# Latest papers in fluid mechanics

### Laboratory investigation of turbulent dissipation in an internal solitary wave breaking over a submerged Gaussian ridge

Laboratory experiments were conducted to investigate an internal solitary wave breaking over a submerged Gaussian ridge. Particle image velocimetry (PIV) was performed with a high-speed camera to analyze the macro- and microstructures of wave-breaking evolution and subsequent induced turbulence and mixing. Four types of wave breaking, namely, plunging breaking, collapsing breaking, plunging-collapsing breaking, and surging breaking, were identified, along with their different evolutionary processes and breaking mechanisms. The turbulent dissipation rates estimated from the PIV results were on the order of 10−6 to 10−4 m2/s3 during the breaking, with the smallest values in the plunging breaking and the largest in surging breaking. Generally, the intensity of turbulence in plunging breakers seems to be insensitive to the changing wave slope; however, the surging breaker shows an opposite trend.

### Interfacial dynamics of gas–water displacement in fractured porous media under high pressure

To deeply understand the dynamics of gas–water displacement in fractured porous media, especially under extreme high-pressure conditions, is essential to prevent water invasion in natural gas reservoirs. To this end, we presented an experimental study on the interfacial dynamics of gas–water displacement in a microfluidic device with fractured porous media, in which the displacement pressure could reach as high as 25 MPa. We found that, under the condition of quasi-static imbibition (i.e., at quite low differential pressure), water preferentially invaded the matrix instead of the fracture. In contrast, invasive water tended to permeate the fracture under high differential pressure; as a consequence, a conical front edge was formed at the gas–water displacing interface. More importantly, the interfacial front in different fractures contacted at the cross junctions and led to the formation of trapped gas in the matrix, due to the velocity of gas–water interface in the fracture being higher than that in the matrix. Besides, with increase in differential pressure and fracture number, the difference in the interfacial velocity between fractures and the matrix increased and hence the gas in the matrix was more easily trapped. Finally, we established a theoretical model to predict the interfacial velocity of gas–water displacement in fractured porous media under high pressure, which was able to well reproduce experimental data.

### On generalist scholarship: A hierarchical view of research

In this Perspective, the author presents his vision of scholarship as consisting of hierarchically nested levels of specialization, each level offering its own perspective and value. He argues that in an era of increasingly sophisticated analysis tools, modern scholarship tends to proceed largely unaware of the benefits of conducting research at the higher, more general levels of the hierarchy. Drawing upon his own research and that of others, he gives examples of the manner in which generalist scholarship may proceed, the type of unique insights it uncovers, and the wisdom afforded us via an awareness of where our scholarship resides within the hierarchy.

### On generalist scholarship: A hierarchical view of research

In this Perspective, the author presents his vision of scholarship as consisting of hierarchically nested levels of specialization, each level offering its own perspective and value. He argues that in an era of increasingly sophisticated analysis tools, modern scholarship tends to proceed largely unaware of the benefits of conducting research at the higher, more general levels of the hierarchy. Drawing upon his own research and that of others, he gives examples of the manner in which generalist scholarship may proceed, the type of unique insights it uncovers, and the wisdom afforded us via an awareness of where our scholarship resides within the hierarchy.

### High-order gas-kinetic scheme on three-dimensional unstructured meshes for compressible flows

In this paper, a high-order gas-kinetic scheme is developed on three-dimensional unstructured meshes for compressible Euler and Navier–Stokes equations. To achieve the high-order spatial accuracy, the three-dimensional weighted essentially non-oscillatory (WENO) reconstruction is extended to the unstructured tetrahedral and hexahedral meshes. A simple strategy is adopted for the selection of candidate stencils, and the topologically independent linear weights are used for the spatial reconstruction. The efficiency and robustness of the classical WENO reconstruction are improved. In addition to the two-stage fourth-order temporal discretization and lower–upper symmetric Gauss–Seidel method, the explicit and implicit high-order gas-kinetic schemes are developed for unsteady and steady problems. Accuracy tests on hexahedral and tetrahedral grids validate the third-order of accuracy, and various three-dimensional incompressible and compressible numerical experiments are also presented. The results validate the accuracy and robustness of the proposed scheme for both inviscid and viscous flows. In the future, the current scheme will be extended to the hybrid unstructured meshes and Reynolds-averaged Navier–Stokes simulation with high Reynolds numbers.

### Dynamics of phase separation of sheared binary mixtures after a nonisothermal quenching

Author(s): Antonio Bertei, Chih-Che Chueh, and Roberto Mauri

A thermodynamics-based phase-field model is developed to simulate phase separation of a binary mixture under a temperature gradient in a constant shear. The effects of meaningful dimensionless numbers, such as the capillary number, the Lewis number, and the dimensionless heat capacity are explored. The temperature gradient breaks the symmetry of phase separation compared to instantaneous quenching while different phase separation patterns, ranging from stripes to drops, can be obtained or even suppressed by a proper choice of parameters.

[Phys. Rev. Fluids 6, 094302] Published Wed Sep 08, 2021

### Hydrodynamic torque on a slender cylinder rotating perpendicularly to its symmetry axis

Author(s): Jean-Lou Pierson, Mohammed Kharrouba, and Jacques Magnaudet

The torque experienced by a circular cylinder rotating steadily about an axis passing trough its centroid and perpendicular to its symmetry axis is computed over a wide range of Reynolds number and aspect ratios using fully resolved simulations. In the creeping-flow regime, numerical results are shown to match predictions of an improved slender-body approximation. In strongly inertial regimes, flow symmetries and boundary layer arguments are employed to derive scaling laws for the various contributions to the torque. We finally obtain an empirical formula for the total torque, valid throughout the parameter range explored in the simulations.

[Phys. Rev. Fluids 6, 094303] Published Wed Sep 08, 2021

### Investigation of properties of superfluid $^{4}\mathrm{He}$ turbulence using a hot-wire signal

Author(s): P. Diribarne, M. Bon Mardion, A. Girard, J.-P. Moro, B. Rousset, F. Chilla, J. Salort, A. Braslau, F. Daviaud, B. Dubrulle, B. Gallet, I. Moukharski, E.-W. Saw, C. Baudet, M. Gibert, P.-E. Roche, E. Rusaouen, Andrei Golov, Victor L'vov, and Sergey Nazarenko

We report hot-wire measurements in flows of high and low turbulence intensities, both in normal and superfluid helium, at 1.6 K, 2 K, and 2.3 K. Consistent with previous studies, we observe a spectral bump at high frequency. Surprisingly, the bump frequency is found to depend on the turbulence intensity of the flow. Using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both flows.

[Phys. Rev. Fluids 6, 094601] Published Wed Sep 08, 2021

### Wind wave growth in the viscous regime

Author(s): Jiarong Wu and Luc Deike

How water surface waves grow under wind forcing has long been an interesting and challenging question. For short gravity-capillary waves, the viscous effects are important but have not been well studied. In this paper, we simulate the wind-wave growth by directly solving the two-phase Navier-Stokes equations. The numerical method features a momentum conserving scheme, interface reconstruction using Volume of Fluid, and adaptive mesh refinement (AMR). As a result, we observe concurrent growth of the irrotational traveling wave and the rotational drift layer (current). The growth rate of the wave and the evolution of the drift layer under different forcing parameters are discussed respectively.

[Phys. Rev. Fluids 6, 094801] Published Wed Sep 08, 2021

### Spectrally wide acoustic frequency combs generated using oscillations of polydisperse gas bubble clusters in liquids

Author(s): Bui Quoc Huy Nguyen, Ivan S. Maksymov, and Sergey A. Suslov

Acoustic frequency combs leverage unique properties of the optical frequency comb technology in high-precision measurements and innovative sensing in optically inaccessible environments such as under water, under ground, or inside living organisms. Because acoustic combs with wide spectra would be r...

[Phys. Rev. E 104, 035104] Published Wed Sep 08, 2021

### Geometry of catenoidal soap film collapse induced by boundary deformation

Author(s): Raymond E. Goldstein, Adriana I. Pesci, Christophe Raufaste, and James D. Shemilt

Experimental and theoretical work reported here on the collapse of catenoidal soap films of various viscosities reveal the existence of a robust geometric feature that appears not to have been analyzed previously; prior to the ultimate pinchoff event on the central axis, which is associated with the...

[Phys. Rev. E 104, 035105] Published Wed Sep 08, 2021

### Flow prediction using dynamic mode decomposition with time-delay embedding based on local measurement

We develop a method for the prediction of flow fields based on local particle image velocimetry (PIV) measurement. High spatial resolution can be achieved by focusing PIV on local flow regions; however, it is difficult for standard dynamic mode decomposition (DMD) to predict the temporally resolved flow field based on limited information in sub-domain. In this regard, the local flow field is embedded using time-delay to augment the spatial dynamics. As such, both high temporally and spatially resolved flow fields can be faithfully obtained from local PIV measurement using the DMD method. Using fabricated patterns, we demonstrate that DMD with time-delay embedding can faithfully predict dynamic patterns over a long time interval, whereas the standard DMD can only match the ground truth briefly following initiation. Using PIV measurement of a wake flow and a highly dynamic sweeping jet flow, the DMD with time-delay embedding can increase the temporal resolution up to 100 times with a prediction error rate of approximately 8%. Compared with wake flow, where unsteady flow patterns are relatively weak, a sweeping jet flow demonstrates that the prediction performance is improved even more significantly using time-delay embedding compared with standard DMD when the flow is highly dynamic. For sweeping jet flow, the prediction error rate can drop from 56% using standard DMD to 8.3% by embedding a time-delay smaller than five steps, for a small cost of calculation time. In addition, the DMD with time-delay embedding shows robustness to small noise. For data with high noise whose signal-to-noise ratio is 15, the method has an error rate of less than 5%.

### Comparison of amplitude method of roughness-induced swept-wing transition prediction with experiment

An amplitude method of laminar-turbulent transition prediction in the boundary layer on a swept wing has been developed and tested. The method computes the amplitudes and spectra of steady cross-flow instability modes generated by surface roughness. The transition criterion is based on the crucial, threshold values of maximal or local amplitudes of these perturbations found from experiments. Statistical methods describing the intermittency in the transition zone based on this criterion are proposed.

### Hydrodynamic regimes and drag on horizontally pulled floating spheres

We use high-speed imaging to investigate the movement of a floating sphere pulled horizontally along a water surface. The model sphere is 10 cm in diameter and has half of the water density resulting in a half-submerged static sphere. By varying the pulling force, we investigate the flow dynamics in the subcritical Reynolds number range, of Re ≈ 2 × 104 to 2 × 105. We characterize three hydrodynamic regimes with the increase in the pulling force, to which we refer to as: low Froude number, Fr < 0.6, intermediate, 0.6 < Fr < 1.2 and high Froude number, Fr > 1.2 regimes. In the low Fr regime, the sphere moves with little disturbance of the water surface and the drag is close to half of the drag on a fully submerged sphere. In the intermediate Fr regime, a pronounced wave pattern is developed which together with the dipping of the sphere below the water level leads to an increase in the drag force. Based on a potential flow approximation for the downward force on the sphere moving along the surface, we derive a semiempirical relation for the sphere dipping as a function of the Froude number. Finally, in the high Fr regime, the sphere movement switches to a mode of periodic dipping below and surfacing above the water surface. The periodic vertical motion portrays a decrease in the average drag force.

### Thermodynamical analysis and constitutive equations for a mixture of viscous Korteweg fluids

A complete thermodynamical analysis for a binary mixture of viscous Korteweg fluids with two velocities and two temperatures is developed. The constitutive functions are allowed to depend on the diffusion velocity and the specific internal energies of both constituents, together with their first gradients, on the symmetric part of the gradient of barycentric velocity as well as on the mass density of the mixture and the concentration of one of the constituents, together with their first and second gradients. Compatibility with the entropy principle is analyzed by applying the extended Liu procedure, and a complete solution of the set of thermodynamical restrictions is recovered in three space dimensions. Finally, the equilibrium configurations are investigated, and it is proved that no restrictions arise on the admissible phase boundaries. The theoretical results here provided may serve as a basis for experimental and/or numerical investigations, in particular for determining the surface levels of phase boundaries at equilibrium and making a comparison with the experimental profiles.

### Experimental investigation into fluid–structure interaction of cavitating flow

The objective of this paper is to study flow-induced vibration in cavitating flow around a steel stainless hydrofoil with the experimental and dynamic mode decomposition (DMD) method. A synchronized measured system consisting of a high-speed camera, lift measurement, and laser Doppler vibrometer is used to observe the cavitation structures, survey the vibrations, and measure the force. The hydrodynamic force and vibration velocity fluctuate most sharply in the cloud cavitation stage among all the cavitation regimes due to the unsteady cloud cavity, corresponding to the largest square root of normal distribution in the cloud cavitation in the analysis of statistic nature. Cavity shedding frequency, system-related frequency, and trailing edge vortex shedding frequency are observed in the vibration velocity frequency spectrum for the whole range of cavitation numbers. Cavity frequency dominates the structure response in the cloud cavitation regime. Two primary shedding mechanisms, re-entrant jet, and shockwave mechanism are identified for the cloud cavitation. The vibration velocity induced by the re-entrant jet mechanism is lower amplitude and larger frequency, while that induced by the shockwave mechanism is higher amplitude and smaller frequency due to the intense collapse of cloud cavity and rapid collapse of the attached cavity. Two peak bands related to the re-entrant jet development frequency and small-scale cavity shedding frequency are identified for the shockwave mechanism with DMD method.

### Flow instabilities and heat transfer in a differentially heated cavity placed at varying inclination angles: Non-intrusive measurements

We report the non-intrusive investigation of the dependence of buoyancy-driven flow instabilities on the orientation angle of a differentially heated cavity of aspect ratio three. The cavity orientation angles considered are 60° and 30°. While moving from 60° to 30°, the cavity is inclined toward its stable configuration, wherein convection reduces. Flow instabilities have been captured through the spectral analysis of the transient history of temperature distribution recorded in a completely non-intrusive manner using a Mach–Zehnder interferometer. By virtue of the fact that in such configurations, corners of the cavity are the most active regions with regard to the interaction of buoyancy-driven fluid with the cavity walls, and the flow behavior is centrosymmetric (diagonal symmetry), the flow field in the top two corners of the cavity has been mapped. The spatio-temporally resolved interferometric measurements identified two distinct frequencies for cavity inclination angle (θ) of 60°. These two frequencies correspond to two different flow instabilities, namely, the Tollmien–Schlichting (TS) and gravity wave-induced instabilities. As the cavity is further inclined toward 30°, the instability in the boundary layer, i.e., the TS instability, ceases to exist, and only the gravity wave-induced instability is observed. The dependence of flow instabilities on cavity orientation angle is explained on the basis of interferometry-based measurements made in the form of interferograms and the corresponding whole field maps of temperature contours. The convective flow field in the differentially heated cavity has also been qualitatively captured using smoke visualization to provide direct support to interferometric measurements.

### Air film evolution during droplet impact onto a solid surface

Recent years see increasing studies of air entrapment during droplet impacting on a solid surface with many results. The dynamics of trapped air film during a droplet impact on a solid surface is investigated in this work by the phase field method in combination with a dynamic contact angle (DCA) model. The DCA model is established experimentally by capturing the droplet dynamics in analogy to the entrapped air evolution. By using the DCA model as the input, the simulation can accurately reproduce the experimental results. The effects of droplet viscosity and surface tension on the dynamics of the air film are then studied, and three possible regimes are identified, demarcated by an effective Ohnesorge number (Ohe). Regime 1 is the case where no daughter droplet is generated and the air bubble is always attached to the substrate, corresponding to the classical case at a high Ohe number (Ohe > 0.073). Regime 3 is a newly discovered regime in this work where a daughter droplet is generated and the air bubble is always detached from the substrate, corresponding to a low Ohe number (Ohe < 0.019) due to combined strong surface tension and vortex effects. Regime 2 is for moderate Ohe numbers where a daughter droplet is generated and the air bubble can either detach from or attach to the substrate. Different from conventional thought that the detachment in this regime is decided by a static contact angle, the DCA plays a leading role in determining the volume ratio of the daughter droplet to the gas bubble, and the combined effects determine the fate of the bubble. Such finding provides better insight on the entrapped air dynamics upon droplet impacting on a solid surface, an area of high engineering importance.

### Effect of the rotor blade installation angle on the structure-borne noise generated by adjustable-blade axial-flow fans

The effect of rotor blade installation angle on the structure-borne noise of adjustable-blade axial-flow fans is analyzed based on the fluid–solid coupling method. The co-simulation environment ANSYS Workbench is adopted to perform one-way fluid–solid coupling analysis. Following this, the properties of the flow field and noise field with different installation angles are simulated. The flow field simulation results reported significant vorticity near the rotor and stator, and a larger installation angle may cause higher pressure fluctuation. The sound field results showed that the frequency spectrum characteristics for the sound pressure level and the sound power level are almost the same while the installation angle changes from −8° to 8°, and the peaks of frequency spectrum occur at the blade passing frequency and its harmonics. The total sound pressure level (TSPL) and the total sound power level (TPWL) all show increasing trends ranging from −8° to +8°. The maxima of TSPL and TPWL reach 134.1 and 176 dB, while their minima reach 123.1 and 163 dB, respectively. Thus, reduction of the installation angle can reduce the structure-borne noise. Besides, the structure-borne noise generated by adjustable-blade axial-flow fans is low-frequency noise, which lies in the range of 0–500 Hz.

### Spatiotemporal instability of a shear-imposed viscous flow

We study the linear spatiotemporal instability of a two-dimensional gravity-driven viscous fluid flow where the fluid surface is subjected to an imposed shear stress. The fourth order Orr–Sommerfeld boundary value problem is derived and solved numerically up to moderate values of the Reynolds number. Numerical solution based on AUTO07p identifies four spatial branches, viz., I, II, III, and IV, where the spatial branches I, II, and IV lie in the upper half zone, while the spatial branch III lies in the lower half zone of the complex wavenumber plane. The spatial growth rate [math] corresponding to branch I becomes stronger as long as the imposed shear stress increases and ensures a destabilizing effect. Furthermore, the spatial branch I enters in the lower half zone of the complex wavenumber plane as soon as the temporal growth rate ωi decreases and may collide with other spatial branch lying in the lower half zone of the complex wavenumber plane. Moreover, a study of absolute and convective instabilities is carried out within the frameworks of saddle point technique and collision criterion. The saddle point technique provides only one unstable branch of the unstable wavepacket, while the collision criterion provides two unstable branches of the wavepacket. The unstable range of the wavepacket with ray velocity enhances in the presence of imposed shear stress. It is observed that the shear-imposed fluid flow is convectively unstable. In addition, the simplified second order two-equation model is developed for a shear-imposed flow in terms of the local fluid layer thickness and local flow rate, which in fact renders three spatial branches rather than four. However, the two-equation model recovers the physically relevant spatial branch I very well. Finally, nonlinear spatiotemporal simulation of the two-equation model displays a formation of the regular train of solitary waves downstream at low forcing frequency.