Existing methods to identify the interfaces separating different regions in turbulent flows, such as turbulent/nonturbulent interfaces, typically rely on subjectively chosen thresholds, often including visual verification that the resulting surface meaningfully separates the different regions. Since machine learning tools are known to help automate such classification tasks, we here propose to use an unsupervised self-organizing map (SOM) machine learning algorithm as an automatic classifier. We use it to separate a boundary layer undergoing bypass transition into two distinct spatial regions, the turbulent boundary layer (TBL) and non-TBL regions, the latter including the laminar portion prior to transition and the outer flow which possibly contains weak free-stream turbulence. Both regions are separated by the turbulent boundary layer interface (TBLI). The data used in this study are from a direct numerical simulation and are available on an open database system. In our analysis of one snapshot in time, every spatial point is characterized by a 16-dimensional vector containing the magnitudes of the components of total and fluctuating velocity, magnitudes of the velocity gradient tensor elements, and the streamwise and wall-normal coordinates, all normalized by their global standard deviation. In an unsupervised fashion, the SOM classifier separates the points into TBL and non-TBL regions, thus identifying the TBLI without the need for user-specified thresholds. Remarkably, it avoids including vortical streaky structures that exist in the laminar portion prior to transition as well as the weak free-stream turbulence in the turbulent boundary layer region. The approach is compared quantitatively with existing methods to determine the TBLI (vorticity magnitude, cross-stream velocity fluctuation). Also, the SOM classifier is cast as a linear hyperplane that separates the two clusters of data points, and the method is tested by finding the TBLI of other snapshots in the transitional boundary layer data set, as well as in a fully turbulent boundary layer with similar levels of free-stream turbulence. Variants in which the approach failed are also summarized.

The motion of wall-bounded drops moving on solid substrates driven by a fully turbulent channel flow is experimentally investigated for four substrates of different wetting properties. An appropriate scaling has been found to describe the dimensionless drop velocity (capillary number) in terms of a dimensionless flow attack velocity, taking into account the surface wetting properties. The derived model agrees very well with the experimental observations.

This paper addresses the interaction of initially antiparallel vortex tubes containing an axial flow that induces a twisting of the vortex lines around the tube axes, using numerical simulations. Vortex tube configurations with both the same and opposite senses of twist—corresponding to the same and opposite signs of kinetic helicity density—are considered. It is found that the topology of the reconnection process is very different between the two cases. For tubes with the same sense of twist, the reconnection is fully three-dimensional (3D): vortex lines reconnect at a finite angle, and 3D vortex null points may be created. Following reconnection the vortex line topology in both bridge and thread structures exhibits a high degree of complexity. For oppositely twisted tubes the reconnection is locally two-dimensional, occurring along vorticity null lines, that in contrast to the untwisted case are not perpendicular to the tube axes. This leads to a break in the symmetry between the two vortex bridges generated during reconnection. For all cases studied, increasing the twist in the vortex tubes leads to a later, faster, and more complete reconnection process.

The motion of small, rigid, nearly neutrally buoyant finite-size particles in a two-sided lid-driven cavity is calculated numerically. The rapid accumulation of particles into coherent structures which is observed experimentally is explained on the basis of single-particle one-way-coupled dynamics. Key is the transfer of the particle from regions of the incompressible flow occupied by chaotic streamlines to regions occupied by regular ones. The particle attractors are caused by lubrication forces which repel the particles from the moving boundaries. This mechanism is independent of particle inertia. Therefore, the particulate structures found represent a class of coherent structures which may be called finite-size coherent structures.

A bubble expanding and collapsing in water near a flat solid boundary is studied numerically. According to current knowledge, it develops a high-speed liquid jet towards the boundary of typically $\sim 100$ m/s. However, the character of jet formation and the jet properties alter strongly when the bubble expands and collapses very close to a solid boundary. In this case, a much thinner and much faster jet of typically $\sim 1000$ m/s is generated. The respective mechanism is demonstrated by solving the Navier-Stokes equations for a model of a laser-induced bubble. The results add substantially to the understanding of the erosion process caused by imploding cavitation bubbles near solid boundaries.

Using volumetric velocity data from a turbulent laboratory water flow and numerical simulations of homogeneous, isotropic turbulence, we present a direct experimental and numerical assessment of Kolmogorov's first refined similarity hypothesis based on three-dimensional measurements of the local energy dissipation rate ${\epsilon }_r$ measured at dissipative scales $r$. We focus on the properties of the stochastic variables $V_L=\mathrm{\Delta }u\left(r\right)/{\left(r{\epsilon }_r\right)}^{1/3}$ and $V_T=\mathrm{\Delta }v\left(r\right)/{\left(r{\epsilon }_r\right)}^{1/3}$, where $\mathrm{\Delta }u\left(r\right)$ and $\mathrm{\Delta }v\left(r\right)$ are longitudinal and transverse velocity increments. Over one order of magnitude of scales $r$ within the dissipative range, the distributions of $V_L$ and $V_T$ from both experiment and simulation collapse when parametrized by a suitably defined local Reynolds number, providing conclusive experimental evidence in support of the first refined similarity hypothesis and its universality.

We study swimming of small spherical particles that regulate fluid flow on their surface by applying tangential squirming strokes. We derive translational and rotational velocities for any given stroke which is not restricted by axial symmetry as assumed usually. The formulation includes inertia of both the fluid and the swimmer, motivated by inertia's relevance for large Volvox colonies. We show that inertial contribution to mean speed comes from dynamic coupling between translation and rotation, which occurs only for strokes that break axial symmetry. Remarkably, this effect enables overcoming the scallop theorem on impossibility of propulsion by time-reversible strokes. We study examples of tangential strokes of an axisymmetric traveling wave and of asymmetric time-reversible flapping. In the latter case, we find that the inertia-driven mean speed is optimized for flapping frequency and the swimmer's size, which fall well within the range of realistic physical values for Volvox colonies. We conjecture that similarly to Paramecia, large Volvox could use time-reversible strokes for inertia-driven swimming coupled with their rotations.

We present measurements of temperature fluctuations in turbulent rotating Rayleigh-Bénard convection. The temperature variance exhibits power-law dependence on the fluid height outside the thermal boundary layers irrespective of the rotating rates. Rotations increase the magnitudes of temperature variance, but reduce the skewness and kurtosis, leading to Gaussian-like temperature distributions. We derive a general theoretical expression for all statistical moments of temperature in terms of the dynamical properties of the thermal plumes, based on the findings that both the amplitude and time width of thermal plumes are log-normally distributed. Our model replicates the statistical properties of the temperature fluctuations and reveals the physical origin of their rotation dependence. Rotations increase the temperature amplitude of thermal plumes by virtue of the Ekman pumping process, but reduce the variations of the plume amplitude in time, presumably through the suppression of turbulent mixing between the plumes and the ambient fluid.

The cessation of a dense granular flow down an inclined plane upon decrease in the angle of inclination is studied using particle-based simulations for the linear and Hertzian particle contact models for ordered and disordered flows. The nature of the flow is examined by progressively decreasing the angle of inclination by fractions of a degree, with the objective of examining the range of angles for which the hard-particle model can be used to describe the flow and the nature of the flow dynamics very close to cessation where the hard-particle approximation fails. For a disordered flow, when the angle inclination exceeds the angle for flow cessation by about $0.5^{\circ }$ for the linear contact model and about $1^{\circ }$ for the Hertzian model, the flow is well described by Bagnold rheology, and the Bagnold coefficients are independent of layer height and the particle stiffness, implying that the flow dynamics is well described by the hard-particle approximation. When the angle of inclination exceeds the angle for flow cessation by less than $0.5^{\circ }$ for the linear contact model and $1^{\circ }$ for the Hertzian contact model, the flow transitions into a layered state consisting of a faster shearing zone of height about 30 particle diameters atop a bottom slowly shearing zone. There are sinusoidal oscillations in the velocity of the center of mass of the flow, and the period of these oscillations is proportional to the characteristic time for particle interactions, indicating that the particle contact time does affect the dynamics of the layered flow. The flow evolution is qualitatively different for an ordered flow. In this case, there is an abrupt transition from a Bagnold flow to a plug flow with sliding at the base when the angle of inclination is decreased by $0.{05}^{\circ }$. There is no discernible intermediate flow regime where the particle contact time becomes relevant. We also examine the deceleration of the flow when the angle of inclination is decreased from a flowing state to a final angle below the cessation angle. The initial decrease in the flow velocity is exponential for both contact models and for all final angles of inclination. This is followed by a more rapid decrease to the static state. The time constant for the initial decrease is significantly higher for an ordered flow in comparison to a disordered flow. The time constant is independent of the contact model and particle stiffness, and increases with height proportional to $h^{3/2}$, as expected for the hard-particle model.

In this paper, we develop a model based on successive linearization to study interactions between different modes in boundary layer flows. Our method consists of two steps. First, we augment the Blasius boundary layer profile with a disturbance field resulting from the linear parabolized stability equations (PSE) to obtain the modified base flow; and, second, we draw on Floquet decomposition to capture the effect of mode interactions on the spatial evolution of flow fluctuations via a sequence of linear progressions. The resulting parabolized Floquet equations (PFE) can be conveniently advanced downstream to examine the interaction between different modes in slowly varying shear flows. We apply our framework to two canonical settings of transition in boundary layers; the H-type transition scenario that is initiated by exponential instabilities, and streamwise elongated laminar streaks that are triggered by the lift-up mechanism. We demonstrate that the PFE capture the growth of various harmonics and provide excellent agreement with the results obtained in direct numerical simulations and in experiments.

This paper addresses three-wave resonant interactions of Rossby-Haurwitz waves in two-dimensional turbulence on a rotating sphere. Zonal modes are often omitted from the “resonant wave set” even when they satisfy the conditions for three-wave resonant interactions, as they do not transfer any energy to other modes in a resonant manner. However, the presence of zonal flows induces phase shifts in other modes, and it is not at all clear that their influence is negligible. Since it is expected that three-wave resonant interactions govern the entire dynamics of turbulence if the rotation rate of the sphere is sufficiently high, by analogy with the theorem regarding three-wave resonant interactions of Rossby waves on a $\beta$ plane with sufficiently large $\beta$ previously proven by Yamada and Yoneda [Physica D 245, 1 (2013)], an appropriate definition of the resonant wave set was determined by comparing the time evolution of several wave sets on a rapidly rotating sphere. It was found that zonal waves of the form $Y_l^{m=0}exp\left(i\omega t\right)$ with odd $l$, where $Y_l^m$ are the spherical harmonics, should be considered for inclusion in the resonant wave set to ensure that the dynamics of the resonant wave set determine the overall dynamics of the turbulence on a rapidly rotating sphere. Consequently, it is suggested that the minimal resonant wave set that must be considered in the discussion of the three-wave interaction of Rossby-Haurwitz waves is the set consisting of nonzonal resonant waves and zonal waves of the form $Y_l^{0}exp\left(i\omega t\right)$ with odd $l$.

When a droplet with a relatively high density falls into a miscible solution with a relatively low density, the droplet breaks up spontaneously. We investigated the number $m$ of breakup in experiments with several density differences $\mathrm{\Delta }\rho$ between two solutions, viscosities $\mu$, and droplet radii $r$. The mode number $m$ has a distribution even under the same experimental conditions. We propose a simple model of mode selection based on the linear Rayleigh-Taylor instability and the growing radius of a vortex ring deformed from the droplet. The model provides the probability distribution $P\left(m\right)$ and a relationship between the nondimensional parameter $G\propto \mathrm{\Delta }\rho g{r}^3/{\mu }^2$ and the average value of $m$, which are consistent with experimental results.

The aim of this work is to shed light by revisiting, from the kernel-wave (KW) perspective, the breakdown of a quasigeostrophic (QG) mixing layer (or vortex strip or filament) in atmosphere under the influence of a background shear. The QG mixing layer is modeled with a family of quasi-Rayleigh velocity profiles in which the potential vorticity (PV) is constant in patches. From the KW perspective, a counterpropagating Rossby wave (CRW) is created at each PV edge, i.e., the edge where a PV jump is located. The important parameters of our study are (i) the vorticity of the uniform shear $m$ and (ii) the Rossby deformation radius $L_d$, which indicates how far the pressure perturbations can vertically propagate. While an adverse shear ($m<0$) stabilizes the system, a favorable shear ($m>0$) strengthens the instability. This is due to how the background shear affects the two uncoupled CRWs by shifting the optimal phase difference towards large (small) wave number when $m<0$ ($m>0$). As a finite $L_d$ is introduced, a general weakening of the instability is noticed, particularly for $m>0$. This is mainly due to the reduced interaction between the two CRWs when $L_d$ is finite. Furthermore, nonlinear pseudospectral simulations in the nominally infinite-Reynolds-number limit were conducted using as the initial base flow the same quasi-Rayleigh profiles analyzed in the linear analysis. The growth of the mixing layer is obstructed by introducing a background shear, especially if adverse, since the vortex pairing, which is the main growth mechanism in mixing layers, is strongly hindered. Interestingly, the most energetic configuration is for $m=0$, which differs from the linear analyses for which the largest growth rates were found for a positive $m$. In the absence of a background shear additional modes are subharmonically triggered by the initial disturbance enhancing the turbulent character of the flow. We also confirm energy spectrum trends for broken-down mixing layers reported in the literature. We interpret the character of mixing-layer breakdown as being a phenomenological hybrid of Kraichnan's [R. H. Kraichnan, Phys. Fluids 10, 1417 (1967)] direct enstrophy cascade picture and the picture of self-similar vortex production.

We study the effect of different forcing functions and of the local gradient Richardson number ${\mathrm{Ri}}_g$ on the vertical transport of Lagrangian tracers in stably stratified turbulence under the Boussinesq approximation and present a wave and continuous-time random-walk model for single- and two-particle vertical dispersion. The model consists of a random superposition of linear waves with their amplitude, based on the observed Lagrangian spectrum of vertical velocity, and a random-walk process to capture overturning that depends on the statistics of ${\mathrm{Ri}}_g$ among other Eulerian quantities. The model is in good agreement with direct numerical simulations of stratified turbulence, where single- and two-particle dispersion differ from the homogeneous and isotropic case. Moreover, the model gives insight into the mixture of linear and nonlinear physics in the problem, as well as on the different processes responsible for vertical turbulent dispersion.

A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres is presented. Their dependence on the Rayleigh number has been found for two pairs of Ekman (E) and small Prandtl (Pr) numbers in the region of parameters where, according to Zhang et al. [J. Fluid Mech. 813, R2 (2017)], the linear stability of the conduction state predicts that they can be preferred at the onset of convection. The bifurcation to periodic torsional solutions is supercritical for sufficiently small $\mathrm{Pr}$. They are not rotating waves, unlike the nonaxisymmetric case. Therefore they have been computed by using continuation methods for periodic orbits. Their stability with respect to axisymmetric perturbations and physical characteristics have been analyzed. It was found that the time- and space-averaged equatorially antisymmetric part of the kinetic energy of the stable orbits splits into equal poloidal and toroidal parts, while the symmetric part is much smaller. Direct numerical simulations for $\mathrm{E}={10}^{-4}$ at higher Rayleigh numbers (Ra) show that this trend is also valid for the nonperiodic flows and that the mean values of the energies remain almost constant with $\mathrm{Ra}$. However, the modulated oscillations bifurcated from the quasiperiodic torsional solutions reach a high amplitude, compared with that of the periodic, increasing slowly and decaying very fast. This repeated behavior is interpreted as trajectories near heteroclinic chains connecting unstable periodic solutions. The torsional flows give rise to a meridional propagation of the kinetic energy near the outer surface and an axial oscillation of the hot nucleus of the metallic fluid sphere.

Macroscopic flow induced by instability is a feature found in both natural phenomena and industrial processes; however, in situ observation of instabilities at an early stage in their formation is rare. In this article, we propose an experimental method for observing the early stages of a Rayleigh-Taylor instability and lock exchange. We successfully used physical gels to form a “static” initial state which is simultaneously “gravitationally” unstable. Fluid instabilities can be observed from the beginning by switching from a static state to a dynamic state by irradiating the system with light. We can also observe flow dynamics under arbitrary boundary conditions using this method. Here we present notable results in the early stages of a Rayleigh-Taylor instability and lock exchange. Our method promises to greatly advance experimental research into many types of instability phenomena, contributing to the elucidation of nonequilibrium phenomena in fluids.

We investigate the hydroelastic waves created by a perturbation moving at constant speed along a thin elastic sheet floating at the surface of deep water. Using a high-resolution cross-correlation imaging technique, we characterize the waves as a function of the perturbation speed, for different sheet thicknesses. The general theoretical expression for the dispersion relation of hydroelastic waves includes three components: gravity, bending, and tension. The bending modulus and the tension in the sheet are independently measured. The experiments represent a direct test of the theory where all components, bending, stretching, and gravity, cannot be neglected. Excellent agreement is found between the experimental data and the theoretical expression.

Laboratory experiments reveal that variations in bottom topography can qualitatively alter the distribution of randomized surface waves. A normally distributed, unidirectional wave field becomes highly skewed and non-Gaussian upon encountering an abrupt depth change. A short distance downstream, wave statistics conform closely to a gamma distribution, affording simple estimates for skewness, kurtosis, and other statistical properties. Importantly, the exponential decay of the gamma distribution is much slower than Gaussian, signifying that extreme events occur more frequently. Under the conditions considered here, the probability of a rogue wave can increase by a factor of 50 or more. We also report on the spectral content of the waves produced in the experiments.

Systematic experiments were conducted to study differences in the threshold flow conditions for initiation of motion of submerged objects (spheres and cylinders) resting on permeable and impermeable beds. The threshold flow conditions were characterized with the Shields parameter, which was estimated with upstream flow velocity measurements obtained with the particle image velocimetry (PIV) technique under conditions of unidirectional, open-channel flow in a laboratory flume. Flow-bed interface geometries were maintained across both permeable and impermeable bed experiments. Plotting the Shields parameter against the ratio of the particle size to bed roughness scale revealed clear differences between permeable and impermeable beds, including a larger Shields parameter value requirement to initiate motion on permeable beds than on impermeable ones, which is connected with the lower lift force on a permeable bed. Neglecting the presence of bed permeability can result in up to half an order of magnitude of variation in critical Shields parameter values. Experimental results also show that greater Shields parameter values are required to initiate the motion of a sphere than for a cylinder with identical diameter for large $L/D$ ratio $(L$ and $D$ are the length and diameter of the cylinder). As the $L/D$ ratio decreases, the cylinder approaches the sphere geometry, and the critical Shields parameter value is similar.