Discoveries of the last decade increasingly support the idea that by flowing through and around the brain, cerebrospinal fluid and other water-like fluids constitute a distinct transport system, important for removing metabolic waste from the brain and relevant to brain injuries. This paper reviews one team’s recent studies of brain cerebrospinal fluid flow. We consider the characteristics of flows and the spaces through which they pass, flow drivers, and application to drug delivery and stroke.

High-precision experimental and numerical data reveal that the power-law scaling (Nu $\sim$ Ra${}^{\gamma }$) of heat transport by geostrophic convection depends strongly on the fluid domain aspect ratio. Contrary to general belief, the data show that the very steep power-law scaling near onset ($\gamma \ge 3$), does not exist in realistic experimental systems, owing to enhanced heat transfer by boundary flows formed near the lateral boundary. These results imply that the scaling relationship of heat transport measured in rotating convection cells with finite aspect ratio cannot be extrapolated to most large-scale, laterally unbounded, geophysical and astrophysical flows.

Pressure-driven flow experiments demonstrate that spherical particles in dilute polymer solutions are focused on the midline and/or the diagonal in the channel cross-section, with details set by the polymer concentration. Numerical simulations based on the FENE-P constitutive model are then used to understand the variation of the focusing position as a function of the Weissenberg number.

We examine the connection between the physiology and wavy kinematics of carangiform swimmers, such as Jack, Tuna, and Sunfish. Using high-fidelity numerical simulations for flows over Jack Fish models obtained through reconstruction of high-speed images of real natural swimmers, it was revealed that undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk.

Most carnivorous mammals (e.g., cats and dogs) lap water with their tongues to drink water at high frequencies by creating a liquid column out of a bath. Presumably, the animals bite just before the pinch-off time of the water column to maximize the water intake. Such a pinch-off phenomenon in the liquid column can be described as the acceleration-induced (i.e., unsteady) inertia balances with the capillary force.

Non-Newtonian fluids have a shear-rate dependent viscosity that is difficult to measure in experiments. We present a physics-informed neural networks (PINN) approach for learning the viscosity using indirect measurements (such as velocity and pressure) subject to the momentum conservation and continuity equations constraints. We use the PINN approach to estimate viscosity of polymer melts and suspensions of particles using velocity measurements from two-dimensional shear flow simulations. The PINN-inferred viscosity models agree with empirical models for shear rates with large absolute values but deviate for shear rates near zero where the empirical models have an unphysical singularity.

We demonstrate a heat transfer (HT) mechanism based on the relocation of an inhomogeneous fluid under acoustic fields. The proposed HT mechanism is studied under gravity and microgravity conditions. When differentially heated fluid is subjected to ultrasonic waves perpendicular to the HT direction, HT is found to be enhanced up to one order. Depending on acoustic properties, different flow patterns are observed for different fluids. A modified Rayleigh number is proposed for HT characterization that accounts for both gravity and acoustic effects. Furthermore, suppression of natural convection HT is observed when acoustic waves are applied parallel to the HT direction.

A three-dimensional unstable oscillatory instability is found for a downward flow of liquid metal in a vertical duct under strong wall heating and a transverse magnetic field. The unstable oscillatory mode first occurs at the specific flow structure which has an upward reverse flow near the heating wall and a downward flow near the opposite wall. The existence of an inflection point is the key instability mechanism of the three-dimensional oscillatory mode which may be regarded as an alternative physical explanation of the high-amplitude, low-frequency pulsations of temperature in experiments and related numerical simulations.

The permeating solvent flux across a lipid bilayer membrane depends on both mechanical and osmotic stresses. In the absence of osmolarity, we use numerical simulations to show that the mechanically induced semipermeability (albeit small) can alter the equilibrium shape of a relaxing vesicle over long timescales, or the hydrodynamics of a vesicle going through the strong confinement of a narrow channel. We further quantify the role of membrane tension and bending on the permeating solvent flux.

We analytically study the motion and deformation of an eccentric compound drop subject to an externally imposed temperature gradient and suspended in a Poiseuille flow, using a bispherical coordinate system. The temperature gradient alters surface tensions at the drop interfaces and triggers strong Marangoni flows, altering the drop dynamics. While a positive temperature gradient speeds up both drops, a negative gradient can potentially lead to a stable equilibrium where both drops move with the same velocity. The Marangoni effect also enhances deformation, particularly in the inner drop, which may take either a prolate or an oblate shape.

Path instability of a millimetric spheroidal bubble in isotropic turbulence is investigated by direct numerical simulation combined with an immersed boundary method. The zigzag frequency and the degree of obliquity of the bubble are enhanced with the strength of the background turbulence.

Evaporating sessile droplets interact with neighboring droplets via their vapor fields, resulting in nonaxisymmetric evaporative fluxes from their surfaces. One of the consequences of this asymmetry is that, unlike the uniform deposits left at the contact lines of isolated droplets, the deposits left at the contact lines of droplets with neighbors are, in general, nonuniform. In this work we develop a theoretical model for the contact-line deposits from multiple evaporating droplets, and find its predictions for a pair of identical droplets to be in excellent agreement with recent experimental results.

Transport mechanisms inside a drying water droplet are studied by a comprehensive model that accounts for all pertinent physics in liquid and gas phases both with and without thermocapillarity. Without thermocapillarity, a single Rayleigh cell drives convection inside the droplet at higher contact angles. With decreasing contact angle, the Rayleigh cell gets smaller and is replaced by the radial flow through a transition stage, where the rotating cell and radial flow coexist. Both thermocapillarity and buoyancy-driven drying processes end with a radial flow, which creates the well-known coffee-ring effect, but it starts at a much earlier phase of droplet lifetime for buoyancy-driven drying.

We develop a simplified nonlinear model for the dynamics of a highly wetting sessile droplet under an alternating (AC) electrostatic field. The model is suitable for weakly conducting fluids with charges confined on the interface, and reproduces the perfect conductor and dielectric droplet limits. The effect of Maxwell stress on droplet shape deformation (DSD) and contact line motion (CLM) are of particular interest. We show the emergence of a favorable forcing frequency which leads to maximum amplitude in DSD and CLM, a consequence of competition between forcing and wetting timescales. Further, the effect of different fluid electromechanical properties on DSD and CLM are investigated.

We present results from the first experimental realization of a two-dimensional confined countercurrent shear layer driven by momentum flows, without the use of suction. Distinct peaks are observed in the frequency spectrum of velocity fluctuations, suggesting the presence of global instabilities. The variation of these frequencies with injected mass flow rate is predicted reasonably well by a spatiotemporal linear stability analysis of local velocity profiles, which checks for the presence of absolute instability, and suggests that confinement destabilizes the shear layer over a broad range of ratio of shear layer thickness to channel width.

The dynamics of molecular mixing and the energy transfer process in the Rayleigh-Taylor instability (RTI) are studied through the collection of simultaneous velocity-density measurements using particle image velocimetry (PIV) and laser induced fluorescence (LIF). Statistically stationary experiments are performed in a convective-type gas tunnel facility which allows long experimental times and enables collection of statistically important turbulence data. The data and analyses presented in this paper are expected to help validate variable-density turbulence models and further our understanding of instability-driven flows.

Complex surfactant-laden interfaces exhibit surface rheological stresses when deforming against themselves, which in turn affects the flow and stability of the adjacent bulk fluids. We investigate, for the first time, the impact of interfacial rheology on the Saffman-Taylor or viscous fingering problem and demonstrate the stabilizing role of surface viscosity. We show that surface viscosity slows the growth of unstable protrusions, resulting in thicker fingers. We use these insights to highlight the quantitative changes that occur when a typical surface-viscous surfactant is present in a multiphase fluid displacement problem.

This study provides distinct and complementary information regarding laminar flow through and around porous bluff bodies. For low permeable cases, the recirculating wake behind a thinner disk is longer than that behind a thicker disk; while the opposite trend is observed for high permeable cases. The bifurcation diagrams for wake-existence can be collapsed on roughly the same curve when varying with Darcy number (Da) modified by the aspect ratio, which are also observed for the drag coefficient and the flow rate at the rear surface of the disk. The aspect ratio does not have large effects on the vorticity accumulation and the vorticity decay rate for fixed Reynolds number and Da.

Exact trajectoires of microswimmers under flow are determined analytically exhibiting intriguing patterns such as a spherical helix.

Hydrodynamic interactions are important in biophysics because they influence the collective behaviour of microorganisms and active particles, and also play a key role in the emergence of swimming gaits. We determine the hydrodynamic interactions between slender filaments by means of asymptotic calculations and numerical simulations, for the case when two filaments are separated by a distance greater than their contour length (d > L). We then show how our theory explains the collective dynamics of two rigid helices rotating side-by-side.

The hydrodynamic flow generated between a biorthogonally stretched membrane and a steadily rotating flow is shown to be an exact self-similar solution to the three-dimensional Navier-Stokes equations. Identifying such exact solutions is significant because these solutions often give illuminating insight into more complex flows. Dual (and in some cases four) solutions are identified for a given ratio of stretching rates and far-field rotation rate, and the stability of these solutions is examined.

We study the biphasic co-flow through an expansion (or contraction) of the shallow (Hele-Shaw) microchannel. Assuming gentle streamwise variation of the flow, we derive the 3rd-order nonlinear differential equation governing the steady-state shape of the interface separating the two fluids. The interfacial profiles obtained by integrating this nonlinear equation are further compared to numerical solution of the two-dimensional free-boundary problem and experimental results. The amplitude of the capillary ridge emerging upstream from a sudden expansion and leading to narrowing of the thread of the inner phase is substantial, however, not large enough to trigger instability and breakup.

The small-scale flow topologies in a moderately dense (gas-particle) turbulent fluidization have been investigated using highly-resolved Eulerian two-fluid model simulations. Enhanced contraction of focal (enstrophy) and nodal (strain) gas phase structures are found as a result of the solid particles presence. The gas structures, thereby, revealed a tendency towards boundary-layer-like turbulence. In the solid phase, the focal topologies are arranged in elongated vortical tubes corresponding to dense clusters, which in turn induce a pseudo-turbulence on the gas phase.

Can a propeller be isotropic? Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, but there are no published measurements on his particle. We 3D-printed his particle and unexpectedly found no measurable translation-rotation coupling. We explain these results by demonstrating theoretically and computationally that Kelvin’s proposed coupling exists, but it is small since it is only due to a weak breaking of a symmetry of non-interacting vanes in Stokes flow.

The effect of geometrical confinement on Rayleigh-Taylor mixing in porous media is investigated by means of numerical simulations. We find a dimensional transition from three-dimensional to two-dimensional phenomenology when the density plumes become larger than the confining scale. In the two-dimensional regime we observe a faster mixing process and a larger value of the density Nusselt number.

Shear flows can form spontaneously in two-dimensional (2D) simulations of convection. These flows disperse convective plumes and decrease vertical transport. What is the physics of these flows? Can they be avoided in 2D? It was previously shown that increasing the simulation aspect ratio can prevent the onset of shear flows. With simulations of penetrative convection we explore a range of aspect ratios. We find that small shear perturbations can lead to the formation of strong shear flows by taking energy from convective motions, but the perturbations are suppressed in domains of large aspect ratio. This could allow 2D studies of convection at a lower computational cost than 3D simulations.

We investigate the significance of turbulent kinetic energy (TKE, $k$) and its variability in the atmospheric surface layer (ASL), needed in many applications. The statistics of $k$ around its mean state is studied using the probability density function $p(k)$ for ASL flows with significant buoyancy forcing. A nonlinear Langevin equation that preserves $p(k)$ but allows linear relaxation of $k$ to its mean state is suggested and tested using multiple ASL data sets that span various stabilities and surface roughness conditions. Model parameters for the proposed Langevin equation are derived from similarity theory, reproducing measured $p(k)$ with minimal Kullback-Leibler divergence.

We derive a logarithmic law for the third-order streamwise structure function in the logarithmic layer of a boundary layer. The derivation is based on Townsend’s hypothesis and the Navier-Stokes equation. In addition to the logarithmic law, we get the Townsend-Perry constant via asymptotic matching. Both the scaling and the constant agree well with high Reynolds number data.

Modeling of turbulent flows remains a very challenging unsolved problem. Based on symmetries of the fluid equations we propose closure equations expressing the Reynolds stress as a quadratic nonlocal functional of the time averaged velocity field only, contrary to RANS models based upon algebraic handling of the fluid equations which lead to complex nonlinear partial differential equations. We test our model on a mixing layer behind a splitter plate in the limit of infinite Reynolds number. We predict the angular spreading of the turbulent domain as a function of the velocity difference, which has not, to our knowledge, been done with other turbulence models in three-dimensional geometry.

Discretizations with inhomogeneous resolution affect large-eddy simulations (LES) through the commutator of the filtering and differentiation operators. We employ a multiscale asymptotic analysis to investigate the statistical characteristics of this commutator, which can serve as a target for commutation models. Further, we demonstrate how the neglect of this commutator manifests numerically, drawing a connection between the so-called commutation error and the dispersion relation of the underlying numerics. A modeling approach for the commutator is proposed that is based on the numerical properties of the LES evolution equation.

Rectangular propulsion nozzles have advantages over circular nozzles, including easier thrust-vectoring and air-frame-integration. Jet noise is easier to study with circular jets (CJ), however, due to azimuthal homogeneity, which, together with low-rank acoustic dynamics enables simpler acoustic models. Using Large Eddy Simulations of rectangular jets (RJ) of various aspect ratios we show that acoustic fluctuation components exhibit comparably rapid convergence in azimuthal Fourier space even for high aspect ratios. A reduced-order model for RJ that retains near-field acoustic asymmetry can be constructed using only three leading azimuthal modes, but with two additional terms relative to CJ.

Particle imaging velocimetry (PIV) measurements were performed for flow around an oriented cube, to study the wake at various Reynolds numbers. The wake shows numerous small eddies and the velocity profiles have multiple peaks. At higher Reynolds number the streamwise to transverse root mean square velocity ratio $U_{rms}/V_{rms}$ ~ 1 indicates homogenizing and better mixing ability of an oriented cube as compared to a normal cube. Proper orthogonal decomposition (POD) has been used to examine the energy content of the flow and the evolution of coherent structure.

A large database of shock/turbulent boundary layer interactions is compiled to study the separation length scaling over the range of flow conditions including hypersonic interactions. Experimental and computational data of two-dimensional and axisymmetric geometries are included with Mach number from 2 to 10 and ratio of wall to adiabatic recovery temperature from 0.3 to 1.9. A new scaling shows weak interactions collapse by the upstream boundary layer properties, strong interactions do not, and strong separation cases depend on the structure of the downstream flow.

Breakdown to turbulence in wall-bounded flows takes place through sporadic bursts of turbulent spots. Wall-modelled large-eddy simulations (LES) of transition to turbulence must dynamically identify the nascent turbulent regions, track their evolution, and apply the appropriate wall stress within and outside the turbulent/non-turbulent (T-NT) interface. Self-organized maps (SOM), a machine learning classifier, objectively and efficiently captures the T-NT interface. Wall-modeled LES with SOM interface identification predicts both orderly and bypass transition.

The Lagrangian and Eulerian acceleration (LA and EA) properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable stratification are studied with direct numerical simulations. A wavelet-based scale-dependent decomposition of LA and EA is performed. Joint probability density functions of LA and EA show a trend of stronger correlation with increasing stratification strength and at larger turbulent scales. From the Navier–Stokes equation, LA is dominated by the pressure-gradient term, and EA by the nonlinear convection term. From geometrical statistics, the magnitude of EA is larger than LA due to mutual cancellation of the Eulerian and convective acceleration.

We investigated the high intermittency of electrokinetic turbulence with experiments and the She-Leveque model. The intermittency factor 𝛽 can be larger than 1 in electrokinetic turbulence. 𝛽 > 1 indicates that the probability of velocity structures on small scales are determined by all the probabilities of velocity structures on large scales. The investigation finds a route to turbulence through a different but tighter relationship between large and small scale velocity structures.

Using large eddy simulations, we demonstrate that windbreaks can enhance the power production of large wind farms. The optimal windbreak height in a wind farm depends on the balance between the flow speedup and drag effects associated with windbreaks. This result is surprising since it has been argued that the added drag would cancel any benefits resulting from the flow speedup. We find the ideal windbreak height in a wind farm is lower than for an individual turbine. This limits the added drag from the windbreaks and enables their effective use in wind farms.

Vortex reconnection is the process whereby two interacting vortex tubes modify their topology. Earlier studies had focused mostly on a very symmetric configuration, where the singular nature of the problem was manifesting itself by the formation of very intense vortex sheets. As revealed by our numerical study, this is just one of the possible scenarios. When the strong symmetry assumptions of earlier studies are relaxed, and the vortex tubes initially make a small angle to each other, the interactions lead to the development of small-scales of motion, via a cascade process involving the deformation of the vortex cores.

Forcing a cylinder in the streamwise direction with a frequency much lower than the stationary shedding frequency significantly alters wake dynamics. During certain portions of the forcing cycle the wake resembles that of a stationary cylinder, while in others it exhibits strong unsteadiness. Although a range of flow phenomena are observed, it is shown that a novel time scaling framework can be used to relate the forced and unforced systems.

Oscillating foils in synchronized pitch and heave motion can harvest hydrokinetic energy while leaving behind a distinct trail of alternating signed vortices. This work correlates the specific foil kinematics (frequency, pitch, and heave amplitude) with the resulting wake structure by defining three modes within the energy harvesting kinematic regime. Using an array of two tandem oscillating foils, the performance of the trailing foil is modeled by analyzing the wake between the two oscillating foils. The resulting efficiency of the trailing foil is redefined by accounting for the steady and unsteady components of the local flow, yielding a closer match to the single foil efficiency curve.

In rotating flows dominated by inertial waves, triadic resonant interactions, and among them the triadic resonance instability, are the elementary bricks of the energy transfers between spatial scales. We demonstrate theoretically and experimentally that the triadic resonance instability of a plane inertial wave is a three-dimensional process, very efficient at redistributing the energy in the plane normal to rotation. A remarkable consequence of this result is that a turbulent sea of weakly nonlinear inertial waves will have a strong tendency to reach statistical axisymmetry.

Bottom boundary layer instability enhances energy dissipation beneath shoaling internal solitary waves, leading to dissipation length scales of ~100 wavelengths.