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1. Direct numerical simulation of bubble rising in turbulence

   https://doi.org/10.1017/jfm.2024.763  

   Liu, Zehua; Farsoiya, Palas Kumar; Perrard, Stéphane; Deike, Luc (November 2024, Journal of Fluid Mechanics)

   We describe the rising trajectory of bubbles in isotropic turbulence and quantify the slowdown of the mean rise velocity of bubbles with sizes within the inertial subrange. We perform direct numerical simulations of bubbles, for a wide range of turbulence intensity, bubble inertia and deformability, with systematic comparison with the corresponding quiescent case, with Reynolds number at the Taylor microscale from 38 to 77. Turbulent fluctuations randomise the rising trajectory and cause a reduction of the mean rise velocity$$\tilde {w}_b$$compared with the rise velocity in quiescent flow$$w_b$$. The decrease in mean rise velocity of bubbles$$\tilde {w}_b/w_b$$is shown to be primarily a function of the ratio of the turbulence intensity and the buoyancy forces, described by the Froude number$$Fr=u'/\sqrt {gd}$$, where$$u'$$is the root-mean-square velocity fluctuations,$$g$$is gravity and$$d$$is the bubble diameter. The bubble inertia, characterised by the ratio of inertial to viscous forces (Galileo number), and the bubble deformability, characterised by the ratio of buoyancy forces to surface tension (Bond number), modulate the rise trajectory and velocity in quiescent fluid. The slowdown of these bubbles in the inertial subrange is not due to preferential sampling, as is the case with sub-Kolmogorov bubbles. Instead, it is caused by the nonlinear drag–velocity relationship, where velocity fluctuations lead to an increased average drag. For$$Fr > 0.5$$, we confirm the scaling$$\tilde {w}_b / w_b \propto 1 / Fr$$, as proposed previously by Ruthet al.(J. Fluid Mech., vol. 924, 2021, p. A2), over a wide range of bubble inertia and deformability. 

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2. On the dynamics of aligned inertial particles settling in a quiescent, stratified two-layer medium

   https://doi.org/10.1017/jfm.2024.462  

   Kang, Soohyeon; Best, James L; Chamorro, Leonardo P (June 2024, Journal of Fluid Mechanics)

   We explored the settling dynamics of vertically aligned particles in a quiescent, stratified two-layer fluid using particle tracking velocimetry. Glass spheres of$$d=4\,{\rm mm}$$diameter were released at frequencies of 4, 6 and 8 Hz near the free surface, traversing through an upper ethanol layer ($$H_1$$), whereHis height or layer thickess, varying from$$10d$$to$$40d$$and a lower oil layer. Results reveal pronounced lateral particle motion in the ethanol layer, attributed to a higher Galileo number ($$Ga = 976$$, ratio of buoyancy–gravity to viscous effects), compared with the less active behaviour in the oil layer ($$Ga = 16$$). The ensemble vertical velocity of particles exhibited a minimum just past the density interface, becoming more pronounced with increasing$$H_1$$, and suggesting that enhanced entrainment from ethanol to oil resulted in an additional buoyancy force. This produced distinct patterns of particle acceleration near the density interface, which were marked by significant deceleration, indicating substantial resistance to particle motion. An increased drag coefficient occurred for$$H_1/d = 40$$compared with a single particle settling in oil; drag reduced as the particle-release frequency ($$\,f_p$$) increased, likely due to enhanced particle interactions at closer proximity. Particle pair dispersions, lateral ($$R^2_L$$) and vertical ($$R^2_z$$), were modulated by$$H_1$$, initial separation$$r_0$$and$$f_p$$. The$$R^2_L$$dispersion displayed ballistic scaling initially, Taylor scaling for$$r_0 < H_1$$and Richardson scaling for$$r_0 > H_1$$. In contrast,$$R^2_z$$followed a$$R^2_z \sim t^{5.5}$$scaling under$$r_0 < H_1$$. Both$$R^2_L$$and$$R^2_z$$plateaued at a distance from the interface, depending on$$H_1$$and$$f_p$$. 

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3. Bridging the Rossby number gap in rapidly rotating thermal convection

   https://doi.org/10.1017/jfm.2025.290  

   van_Kan, Adrian; Julien, Keith; Miquel, Benjamin; Knobloch, Edgar (May 2025, Journal of Fluid Mechanics)

   Geophysical and astrophysical fluid flows are typically driven by buoyancy and strongly constrained at large scales by planetary rotation. Rapidly rotating Rayleigh–Bénard convection (RRRBC) provides a paradigm for experiments and direct numerical simulations (DNS) of such flows, but the accessible parameter space remains restricted to moderately fast rotation rates (Ekman numbers$${ {Ek}} \gtrsim 10^{-8}$$), while realistic$${Ek}$$for geo- and astrophysical applications are orders of magnitude smaller. On the other hand, previously derived reduced equations of motion describing the leading-order behaviour in the limit of very rapid rotation ($$ {Ek}\to 0$$) cannot capture finite rotation effects, and the physically most relevant part of parameter space with small but finite$${Ek}$$has remained elusive. Here, we employ the rescaled rapidly rotating incompressible Navier–Stokes equations (RRRiNSE) – a reformulation of the Navier–Stokes–Boussinesq equations informed by the scalings valid for$${Ek}\to 0$$, recently introduced by Julienet al.(2024) – to provide full DNS of RRRBC at unprecedented rotation strengths down to$$ {Ek}=10^{-15}$$and below, revealing the disappearance of cyclone–anticyclone asymmetry at previously unattainable Ekman numbers ($${Ek}\approx 10^{-9}$$). We also identify an overshoot in the heat transport as$${Ek}$$is varied at fixed$$\widetilde { {Ra}} \equiv {Ra}{Ek}^{4/3}$$, where$$Ra$$is the Rayleigh number, associated with dissipation due to ageostrophic motions in the boundary layers. The simulations validate theoretical predictions based on thermal boundary layer theory for RRRBC and show that the solutions of RRRiNSE agree with the reduced equations at very small$${Ek}$$. These results represent a first foray into the vast, largely unexplored parameter space of very rapidly rotating convection rendered accessible by RRRiNSE. 

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4. Nonlinear electrophoretic velocity of a spherical colloidal particle

   https://doi.org/10.1017/jfm.2023.537  

   Cobos, Richard; Khair, Aditya S. (August 2023, Journal of Fluid Mechanics)

   Electrophoresis is the motion of a charged colloidal particle in an electrolyte under an applied electric field. The electrophoretic velocity of a spherical particle depends on the dimensionless electric field strength$$\beta =a^*e^*E_\infty ^*/k_B^*T^*$$, defined as the ratio of the product of the applied electric field magnitude$$E_\infty ^*$$and particle radius$$a^*$$, to the thermal voltage$$k_B^*T^*/e^*$$, where$$k_B^*$$is Boltzmann's constant,$$T^*$$is the absolute temperature, and$$e^*$$is the charge on a proton. In this paper, we develop a spectral element algorithm to compute the electrophoretic velocity of a spherical, rigid, dielectric particle, of fixed dimensionless surface charge density$$\sigma$$over a wide range of$$\beta$$. Here,$$\sigma =(e^*a^*/\epsilon ^*k_B^*T^*)\sigma ^*$$, where$$\sigma ^*$$is the dimensional surface charge density, and$$\epsilon ^*$$is the permittivity of the electrolyte. For moderately charged particles ($$\sigma ={O}(1)$$), the electrophoretic velocity is linear in$$\beta$$when$$\beta \ll 1$$, and its dependence on the ratio of the Debye length ($$1/\kappa ^*$$) to particle radius (denoted by$$\delta =1/(\kappa ^*a^*)$$) agrees with Henry's formula. As$$\beta$$increases, the nonlinear contribution to the electrophoretic velocity becomes prominent, and the onset of this behaviour is$$\delta$$-dependent. For$$\beta \gg 1$$, the electrophoretic velocity again becomes linear in field strength, approaching the Hückel limit of electrophoresis in a dielectric medium, for all$$\delta$$. For highly charged particles ($$\sigma \gg 1$$) in the thin-Debye-layer limit ($$\delta \ll 1$$), our computations are in good agreement with recent experimental and asymptotic results. 

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5. Large monochromatic components in expansive hypergraphs

   https://doi.org/10.1017/S096354832400004X  

   Bal, Deepak; DeBiasio, Louis (March 2024, Combinatorics, Probability and Computing)

   Abstract A result of Gyárfás [12] exactly determines the size of a largest monochromatic component in an arbitrary$$r$$-colouring of the complete$$k$$-uniform hypergraph$$K_n^k$$when$$k\geq 2$$and$$k\in \{r-1,r\}$$. We prove a result which says that if one replaces$$K_n^k$$in Gyárfás’ theorem by any ‘expansive’$$k$$-uniform hypergraph on$$n$$vertices (that is, a$$k$$-uniform hypergraph$$G$$on$$n$$vertices in which$$e(V_1, \ldots, V_k)\gt 0$$for all disjoint sets$$V_1, \ldots, V_k\subseteq V(G)$$with$$|V_i|\gt \alpha$$for all$$i\in [k]$$), then one gets a largest monochromatic component of essentially the same size (within a small error term depending on$$r$$and$$\alpha$$). As corollaries we recover a number of known results about large monochromatic components in random hypergraphs and random Steiner triple systems, often with drastically improved bounds on the error terms. Gyárfás’ result is equivalent to the dual problem of determining the smallest possible maximum degree of an arbitrary$$r$$-partite$$r$$-uniform hypergraph$$H$$with$$n$$edges in which every set of$$k$$edges has a common intersection. In this language, our result says that if one replaces the condition that every set of$$k$$edges has a common intersection with the condition that for every collection of$$k$$disjoint sets$$E_1, \ldots, E_k\subseteq E(H)$$with$$|E_i|\gt \alpha$$, there exists$$(e_1, \ldots, e_k)\in E_1\times \cdots \times E_k$$such that$$e_1\cap \cdots \cap e_k\neq \emptyset$$, then the smallest possible maximum degree of$$H$$is essentially the same (within a small error term depending on$$r$$and$$\alpha$$). We prove our results in this dual setting. 

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