Classical Rayleigh Research Articles

Instability in heated water-porous system

This paper investigates the stability in a heated fluid-porous system. Darcy’s law is used for the flow in the porous medium. Previous studies indicate that the classical Rayleigh–Bénard instability in this flow is independent of the mutual positions of the fluid layer and porous layer. This paper demonstrates that the instability depends on the mutual positions of the fluid layer and porous layer when the liquid density is nonlinearly dependent on temperature. When porous medium is located at the bottom of the system, onset of convection may occur in lower porous layer (pure-porous mode), upper water layer (pure-water mode) or across both layers (porous-water mode). However, onset of convection cannot take place only in the upper porous layer when porous medium is placed at the top of the system. The influence of depth ratio dˆ and the density inversion parameter θM on instability of bilayer system are investigated in detail and dependence of critical modes on parameters are summarized in phase diagrams. In addition, direct numerical simulation is used to analyse the instability mechanism and identify subcritical or supercritical instability for bilayer systems.

Aspect-ratio-dependent heat transport by baroclinic acoustic streaming

Standing acoustic waves have been known to generate Eulerian time-mean ‘streaming’ flows at least since the seminal investigation of Lord Rayleigh in the 1880s. Nevertheless, a recent body of numerical and experimental evidence has shown that inhomogeneities in the ambient density distribution lead to much faster flows than arise in classical Rayleigh streaming. The emergence of these unusually strong flows creates new opportunities to enhance heat transfer in systems in which convective cooling cannot otherwise be easily achieved. To assess this possibility, a theoretical study of acoustic streaming in an ideal gas confined in a rectangular channel with top and bottom walls maintained at fixed but differing temperatures is performed. A two time scale system of equations is utilized to efficiently capture the coupling between the fast acoustic waves and the slowly evolving streaming flow, enabling strongly nonlinear regimes to be accessed. A large suite of numerical simulations is carried out to probe the streaming dynamics, to highlight the critical role played by baroclinically generated wave vorticity and to quantify the additional heat flux induced by the standing acoustic wave. Proper treatment of the two-way coupling between the waves and mean flow is found to be essential for convergence to a self-consistent steady state, and the variation of the resulting acoustically enhanced steady-state heat flux with both the amplitude of the acoustic wave and the $O(1)$ aspect ratio of the channel is documented. For certain parameters, heat fluxes almost two orders of magnitude larger than those realizable by conduction alone can be attained.

Brinkman–Bénard convection in a box with temperature modulation

A bounded porous box saturated with Newtonian fluid and subjected to a sinusoidal temperature gradient has various practical applications, such as solar energy storage, groundwater remediation, food processing, and chemical reactors. We address the generalization of the classical Rayleigh–Bénard convection problem in a horizontal fluid layer in an infinitely large domain heated from below to a finite three-dimensional box. We also look into a more intricate form of the modulated Rayleigh–Bénard problem in which the temperature at the bottom boundary varies sinusoidally. The Rayleigh number quantifies the non-sinusoidal part of the temperature gradient, while the amplitude and frequency of modulation describe the sinusoidal one. The critical Rayleigh number is determined using linear and nonlinear stability analyses; for the latter, the energy method is used. There is a possibility of subcritical instabilities, as evidenced by the energy stability estimates being lower than the linear ones. Furthermore, eigenvalues are obtained as a function of aspect ratios, modulation amplitude, and frequency for varying Darcy numbers. Modulation amplitude more significantly triggers a change in flow patterns at the onset of convection compared to the effect of other parameters. Considering water-saturated porous media made up of different materials, we report the critical temperature difference between lower and upper surfaces required for the onset of convection. In addition, a comparison between such a temperature difference obtained from linear theory and the energy method is also provided in the same manner. It is observed that subharmonic instability occurs for all considered porous media packed densely or sparsely.

A Variational Model of Charged Drops in Dielectrically Matched Binary Fluids: The Effect of Charge Discreteness

This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. Introducing the model that describes two immiscible fluids with the same dielectric constant, with a drop of one fluid containing a fixed number of elementary charges together with their solvation spheres, we interpret the equilibrium shape of the drop as a global minimizer of the sum of its surface energy and the electrostatic repulsive energy between the charges under fixed drop volume. For all model parameters, we establish the existence of generalized minimizers that consist of at most a finite number of components “at infinity”. We also give several existence and non-existence results for classical minimizers consisting of only a single component. In particular, we identify an asymptotically sharp threshold for the number of charges to yield existence of minimizers in a regime corresponding to macroscopically large drops containing a large number of charges. The obtained non-trivial threshold is significantly below the corresponding threshold for the Rayleigh model, consistently with the ill-posedness of the latter and demonstrating a particular regularizing effect of the charge discreteness. However, when a minimizer does exist in this regime, it approaches a ball with the charge uniformly distributed on the surface as the number of charges goes to infinity, just as in the Rayleigh model. Finally, we provide an explicit solution for the problem with two charges and a macroscopically large drop.

Probing the melting dynamics in a phase change Rayleigh–Bénard system under low gravity conditions

The present work aims to investigate dynamic characteristics of Rayleigh–Bénard convection during the solid–liquid phase change process under the influence of variable low-gravity conditions. Low-gravity conditions are crucial to gain physical insights into the complex convection dynamics relevant in terrestrial and space environments that feature diverse gravitational fields. The melting dynamics of a paraffin-based phase change material with Prandtl number Pr ≈ 71 in a square rigid walled enclosure is analyzed by subjecting it to a fixed temperature difference resulting in a Stefan number Ste ≈ 0.33. The enthalpy porosity method is employed to simulate the solid-liquid phase change process in Rayleigh number range 105<Ra <107 to take wide range of gravitational acceleration (0.0g, 0.1g, 0.2g, 0.4g, 0.6g, 0.8g, and g) into account. The simulation results allow detailed insights on the buoyancy-driven convective flow phenomena in a phase-change Rayleigh–Bénard system. Various characteristic flow regimes, the criteria for the onset of convective instabilities, and scaling analysis are presented under varied gravitational acceleration. The findings reveal that the critical Rayleigh number (Racr) for the onset of convection is found to vary between 1351.5 and 1810.5 under the gravity range investigated in contrast to the Racr ≈ 1707.7 for classical Rayleigh-Bénard system under the standard gravity. Furthermore, the scale analysis based on the numerical results shows that the relationship between effective Nusselt number (Nue) and effective Rayleigh number (Rae) follows a power law behavior Nue = 0.27Rae0.25 under each gravity condition, similar to the classical Rayleigh–Bénard system.

Searching for Protoplanets around MWC 758 and MWC 480 in Br-γ Using Kernel Phase and SCExAO/CHARIS

Discovering new actively accreting protoplanets is crucial to answering open questions about planet formation. However, identifying such planets at orbital distances where they are expected to be abundant is extremely challenging, both due to the technical requirements and large distances to star-forming regions. Here we use the kernel phase interferometry (KPI) technique to search for companions around the ∼6 and ∼8 Myr old Herbig Ae stars MWC 758 and MWC 480. KPI is a data analysis technique that is sensitive to moderate asymmetries, arising from, e.g., a circumstellar disk or companions with contrasts of up to 6–8 mag, at separations down to and even below the classical Rayleigh diffraction limit (∼1.2λ/D). Using the high-spectral-resolution K-band mode of the SCExAO/CHARIS integral field spectrograph, we search for both excess Br-γ line emission and continuum emission from companions around MWC 480 and MWC 758. We are able to set limits on the presence of rapidly accreting protoplanets and brown dwarfs between 4 and 16 au, well interior to those of previous studies. In Br-γ, we set limits on excess line emission equivalent to accretion rates ranging from 10−5Mj2.yr−1 to 10−6Mj2.yr−1 . Our achievable contrasts demonstrate that KPI using SCExAO/CHARIS is a promising technique to search for giant accreting protoplanets at smaller separations compared to conventional imaging.

Swirl flow stability: thermodynamic analysis and experiments

The current paper presents a theoretical analysis of swirl flow stability, both inside a tube (vortex tube) and in a free annular swirl flow. The starting concept is the study of the evolution of velocity and temperature fluctuations. Methods of non-equilibrium thermodynamics are used to describe the magnitude of fluctuations and their properties. The important role of the total enthalpy follows from a variational analysis. Moreover, the thermodynamic criterion of the stability is formulated using the total enthalpy, and compared with experiments, numerical results and classical Rayleigh theory support its applicability. It was shown that the solid body vortex is at the margin of stability, which is experimentally observed. Analogously, the potential vortex is by the thermodynamic criterion stable; however, by the Rayleigh criteria it is on the onset of stability. The classical Taylor experiment of flow between two rotating cylinders is analysed from the point of view of this criterion. These results are underlined by swirl tube experiments at the Institute of Aerospace Thermodynamics at Stuttgart University and the annular nozzle experiments performed in the Institute of Thermomechanics CAS in Prague. Both independent experiments confirm the transformation of the initial annular vortex into a stable potential-type vortex. The results of this theory can also be used to explain the exceptional stability of tropical cyclones.

Free vibration analysis of hybrid CNT/GPL-reinforced Porous composite plates under fluid-loading

The present study aims to explore free vibration analysis of hybrid reinforced porous composite plates subjected to fluid loading. The hybrid composite comprises a porous core layer covered by two reinforced porous face sheets. Graphene Platelets (GPLs) and Carbon Nanotubes (CNTs) are considered as reinforcement materials. The linear three-dimensional piezo-elasticity theory is employed to model the structural part of the system, while the classical Rayleigh integral is used to obtain the fluid interaction part. The accuracy and reliability of the proposed model are validated by comparing the calculated natural frequencies of the plate in vacuum and water-loaded conditions with those reported in the literature. For the first time, several parametric studies are performed to investigate the effects of dimension ratios, porosity distributions, reinforcement dispersion pattern, porosity coefficient, and weight fraction of nanofiller on the natural frequency of hybrid reinforced porous composites. The results indicate that adjusting the porosity and weight fraction of the face sheets can enhance stiffness without changing the mass, emphasizing the importance of hybrid composites for achieving optimal stiffness while maintaining a constant mass. Furthermore, the influence of core layer porosity distributions on the composite behavior differs from that of porosity distributions in the face layers. Additionally, the effectiveness of the reinforcement pattern depends on the type of porosity distribution in the face layers.

Spatial Fluctuations of Optical Turbulence Strength in a Laboratory Turbulence Simulator

Controlled turbulence simulators in the laboratory have been extensively employed to investigate turbulence effects on light propagation in the atmosphere, driven by some advanced optical engineering such as remote sensing, energy-delivery systems, and free-space optical communication systems. Many studies have achieved rich results on the optical turbulence intensity, scintillation index, and power spectral density characteristics of the light propagation path in the center of a turbulence simulator, but a comprehensive analysis of the optical turbulence characteristics for different spatial locations is still lacking. We simulate turbulence with air as the medium in a classical convective Rayleigh–Bénard turbulence simulator through high-resolution computational fluid dynamics methods, the three-dimensional refractive index distribution is obtained, and the optical properties are analyzed comprehensively. It is found that the hot and cold plumes and the large-scale circulation strongly influence the inhomogeneity of Cn2 in the turbulence tank, making it weak in the middle and strong near the boundary. The refractive index power spectral density at different heights is centrally symmetric, with the slope gradually deviating from the −5/3 scaling power with increasing distance from the central region. Under the log-log plot, the variation of the refractive index variance with height exhibits a three-segmented feature, showing in order: a stable region, a logarithmic profile, and a power-law profile, in the region close to the boundary. These results will contribute to the construction of a suitable turbulence simulator for optical engineering applications.

Dynamics of cylindrical crevice microbubbles

Microbubbles are theorized to form in crevices on mineralizations causing twinkling, a rapid color shift observed when imaging hard mineralizations with Doppler ultrasound. While the classic Rayleigh–Plesset equation and subsequent modifications describe bubble dynamics in a free field, they do not account for crevice boundaries. In this study, cylindrical boundary conditions were incorporated into the derivation of the Rayleigh–Plesset equation and validated experimentally. Cylindrical crevices with diameters ranging from 0.08–1.2 μm and depths of 1 μm were etched into a silicon wafer. Bubbles that formed in these crevices were photographed at high-speed through an inverted microscope while being driven with ultrasound at 0.75, 2.5, and 5 MHz. Experimentally, for all tested crevice sizes, the bubbles did not visibly grow. In contrast, computational results using standard water surface tension (72.5 mN/m) predicted the bubbles should grow ∼6 mm. However, when applying a higher surface tension that was measured on the silicon-water interface (∼3000 mN/m), the bubbles were only predicted to grow ∼1 nm, supporting the experimental findings. These results offer insight into the mechanism causing twinkling and provides avenues for future investigation into the effect of crevice size and shape on twinkling. [Work supported by NSF CAREER 1943937 and GRFP DGE1255832.]

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory. In semi-infinite space, a nondispersive Rayleigh wave mode exists, and the eigendisplacement decays exponentially with depth. In a layered model with increasing layer velocity, the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer. If the phase velocity is the same as the P- or S-wave velocity of the layer, which is called the critical mode or critical phase velocity of surface waves, the general solution of the wave equation is not a homogeneous (expressed by trigonometric functions) or inhomogeneous (expressed by exponential functions) plane wave, but one whose amplitude changes linearly with depth (expressed by a linear function). Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode, owing to the singularity at the critical phase velocity. In this study, based on the classical framework of generalized reflection and transmission coefficients, the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity. Therefore, the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem. The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models. In contrast to the normal mode, the eigendisplacement associated with the critical phase velocity exhibits different characteristics. If the phase velocity is equal to the S-wave velocity in the bottom half-space, the eigendisplacement remains constant with increasing depth.

Surface-mediated spontaneous emulsification of the acylated peptide semaglutide

Acylated peptides composed of glucagon-like peptide-1 receptor agonists modified with a fatty acid side chain are an important class of therapeutics for type 2 diabetes and obesity but are susceptible to an unusual physical instability in the presence of hydrophobic surfaces, i.e., spontaneous emulsification, also known as ouzo formation in practice. In this work, light scattering, small-angle X-ray scattering, and circular dichroism measurements are used to characterize the physical properties of the semaglutide colloidal phase, including size distribution, shape, secondary structure, internal structure, and internal composition, as a function of solution physico-chemical conditions. The existence and size of the colloids formed are successfully predicted by a classical Rayleigh model, which identifies the parameters controlling their size and formation. Colloid formation is found to be catalyzed by hydrophobic surfaces, and formation rates are modeled as an autocatalytic reaction, enabling the formation of a master curve for various surfaces that elucidates the mechanism. Surfaces differ due to differences in surface wettability, which can be correlated with Hansen solubility parameters. This work provides insights into this unusual colloidal phenomenon and guides the peptide synthesis process and drug product formulation in the pharmaceutical industry.

Double-diffusive convection in a porous layer subjected to an inclined temperature gradient incorporating Soret effect

In several commonly occurring natural convection phenomena, the system is subjected to non-uniform heating that causes an inclined thermal gradient. As a result, the natural convection problem deviates from the classical Rayleigh–Bénard problem, in which the thermal gradient has only a vertical component. In this study, we present linear and global stability analyses results concerning thermosolutal convection in a Newtonian fluid-saturated Darcy porous layer subjected to an inclined thermal gradient in the presence of the Soret effect (associated with thermophoresis). The thermal gradient is assumed to have horizontal and vertical components, resulting in the formulation having two thermal Rayleigh numbers as system parameters, viz. horizontal and vertical Rayleigh numbers. The horizontal thermal gradient gives rise to a Hadley-type circulation. This circulation can become unstable if the vertical thermal gradient attains a certain threshold. We focus on the effect of the Soret parameter on the system’s stability under non-uniform inclined heating. The analyses reveal that the solutal Darcy–Rayleigh number and Lewis number destabilise the system, while the Soret parameter has a non-monotonic effect on the system’s stability depending on the horizontal Rayleigh number. The energy stability bounds do not coincide with linear ones for the present problem; hence, subcritical instabilities are possible.

The precursor structure in relativistic shocks

ABSTRACT We present a common unifying macroscopic framework for precursors in relativistic shock waves. These precursors transfer energy and momentum from the hot downstream to the cold upstream, modifying the shock structure. It was shown that in a steady state, there is a maximal fraction of the downstream energy flux that the precursor can carry. We show here that at this critical value, the shock disappears, and the flow passes through a sonic point. This behaviour resembles the classical Newtonian Rayleigh flow problem. At the critical value, the transition is unstable as perturbations in the upstream accumulate at the sonic point. Thus, if such a point is reached, the shock structure is drastically modified, and the flow becomes turbulent.

Rayleigh — Benard problem for Polymer Solution

There are three mathematical models describing the motion of aqueous solutions of polymers: the second grade fluid model (Rivlin — Eriksen), the hereditary model (Voitkunsky — Amfilokhiev — Pavlovsky), and its asymptotic simplification (Pavlovsky). This work considers the problem of fluid equilibrium stability in a horizontal fluid layer heated from below or from above. Also, equations of thermal gravitational convection for all three models are derived. Three types of boundary conditions are considered: two solid boundaries; the lower solid boundary and the upper free boundary; two free boundaries (the Rayleigh problem). For the case of heating from below, the principle of perturbation monotonicity is established that ensures the spectral problem eigenvalues to be of real type. This greatly simplifies the determination of the critical Rayleigh numbers. It turned out that these numbers coincide with the critical Rayleigh numbers in the classical Rayleigh — Benard problem. In the case of heating from above at large temperature gradients, the perturbation decrements become complex, but their real parts are negative. The conclusion that the relaxation properties of a second grade fluid and an aqueous solution of polymers do not lead to a change in the critical Rayleigh number may seem strange at first glance. According to our assumption, it is explained by the base state of the liquid being a state of rest.

Self-sustained Oscillations and Limit Cycles in Rayleigh System with Cubic Return Force

An oscillatory system with an excitation mechanism as in a Rayleigh oscillator, but with a nonlinear (cubic) returning force, is investigated. Using the accelerated convergence method and the continuation procedure for the parameter, limit cycles are constructed and the amplitudes and periods of self-oscillations are calculated. This is done for a wide range of feedback coefficient values, in which this coefficient is not asymptotically small or large. The proposed iterative procedure allows to achieve the specified accuracy of calculations. The analysis of the features of the limit cycle caused by an increase in the self-excitation coefficient is carried out. The results obtained are compared with the self-oscillations of a classical Rayleigh oscillator with a linear returning force.

Super-resolution imaging system developed from vector superoscillatory field illumination.

Superoscillations are oscillations of a band limited waveform with a local frequency higher than the bandlimit. Spatial superoscillations show great potential for performing super-resolution imaging. However, these superoscillatory waveforms are inevitably surrounded by high intensity sidelobes which severely limit the usable super-resolved area of an image. In this study, we demonstrate how polarization engineering can be used in some circumstances to suppress superoscillation sidelobes, taking advantage of the transverse wave nature of light. We illustrate the principle by a model super-resolution imaging system that can image Rayleigh scatterers with separations smaller than the classic Rayleigh criterion.

The Radiation Efficiency Measurements of Real System of a Thin Circular Plate Embedded Into a Thick Square Baffle

Most of sound sources are complex vibroacoustic objects consist of numerous elements. Some coupled vibrating plates of different shapes and sizes can be easily found in urban environments. The main aim of this study is to determine the sound radiation of coupled plates system of practical importance. The investigated vibroacoustic system consist of a thin circular plate coupled with a thick flat baffle with a circular hole. The circular plate has been mounted to the baffle’s hole using screws and two steel rings. The measurement setup was located inside a semi-anechoic chamber to assure the free field conditions. It was necessary to take into account the whole system surface to obtain the radiation efficiency based on the Hashimoto’s method. Such an approach can be troublesome and time-consuming. Therefore, the criterion has been proposed which allows the vibration velocity measurements and calculations to be performed only for the thin plate’s area. An alternative approach has been proposed based on the classical Rayleigh integral formula. Its advantage is a simpler implementation in a computer code. The obtained results have been compared with the theoretical results obtained for the elastically supported circular plate. A good agreement has been obtained at low frequencies.

Modification of flow transition for a vortex ring by a bubble released at the axis

The interactions between a vortex ring and a gas bubble released at the axis are studied numerically, which shed light on understanding more complicated bubble–turbulence coupling. We fix the Reynolds number at $Re_{\tau }=7500$ and consider various Weber numbers in the range of $We=130\unicode{x2013}870$ . We find that the translating speed of the vortex ring is substantially lower than the case of the vortex ring without a bubble. It is explained with two different mechanisms, depending on the Weber number. In the low- $We$ range, the reduction of translating speed of the ring is due to the capture of bubbles into the ring core, leading to significant changes in the vorticity distribution within the core. In the high- $We$ range, the repeatedly generated secondary vortex rings perturb the primary one, which bring about an earlier flow transition, thereby reducing the translating speed of the vortex ring. On the other hand, the evolution of a gas bubble is also affected by the presence of the vortex ring. In the low- $We$ range, we observe binary breakup of the bubble after it is captured by the primary vortex ring. In contrast, in the high- $We$ range, it is interesting to find that the bubble experiences sequentially stretching, spreading and breakup stages. In the high- $We$ range, the numbers of smaller bubbles predicted by the classical Rayleigh–Plateau instability of a stretched cylindrical bubble agree well with our numerical simulations. Consistent with the previous experiments, this number keeps unchanged at 16 as $We$ further increases. An additional comparison is made between two higher Reynolds numbers, indicating that the finer eddies in a vortical field with a higher Reynolds number tend to tear the bubble into more fragments.

Experimental study of heat transfer in a rectangular cell with built-in lattice channels

We experimentally study the heat transfer and flow characteristics of thermal convection in a rectangular cell with built-in lattice channels. The working fluid used is water with a Prandtl number of 5.5, and the Rayleigh number ranges from 2.5×108 to 6.9×109. Three proposed models with different channel sizes and positions and the classical Rayleigh–Bénard convection (RBC) are studied, and the heat transfer and flow structure characteristics are analyzed using measured temperature signals. The first model included two short channels placed near the top and bottom plates, which disrupt the mixing zone and enhance heat transport. The second model involves relatively long channels positioned at the center of the cell, but far from the thermal boundary layer, resulting in a more coherent bulk flow that also enhances heat transport. For these two configurations, the heat transfer enhancement rate is approximately 20% compared to standard RBC. The third model uses long lattice channels that almost touches the top and bottom plates. This configuration results in a maximum heat transfer enhancement of about 138% due to the organized boundary layer and bulk flow induced by lattice channels. The presence of channels also results in a two-order smaller standard deviation of temperature, indicating a significant reduction in fluctuations. However, the average temperatures in the center of some channels were significantly different from the mean system temperature, suggesting the existence of cold or hot fluid flow through the channel. Our experimental results show that the inclusion of channels with appropriate lengths and positions can effectively regulate the flow near the boundary layer and in the bulk, leading to significant enhancements in heat transfer.