Resolvent analysis provides a framework to predict coherent spatio-temporal structures of the largest linear energy amplification, through a singular value decomposition (SVD) of the resolvent operator, obtained by linearising the Navier–Stokes equations about a known turbulent mean velocity profile. Resolvent analysis utilizes a Fourier decomposition in time, which has thus far limited its application to statistically stationary or time-periodic flows. This work develops a variant of resolvent analysis applicable to time-evolving flows, and proposes a variant that identifies spatio-temporally sparse structures, applicable to either stationary or time-varying mean velocity profiles. Spatio-temporal resolvent analysis is formulated through the incorporation of the temporal dimension to the numerical domain via a discrete time-differentiation operator. Sparsity (which manifests in localisation) is achieved through the addition of an $l_1$-norm penalisation term to the optimisation associated with the SVD. This modified optimisation problem can be formulated as a nonlinear eigenproblem and solved via an inverse power method. We first showcase the implementation of the sparse analysis on a statistically stationary turbulent channel flow, and demonstrate that the sparse variant can identify aspects of the physics not directly evident from standard resolvent analysis. This is followed by applying the sparse space–time formulation on systems that are time varying: a time-periodic turbulent Stokes boundary layer and then a turbulent channel flow with a sudden imposition of a lateral pressure gradient, with the original streamwise pressure gradient unchanged. We present results demonstrating how the sparsity-promoting variant can either change the quantitative structure of the leading space–time modes to increase their sparsity, or identify entirely different linear amplification mechanisms compared with non-sparse resolvent analysis.

This study investigates the influence of surface wave characteristics, specifically wave steepness and directional spreading, on intermittency in deep-water gravity wave turbulence through long-term numerical simulations of three-dimensional potential fully nonlinear periodic gravity waves. We conducted this investigation by estimating the scaling exponent of the surface elevation under different sea state conditions. With our numerical methods, we were able to evaluate the scaling exponents of the structure-function up to 12th order. The observed increased intermittency in directionally narrower sea states and in higher steepness conditions aligns with known effects of quasi-resonant wave–wave interactions and wave breaking. Comparative analyses reveal that both the conventional She–Leveque model and the multifractal models, also used to represent intermittency in wave turbulence of a different nature, exhibit a strong correlation in this study. This observation underscores the universality of intermittency phenomena within wave turbulence.

We study the effect of gas rarefaction on the interaction of small thermodynamic non-uniformities with a finite body. Considering a two-dimensional set-up, the initial system state is modelled as slight perturbations over its uniform density and temperature fields, prescribed in the vicinity of a thin plate. The problem is analysed in the collisionless limit and complemented by direct simulation Monte Carlo computations to cover the entire range of gas rarefaction rates. The high-Knudsen ‘sink-like’ and ‘source-like’ propagation patterns observed in the density- and temperature-driven set-ups, respectively, are discussed, together with the impact of specular (smooth) and diffuse (isothermal) wall reflections. At highly rarefied conditions, the solid body obstructs part of the gas domain, preventing the propagation of acoustic disturbances therein. With decreasing gas rarefaction, the acoustic field penetrates the obscured area via the effect of molecular collisions. Inspecting the near-field description, the propagation of flow disturbances along the plate surface is examined, and the acoustic force on the body is computed. In the thermally excited case, both normal- and shear-force components change sign at late times, attracting the plate towards the initial perturbation location. With reducing gas rarefaction, the shear force diminishes while the normal force sharply increases due to the decrease in signal decay. Finally, we apply the analysis to study the impact of gas rarefaction on acoustic reciprocity. Notably, acoustic reciprocity does not hold at non-continuum conditions over non-specular surfaces, where boundary reflections propagate in the presence of few molecular collisions, insufficient to retain reciprocal symmetry.