In this study, the effects of antagonistic muscle actuation on the propulsion of a bilaminar-structure fish fin ray were investigated using a two-dimensional computational flow–structure interaction (FSI) model. The structure and material properties of the model were based on the realistic biological data of the sunfish fin. The effect of muscle actuation was modelled using root displacement offset between the two hemitrichs. Parametric FSI simulations were conducted by assuming a sinusoidal function of the offset over a cycle and varying the amplitude and phase difference between the actuations and pitching/plunging motions. The results show that the phase of muscle actuation is a critical factor affecting its effects. Three performance regions can be identified with different phase ranges, including a thrust-favour region, an efficiency-favour region and a thrust-efficiency-unfavour region. In each region, the relationships among the root actuations, fin-ray kinematics, vortex dynamics and resulting performance are studied and discussed. Furthermore, a strong positive correlation between the trailing–leading amplitude ratio and thrust coefficient as well as a negative relationship between the efficiency and angle of attack at the centre of mass of the fin ray are observed.

We investigate the effects of fluid elasticity on the flow forces and the wake structure when a rigid cylinder is placed in a viscoelastic flow and is forced to oscillate sinusoidally in the transverse direction. We consider a two-dimensional, uniform, incompressible flow of viscoelastic fluid at $Re=100$, and use the FENE-P model to represent the viscoelastic fluid. We study how the flow forces and the wake patterns change as the amplitude of oscillations, $A^*$, the frequency of oscillations (inversely proportional to a reduced velocity, $U^*$), the Weissenberg number, $Wi$, the square of maximum polymer extensibility, $L^2$, and the viscosity ratio, $\beta$, change individually. We calculate the lift coefficient in phase with cylinder velocity to determine the range of different system parameters where self-excited oscillations might occur if the cylinder is allowed to oscillate freely. We also study the effect of fluid elasticity on the added mass coefficient as these parameters change. The maximum elastic stress of the fluid occurs in between the vortices that are observed in the wake. We observe a new mode of shedding in the wake of the cylinder: in addition to the primary vortices that are also observed in the Newtonian flows, secondary vortices that are caused entirely by the viscoelasticity of the fluid are observed in between the primary vortices. We also show that, for a constant $Wi$, the strength of the polymeric stresses increases with increasing reduced velocity or with decreasing amplitude of oscillations.

Insights gained from modal analysis are invoked for predictive large-eddy simulation (LES) wall modelling. Specifically, we augment the law of the wall (LoW) by an additional mode based on a one-dimensional proper orthogonal decomposition (POD) applied to a two-dimensional turbulent channel. The constructed wall model contains two modes, i.e. the LoW-based mode and the POD-based mode, and the model matches with the LES at two, instead of one, off-wall locations. To show that the proposed model captures non-equilibrium effects, we perform a priori and a posteriori tests in the context of both equilibrium and non-equilibrium flows. The a priori tests show that the proposed wall model captures extreme wall-shear stress events better than the equilibrium wall model. The model also captures non-equilibrium effects due to adverse pressure gradients. The a posteriori tests show that the wall model captures the rapid decrease and the initial decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients, respectively, both of which are missed by currently available wall models. These results show promise in applying modal analysis for turbulence wall modelling. In particular, the results show that employing multiple modes helps in the modelling of non-equilibrium flows.

Trip-resolved large-eddy simulations of the DARPA SUBOFF are performed to investigate the development of turbulent boundary layers (TBLs) in model-scale studies. The primary consideration of the study is the extent to which the details of tripping affect statistics in large-eddy simulations of complex geometries, which are presently limited to moderate Reynolds number TBLs. Two trip wire configurations are considered, along with a simple numerical trip (wall-normal blowing), which serves as an exemplar of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip wire also induces a large jump in the boundary layer thickness, which affects the way in which the TBL responds to the pressure gradients and streamwise curvature of the hull. The trip-induced turbulence decays along the edge of the TBL as a wake component that sits on top of the underlying TBL structure, which dictates the evolution of the momentum and displacement thicknesses. In contrast, for a trip wire height shorter than the laminar boundary layer thickness, transition is initiated at the reattachment point of the trip-induced recirculation bubble, and the artificial trip reasonably replicates the resolved trip wire behaviour relatively shortly downstream of the trip location. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses and mean momentum balance, which is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, and finally against the 99 % thickness. By this point, the lasting impact of the trip is the offset in boundary layer thickness due to the trip itself, which becomes a diminishing fraction of the total boundary layer thickness as the TBL grows. The importance of tripping the model appendages is also highlighted due to their lower Reynolds numbers and susceptibility to laminar separations.

In this paper, transient granular flows are examined both numerically and experimentally. Simulations are performed using the continuous three-dimensional (3-D) granular model introduced in Daviet & Bertails-Descoubes (ACM Trans. Graph., vol. 35, no. 4, 2016b, p. 102), which represents the granular medium as an inelastic and dilatable continuum subject to the Drucker–Prager yield criterion in the dense regime. One notable feature of this numerical model is to resolve such a non-smooth rheology without any regularisation. We show that this non-smooth model, which relies on a constant friction coefficient, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds, provided the friction coefficient is set to the avalanche angle – and not to the stop angle, as generally done. In order to better characterise the range of validity of the fully plastic rheology in the context of transient frictional flows, we further revisit scaling laws relating the shape of the final collapse deposit to the initial column aspect ratio, and accurately recover established power-law dependences up to aspect ratios of the order of 10. The influence of sidewall friction is then examined through experimental and simulated collapses with varying channel widths. The analysis offers a comprehensive framework for estimating the effective flow thickness in relation to the channel width, thereby challenging previously held assumptions regarding its estimation in the literature. Finally, we discuss the possibility to extend the constant coefficient model with a hysteretic model in order to refine the predictions of the early-stage dynamics of the collapse. This illustrates the potential effects of such phenomenology on transient flows, paving the way to more elaborate analysis.

We study a fifty-year-old problem of fast acoustic streaming, that is, the generation of moderate or large hydrodynamic Reynolds number ($\textit {Re}$) acoustic streaming (or steady flow) by the convection of momentum in an acoustic wave (or another periodic flow), while the latter is simultaneously altered by the former. The intrinsic disparity of length and time scales makes a brute-force solution of the full Navier–Stokes and continuity equations a formidable problem. Circumventing this difficulty, we split the problem into a time-averaged system of equations for the steady flow component and a dynamic system of equations for its quasi-periodic flow counterpart. The latter system of equations is obtained by subtracting the time-averaged Navier–Stokes equation from its original dynamic form, and is rendered a nonlinear wave equation using the continuity equation and an adiabatic connection between density and pressure. The resulting equations are compatible with the theory by Eckart for small $\textit {Re}$ flow, and capture large-$\textit {Re}$ effects. Scaling analysis and a case study show that acoustic streaming is weak and does not contribute to the acoustic wave close to the wave source, relevant to many microfluidic systems. At small $\textit {Re}$, the streaming magnitude is proportional to an inverse Strouhal number, a small quantity in experiments. Moderate and large $\textit {Re}$ render the streaming magnitude comparable to the pre-attenuating periodic flow (or particle velocity of the wave) at approximately a wave attenuation length away from the wave source or further; the wave is altered by the streaming that it generates, and the streaming dominates the flow far from the wave source.

When a saturated brine layer is cooled from above, both a convective temperature front as well as a front of sedimenting salt crystals can form. We employ direct numerical simulations to investigate the evolution and interaction of these two density fronts. Depending on the ratio of the temperature front velocity and the crystal settling velocity, which is governed by a dimensionless parameter in the form of a Rayleigh number, we find that either two separate fronts exist for all times, two initially separate fronts combine into a single front after some time or a single front exists at all times. We furthermore propose approximate scaling laws for the propagation of the thermal and crystal fronts in each regime and compare them with the simulation data, with generally good agreement.

We use the Dyson–Wyld diagrammatic technique to analyse the infinite series for the correlation functions of the velocity in hydrodynamic turbulence. We demonstrate the fundamental role played by the triple correlator of the velocity in determining the entire statistics of the hydrodynamic turbulence. All higher-order correlation functions are expressed through the triple correlator. This is shown through the suggested triangular re-summation of the infinite diagrammatic series for multi-point correlation functions. The triangular re-summation is the next logical step after the Dyson–Wyld line re-summation for the Green's function and the double correlator. In particular, it allows us to explain why the inverse cascade of the two-dimensional hydrodynamic turbulence is close to Gaussian. Since the triple correlator dictates the flux of energy $\varepsilon$ through the scales, we support the Kolmogorov-1941 idea that $\varepsilon$ is one of the main characteristics of hydrodynamic turbulence.

The dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state to predict the flow based on a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live. The latent space is found by a series of nonlinear filtering operations, which are performed by a convolutional autoencoder (CAE). The CAE provides the decomposition in space. Second, we predict the time evolution of the turbulent state in the latent space, which is performed by an echo state network (ESN). The ESN provides the evolution in time. Third, by combining the CAE and the ESN, we obtain an autonomous dynamical system: the CAE-ESN. This is the reduced-order model of the turbulent flow. We test the CAE-ESN on the two-dimensional Kolmogorov flow and the three-dimensional minimal flow unit. We show that the CAE-ESN: (i) finds a latent-space representation of the turbulent flow that has ${\lesssim }1\,\%$ of the degrees of freedom than the physical space; (ii) time-accurately and statistically predicts the flow at different Reynolds numbers; and (iii) takes ${\lesssim }1\,\%$ computational time to predict the flow with respect to solving the governing equations. This work opens possibilities for nonlinear decomposition and reduced-order modelling of turbulent flows from data.

We develop a theoretical model to study (dense) two-dimensional gravity current flow in a laterally extensive porous medium experiencing leakage through a discrete fissure situated along this boundary at some finite distance from the injection point. Our model, which derives from the depth-averaged mass and buoyancy equations in conjunction with Darcy's law, considers dispersive mixing between the gravity current and the surrounding ambient by allowing two different gravity current phases. Thus do we define a bulk phase consisting of fluid whose density is close to that of the source fluid and a dispersed phase consisting of fluid whose density is close to that of the ambient. We characterize the degree of dispersion by estimating, as a function of time, the buoyancy of the dispersed phase and the separation distance between the bulk nose and the dispersed nose. On this basis, it can be shown that the amount of dispersion depends on the flow conditions upstream of the fissure, the fissure permeability and the vertical and horizontal extents of the fissure. We also show that dispersion is larger when the gravity current propagates along an inclined barrier rather than along a horizontal barrier. Model predictions are fitted against numerical simulations. The simulations in question are performed using COMSOL and consider different inclination angles and fissure and upstream flow conditions. Our study is motivated by processes related to underground $\mathrm {H}_2$ storage e.g. an irrecoverable loss of $\mathrm {H}_2$ when it is injected into the cushion gas saturating an otherwise depleted natural gas reservoir.