature evolution of bubbles and spikes across various density ratios. Moreover, both the present model and experiments demonstrate that the continuous density reduction in rarefaction-driven flows causes larger asymptotic velocities of bubbles and spikes, leading to higher Froude numbers relative to those under constant or time-dependent acceleration.

This study uses the diffusion analogy (Miyake, Sci. Rep., 5R-6, 1965, Univ. of Washington, Seattle, USA) to predict the full growth behaviour of internal boundary layers (IBLs) induced by a roughness change for neutrally – and especially stably – stratified boundary layers with finite thickness. The physics of the diffusion analogy shows that the streamwise variation of the IBL thickness is dictated by $\sigma _w/U$ at the interface, where $\sigma _w$ and $U$ represent wall-normal Reynolds stress and mean streamwise velocity, respectively. The existing variants of the model, summarised by Savelyev & Taylor (2005, Boundary-Layer Meteorol., vol. 115, pp. 1–25), are tailored to IBLs confined within the constant shear stress layer. To extend the applicability of the model to the outer region, we investigate the relation between $\sigma _w/U$ and $U/U_\infty$ in the outer region across varying stratification, where $U_\infty$ is the free-stream velocity. Our analysis reveals that wind tunnel data from a number of facilities collapse onto a master curve when $\sigma _w/U$ is premultiplied by a height-independent parameter, which is a function of the ratio of Monin–Obukhov length to the boundary layer thickness. The scaled $\sigma _w/U$ decreases inversely with $U/U_\infty$ in the surface layer, transitioning to a linear decrease as $U/U_\infty$ increases. The new model, which integrates these findings, along with the effects of streamline displacement and acceleration, captures the complete characteristics of IBLs as they develop within turbulent boundary layers of finite thickness.

Turbulent flows exhibit large intermittent fluctuations from inertial to dissipative scales, characterised by multifractal statistics and breaking the statistical self-similarity. It has recently been proposed that the Navier–Stokes turbulence restores a hidden form of scale invariance in the inertial interval when formulated for a dynamically (nonlinearly) rescaled quasi-Lagrangian velocity field. Here we show that such hidden self-similarity extends to the large-eddy-simulation (LES) approach in computational fluid dynamics (CFD). In particular, we show that classical subgrid-scale models, such as implicit or explicit Smagorinsky closures, respect the hidden scale invariance at all scales – both resolved and subgrid. In the inertial range, they reproduce the hidden scale invariance of Navier–Stokes statistics. These properties are verified very accurately by numerical simulations and, beyond CFD, turn LES into a valuable tool for fundamental turbulence research.

We present a theoretical framework for porous media gravity currents propagating over rigid curvilinear surfaces. By reducing the flow dynamics to low-dimensional models applicable on surfaces where curvature effects are negligible, we demonstrate that, for finite-volume releases, the flow behaviour in both two-dimensional and axisymmetric configurations is primarily governed by the ratio of the released viscous fluid volume to the characteristic volume of the curvilinear surface. Our theoretical predictions are validated using computational fluid dynamics simulations based on a sharp-interface model for macroscopic flow in porous media. In the context of carbon dioxide geological sequestration, our findings suggest that wavy cap rock geometries can enhance trapping capacity compared with traditional flat-surface assumptions, highlighting the importance of incorporating realistic topographic features into subsurface flow models.

In this work, we study the effectiveness of the time-localised principal resolvent forcing mode at actuating the near wall cycle of turbulence. This mode is restricted to a wavelet pulse and computed from a singular value decomposition of the windowed wavelet-based resolvent operator (Ballouz et al. 2024b, J. Fluid Mech. vol. 999, A53) such that it produces the largest amplification via the linearised Navier–Stokes equations. We then inject this time-localised mode into the turbulent minimal flow unit at different intensities, and measure the deviation of the system’s response from the optimal resolvent response mode. Using the most energetic spatial wavenumbers for the minimal flow unit – i.e. constant in the streamwise direction and once-periodic in the spanwise direction – the forcing mode takes the shape of streamwise rolls and produces a response mode in the form of streamwise streaks that transiently grow and decay. Though other works such as Bae et al. (2021 J. Fluid Mech. vol. 914, A3) demonstrate the importance of principal resolvent forcing modes to buffer layer turbulence, none instantaneously track their time-dependent interaction with the turbulence, which is made possible by their formulation in a wavelet basis. For initial times and close to the wall, the turbulent minimal flow unit matches the principal response mode well, but due to nonlinear effects, the response across all forcing intensities decays prematurely with a higher forcing intensity leading to faster energy decay. Nevertheless, the principal resolvent forcing mode does lead to significant energy amplification and is more effective than a randomly generated forcing structure and the second suboptimal resolvent forcing mode at amplifying the near-wall streaks. We compute the nonlinear energy transfer to secondary modes and observe that the breakdown of the actuated mode proceeds similarly across all forcing intensities: in the near-wall region, the induced streak forks into a structure twice-periodic in the spanwise direction; in the outer region, the streak breaks up into a structure that is once-periodic in the streamwise direction. In both regions, spanwise oscillations account for the dominant share of nonlinear energy transfer.