3D Instability Research Articles

Local gravitational instability of two-component thick discs in three dimensions

Aims. The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study the local gravitational instability of two-component thick discs in three dimensions. Methods. We use as a starting point a recently proposed analytic three-dimensional (3D) instability criterion for discs with non-negligible thickness that takes the form Q3D < 1, where Q3D is a 3D version of the classical 2D Toomre Q parameter for razor-thin discs. Here, we extend the 3D stability analysis to two-component discs, considering first the influence on Q3D of a second unresponsive component, and then the case in which both components are responsive. We present the application to two-component discs with isothermal vertical distributions, which can represent, for instance, galactic discs with both stellar and gaseous components. Finally, we relax the assumption of vertical isothermal distribution, by studying one-component self-gravitating discs with polytropic vertical distributions for a range of values of the polytropic index corresponding to convectively stable configurations. Results. We find that Q3D < 1, where Q3D can be computed from observationally inferred quantities, is a robust indicator of local gravitational instability, depending only weakly on the presence of a second component and on the vertical gradient of temperature or velocity dispersion. We derive a sufficient condition for local gravitational instability in the midplane of two-component discs, which can be employed when both components have Q3D > 1.

Adjoint-based optimisation of time- and span-periodic flow fields with Space–Time Spectral Method: Application to non-linear instabilities in compressible boundary layer flows

We aim at computing time- and span-periodic flow fields in span-invariant configurations. The streamwise and cross-stream derivatives are discretised with finite volumes while time and the span-direction are handled with pseudo-spectral Fourier-collocation methods. Doing so, we extend the classical Time Spectral Method (TSM) to a Space–Time Spectral Method (S-TSM), by considering non-linear interactions of a finite number of time and span harmonics. For optimisation, we introduce an adjoint-based framework that allows efficient computation of the gradient of any cost functional with respect to a large-dimensional control parameter. Both theoretical and numerical aspects of the methodology are described: evaluation of matrix–vector products with S-TSM Jacobian (or its transpose) by algorithmic differentiation, solution of fixed-points with quasi-Newton method and de-aliasing in time and space, solution of direct and adjoint linear systems by iterative algorithms with a block-circulant preconditioner, performance assessment in CPU time and memory. We illustrate the methodology on the case of 3D instabilities (first Mack mode) triggered within a developing adiabatic boundary layer at M = 4.5. A gradient-ascent method allows to identify a finite-amplitude 3D forcing that triggers a non-linear response exhibiting the strongest time- and span-averaged drag on the flat-plate. In view of flow control, a gradient-descent method finally determines a finite amplitude 2D wall-heat flux that minimises the averaged drag of the plate in presence of the previously determined non-linear optimal forcing.

A 3D view on the local gravitational instability of cold gas discs in star-forming galaxies at 0 ≲ z ≲ 5

Local gravitational instability (LGI) is considered crucial for regulating star formation and gas turbulence in galaxy discs, especially at high redshift. Instability criteria usually assume infinitesimally thin discs or rely on approximations to include the stabilising effect of the gas disc thickness. We test a new 3D instability criterion for rotating gas discs that are vertically stratified in an external potential. This criterion reads Q3D < 1, where Q3D is the 3D analogue of the Toomre parameter Q. The advantage of Q3D is that it allows us to study LGI in and above the galaxy midplane in a rigorous and self-consistent way. We apply the criterion to a sample of 44 star-forming galaxies at 0 ≲ z ≲ 5 hosting rotating discs of cold gas. The sample is representative of galaxies on the main sequence at z ≈ 0 and includes massive star-forming and starburst galaxies at 1 ≲ z ≲ 5. For each galaxy, we first apply the Toomre criterion for infinitesimally thin discs, finding ten unstable systems. We then obtain maps of Q3D from a 3D model of the gas disc derived in the combined potential of dark matter, stars and the gas itself. According to the 3D criterion, two galaxies with Q < 1 show no evidence of instability and the unstable regions that are 20% smaller than those where Q < 1. No unstable disc is found at 0 ≲ z ≲ 1, while ≈60% of the systems at 2 ≲ z ≲ 5 are locally unstable. In these latter, a relatively small fraction of the total gas (≈30%) is potentially affected by the instability. Our results disfavour LGI as the main regulator of star formation and turbulence in moderately star-forming galaxies in the present-day Universe. LGI likely becomes important at high redshift, but the input by other mechanisms seems required in a significant portion of the disc. We also estimate the expected mass of clumps in the unstable regions, offering testable predictions for observations.

Numerical Prediction of Tonal Aeroacoustic Noise Produced by Small Wind Turbines

The aeroacoustic design of small wind turbines (SWTs) can be challenging due to the possibility of the low Reynolds number (Re) flow over the blades generating tonal noise. The numerical prediction of this tonal noise using computational aeroacoustics can improve the understanding of the flow mechanisms behind the tonal noise to improve SWT blade design. In this study, wall-resolved incompressible large eddy simulation (LES) and the Ffowcs-Williams and Hawkings (FW-H) acoustic analogy are applied to a low Re airfoil, SD 7037, at Re = 4.1 × 104 to assess the ability of this method to predict tonal noise. The tonal prediction at 1° angle of attack aligned with experimental measurements and further analysis confirmed that the Kelvin-Helmholtz (K-H) rolls in the suction side laminar separation bubble (LSB) are the source of the aeroacoustic tone. The tone is due to the K-H rolls passing the trailing edge of the airfoil, and a secondary tone intermittently appears due to a 3D instability in the K-H roll. The accurate prediction of tonal noise using LES and FW-H opens the possibility of incorporating this method into the aeroacoustic design of low Re airfoils used for SWTs.

3D Size-Dependent Dynamic Instability Analysis of FG Cylindrical Microshells Subjected to Combinations of Periodic Axial Compression and External Pressure Using a Hermitian C2 Finite Layer Method Based on the Consistent Couple Stress Theory.

This work develops a three-dimensional (3D) weak formulation, based on the consistent couple stress theory (CCST), for analyzing the size-dependent dynamic instability behavior of simply-supported, functionally graded (FG) cylindrical microshells that are subjected to combinations of periodic axial compression and external pressure. In our formulation, the microshells are artificially divided into nl layers. The displacement components of each individual layer are selected as the primary variables, which are expanded as a double Fourier series in the in-plane domain and are interpolated with Hermitian C2 polynomials in the thickness direction. Incorporating the layer-wise displacement models into our weak formulation, we develop a Hermitian C2 finite layer method (FLM) for addressing the current issue. The accuracy and the convergence rate of our Hermitian C2 FLM are validated by comparing the solutions it produces with the accurate two-dimensional solutions of critical loads and critical pressures of FG cylindrical macroshells and single-walled carbon nanotubes, which were reported in the literature. The numerical results show the effects of the material length-scale parameter, the inhomogeneity index, the radius-to-thickness and length-to-radius ratios, the load magnitude ratio, and the static and dynamic load factors on the first principal and first secondary instability regions of parametric resonance of simply-supported FG cylindrical microshells are significant.

Investigation on deformation behaviors and dynamic recrystallization mechanism of spray formed Al–Zn–Mg–Cu alloy under hot compression

The thermal deformation behavior of spray formed Al–Zn–Mg–Cu alloy was investigated by the isothermal hot compression tests at the strain rates of 0.001–10 s−1 with the temperature range of 350–450 °C. An Arrhenius constitutive equation was established by the corrected strain-stress curves, and then the processing map was constructed based on the 3D instability map and 3D power dissipation map. The influence of strain rate and temperature on both flow stress and dynamic softening has been unveiled. The results show that dynamic recovery (DRV) is the primary softening mechanism and dynamic recrystallization (DRX) is substantively retarded due to the fine dispersed particles uniformly distributed in the spray formed alloy. Continuous dynamic recrystallization (CDRX) is the primary DRX mechanism at a low temperature or high strain rate. DRX grain was observed at the grain boundaries, especially at the triple junctions. The appropriate thermal deformation condition is recommended at the temperature range from 430 °C to 450 °C and strain rates from 0.003 s−1 to 0.1 s−1.

(Invited) Fundamentals of Thin Film Growth and Etching: How Small Atomic Processes Govern Macroscopic Effects

In order not to have our children inherit a huge problem in the future, we quickly have to realize the energy transition to renewable sources, which requires also energy storage devices and, thus, Li ion batteries. Although significant progress has been made during recent years regarding battery capacitance, cycle life time, deterioration, and fast charging capabilities, any further improvement becomes increasingly more difficult.The reason for this is manifested in the top-down approach, which quickly delivers results, and thus products, by screening the parameter space and evaluating available options. At this point, however, further improvements often require a deep, fundamental understanding of all processes, and a change to a bottom-up approach is highly recommended, if not even essential.Using Scanning Tunneling Microscopy movies, I will show in my talk how a small change in adatom formation energy and adatom diffusion barrier leads to a huge morphology change of the growing film. After providing the insights to the well-known homoepitaxial growth modes, I will introduce one specific atomic barrier that leads to an instability and triggers 3D growth. The 2D analogous of this barrier at a step edge, leads to dendritic island shapes, and the combination of both, the 2D and 3D instability, leads to dendrites as observed also in the batteries. With this in mind, I will show the dualism between adatoms and vacancies, which naturally explains also the equivalent, inverse growth modes during etching or dissolution including their instabilities.From here we will switch gears and focus on polycrystalline film aspects, and, thus, the grain boundary network. I will show, again on the atomic scale, how the grain boundary energy determines the surface structure from extremely rough to flat and smooth. Quite surprisingly, I will further demonstrate how a tiny variation in the dilute adatom/vacancy equilibrium-pressure on the surface, during growth or dissolution, can setup pressures variations in the grain boundary network that exceed the pressure of the deepest point of all our world seas: the Mariana Trench.These enormous compressive (and tensile) stresses are to a large extent reversible. However, due to the differences in diffusion constants in combination with the huge reservoir of grain boundary volume in the film, complications arise on the atomic scale at the triple point/lines, where the grain boundaries penetrate the surface. Mass accumulation or depletion leads to hillocks and grooves. Moreover, the remaining accumulated intrinsic film stress can also trigger whisker growth, which, on the basis of the involved atomic processes, clearly has to be distinguished from dendritic growth.Although fundamentally still not understood, whisker growth leads to many failures, like short circuits in electronic devices and batteries. Their penetrating forces can be enormous, pushing through even hard oxide layers and films (and the SEI).As many of the described effects play a major and critical role in Li ion batteries, and while I realize that I am adding seemingly hopeless, additional complexity, I will finally provide some basic strategies and concepts that we learned on how to tune and influence the previously mentioned effects efficiently on the atomic scale by using additives.

Generalized mean state of the isothermal Darcy–Benard problem and its instability onset

Thermally-driven natural convection is theoretically explored in the present work within a porous layer with respect to the Darcy’s law. The usual non circulating basic cellular flow between two infinitely long horizontal Darcy porous plates leads to generalized basic state considering the isothermal boundary conditions leading to the Hadley flow configuration. Such a motion is governed by a circulatory flow together with a temperature both varying along the horizontal axis. Hence, besides the buoyancy Rayleigh parameter, yet another parameter appears dominating the evolution of basic cellular circulation and thermal progress. Instability onset of this basic state is targeted based on the linear stability analysis of small normal modes. The resulting 3D instability system of equations is treated numerically and the stationary modes leading to convective neutral stability are determined. The found eigenvalues are also justified to be those deviating from the well-known no-flow Darcy porous solution through an asymptotic perturbation method in the special circumstances. The bounds of neutral stability curves in regard to the longitudinal, oblique and transverse modes are thoroughly investigated and it is shown that longitudinal modes are always the most unstable ones, while the transverse and oblique modes having finite encapsulated zone of instability can undergo a complete stability after a threshold value of horizontal temperature gradient parameter.

Plasmoid-mediated reconnection during nonlinear peeling–ballooning edge-localized modes

Plasmoid-mediated reconnection is investigated for nonlinear peeling–ballooning edge-localized modes (P-B ELMs). The formation of current sheets and the transition to 3D current sheet instability is demonstrated through fully nonlinear resistive MHD simulations of P-B ELMs in DIII-D discharges. Large-scale axisymmetric current sheets, as well as small-scale poloidally extended current sheets, are formed as the coherent P-B ELM filaments nonlinearly evolve. It is observed that, at high Lundquist numbers, these current sheets break during a reconnection burst, i.e. a secondary exponential growth of intermediate modes followed by relaxation due to the suppression of P-B drive.

Hot deformation behavior, dynamic recrystallization mechanism and processing maps of Ti–V microalloyed high strength steel

The hot deformation behavior, dynamic recrystallization mechanism and processing maps of Ti–V complex microalloyed high strength steel under temperatures ranging from 840 to 1040 °C and strain rates varying from 0.01 to 10 s−1 were studied by using thermal-mechanical simulation (Gleeble-3800), optical microscopy (OM), and electron backscatter diffraction (EBSD). The true stress–strain curves of the investigated steel were obtained under the different deformation conditions, the thermal deformation activation energy was calculated, the thermal constitutive equations based on the true stress–strain curves were established, and the 3D power dissipation diagrams, the 3D plastic instability diagrams, and the thermal processing maps under different true strains were drawn. The results show that the flow stress curves are of dynamic recrystallization type at 960–1040 °C and strain rate of 0.01 s−1 and at 1040 °C and strain rate of 0.1 s−1, and the peak stress decreases gradually with the increase of the deformation temperature and the decrease of the strain rate. The hot deformation activation energy of Ti–V microalloyed steel was calculated to be 349.681 kJ/mol. The average grain size of austenite first decreases and then increases with increasing the strain rate under the deformation temperatures of 1000 °C and 1040 °C, and has the smallest value of 15.0 μm and 16.1 μm, respectively, after deformation at the strain rate of 1 s−1. With the true strain increasing from 0.2 to 0.6, the area occupied by the destabilized region increases and the machinable region area decreases. It reveals that the most available hot processing parameter ranges of Ti–V complex microalloyed steel are at the temperature range of 1000∼1040 °C with the strain rate of 0.01–1 s−1.

The Initiation and Back-reaction of the X5.4 Flare on 2012 March 7

In this paper, we study the evolution of the X5.4 flare (SOL2012-03-07T00:02) in NOAA Active Region 11429, focusing on its initiation mechanisms and back-reaction effects. To help our study, three-dimensional (3D) coronal magnetic field models are extrapolated from the photospheric magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory under the assumptions of nonlinear force-free field (NLFFF) and non-force-free field (non-FFF). We investigate the 3D magnetic structure and MHD kink instability, torus instability, and double-arc instability (DAI), and find that this flare is most likely triggered by the tether-cutting reconnection and the subsequent DAI. For the back-reactions of the flare, both NLFFF and non-FFF models clearly show an increase in horizontal magnetic field (B h ) and a decrease in inclination angle (ϕ) of the magnetic field near the polarity inversion line, from the photosphere up to a certain height (5 Mm and 8 Mm for non-FFF and NLFFF, respectively). In addition, the non-FFF model shows an enhancement of the downward Lorentz force acting on the photosphere, and the location of the enhancement spatially coincides with the location of the flare onset. The observed back-reaction is likely a consequence of magnetic reconnection.

Morphological instability and roughening of growing 3D bacterial colonies.

How do growing bacterial colonies get their shapes? While colony morphogenesis is well studied in two dimensions, many bacteria grow as large colonies in three-dimensional (3D) environments, such as gels and tissues in the body or subsurface soils and sediments. Here, we describe the morphodynamics of large colonies of bacteria growing in three dimensions. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria generically become morphologically unstable and roughen as they consume nutrients and grow beyond a critical size-eventually adopting a characteristic branched, broccoli-like morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between two-dimensional (2D) and 3D colonies; while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient limited in its interior, driving a transition to unstable growth at its surface. We elucidate the onset of the instability using linear stability analysis and numerical simulations of a continuum model that treats the colony as an "active fluid" whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies-as well as other forms of growing active matter, such as tumors and engineered living materials-in 3D environments.

Molecular Clouds as Gravitational Instabilities in Rotating Disks: A Modified Stability Criterion

Molecular gas disks are generally Toomre stable (Q T > 1) and yet clearly gravitationally unstable to structure formation as evidenced by the existence of molecular clouds and ongoing star formation. This paper adopts a 3D perspective to obtain a general picture of instabilities in flattened rotating disks, using the 3D dispersion relation to describe how disks evolve when perturbed over their vertical extents. By explicitly adding a vertical perturbation to an unperturbed equilibrium disk, stability is shown to vary with height above the midplane. Near z = 0, where the equilibrium density is roughly constant, instability takes on a Jeans-like quality, occurring on scales larger than the Jeans length and subject to a threshold Q M = κ 2/(4π G ρ) = 1 or roughly Q T ≈ 2. Far from the midplane, on the other hand, stability is pervasive, and the threshold for the total disk (out to z = ±∞) to be stabilized is lowered to Q T = 1 as a consequence. In this new framework, gas disks are able to fragment through partial 3D instability even where total 2D instability is suppressed. The growth rates of the fragments formed via 3D instability are comparable to, or faster than, Toomre instabilities. The rich structure in molecular disks on the scale of tens of parsecs can thus be viewed as a natural consequence of their 3D nature and their exposure to a variety of vertical perturbations acting on roughly a disk scale height, i.e., due to their situation within the more extended galaxy potential, participation in the disk-halo flow, and exposure to star formation feedback.

Computational investigation into the effect of constitutive formulations for flow modeling of high elasticity

• Three constitutive formulations of the Leonov model are numerically investigated. • It is verified that keeping positive-definiteness of the conformation tensor is crucial for computational evolution while appropriate interpolation of exponentially convecting domain is essential for accuracy. • Swirling asymmetric corner vortices are described in 3D contraction flow modeling. For the purpose of defeating the high Deborah (or Weissenberg) number problems in viscoelastic flow modeling, the matrix-logarithmic formulation of the constitutive equations has been suggested and proven probably the most effective. This transformation of the conformation tensor endows proper resolution of the boundary layer with exponential convection as well as conservation of its positive definiteness. Herein we make an attempt to evaluate numerical consequences of these two features independently for the Leonov viscoelastic model mainly in the contraction flow. To this end, we from the viewpoint of computational stability and accuracy investigate three formulations written with variables such as the original conformation tensor c (c form), its matrix-logarithm (h form) and additive decomposition (b form). 2D planar 4:1 contraction flow in the limit of vanishing inertia in addition to its 1D toy problem is considered in the framework of finite element method. The h and b forms are designed to preserve the positive definiteness of c , and furthermore the h form grants efficient interpolation of exponentially convecting variables. The 1D analogy expresses the characteristics qualitatively equivalent to the original problem in a simpler fashion. The c form modeling of 2D flow exhibits typical nonevolutionary behavior when the Deborah number ( De ) exceeds a certain limit, and this degradation gets worse with finer mesh. While the h and b forms have always been computationally stable with proper description of steady behavior or elastic instability otherwise, the h form manifests faster mesh convergence. As a complementary study, the h form calculation of full 3D flow along an axisymmetric contraction channel has been performed, which also attests well-posedness without upper bound in De . Its steady result is corroborated with the one under axisymmetric flow approximation. Loss of convergence in the axisymmetric flow regime at high De is verified to result from the occurrence of 3D instability, which is then well portrayed in 3D modeling. In this instability, swirling of asymmetric structure for the corner vortices about the geometrical symmetry axis plausibly mimics experimental observation. Consequently, maintaining the positive definiteness in terms of h or b form is crucial for numerically stable evolution, and the h form interpolation delineating appropriately the exponential convection assures the fastest mesh convergence, hence enhancing the accuracy.

Excitation of instabilies in a Blasius boundary layer by surface vibration

Here we have demonstrated that small amplitude vibration can artificially excite both two dimensional (2D) and three dimensional (3D) instability modes. The 2D modes were typical of Tollmien–Schlichting (TS) waves provided that the frequency of excitation lies within the unstable region of the neutral stability predicted by modal linear stability theory. However, even if the frequency of the mechanically forced mode was within the stable bounds of the neutral curve the harmonics generated by the non-linear response of the flow could develop as instability modes. Further analysis of the streamwise and spanwise evolution of the instability modes identified from the temporal Fourier transform confirmed the presence of 3D modes excited due to the nature of the mode shape deflection of the vibrating panel which was not uniform in the spanwise direction. The effect of spanwise non-uniformity could be increased by activating the motors along the spanwise direction. However, due to the forcing from a combination of both streamwise and spanwise motors, strong interaction with the 3D mode led to a reduction in the growth rate of the TS wave in the far-field region despite higher initial perturbation generated by a larger number of motors.

DNS of the spatiotemporal evolution of the vorticity in (pure) mode B of a circular cylinder’s wake

In the present paper, the spatio-temporal evolution of the vorticity field in the second wake instability, i.e. (pure) mode B is investigated to understand the wake vortex dynamics and sign relationships among the three vorticity components. Direct numerical simulation of the flow past a circular cylinder in the three-dimensional (3D) wake transition is performed, typically at a Reynolds number of 300. According to the time histories of fluid forces and frequency analysis, three different stages are identified. In the fully developed wake (FDW), the spanwise vortex core is almost two-dimensional, while the vortex braid is 3D due to the dominant streamwise interaction. However, streamwise and vertical vorticities owing to the intrinsic 3D instability are already generated first on cylinder surfaces early in the computational transition (CT). The evolution of additional vorticities with the same features as mode B shows that (pure) mode B could already be formed in the late CT. In the FDW, a special sign symmetry of these additional vorticities on the rear surface is observed, which is exactly opposite to that in (pure) mode B. Similarly, the two sign laws found in (pure) mode A are also verified in three typical regions, independent of the Reynolds number, for (pure) mode B. Particularly, the mechanism for the physical origin of streamwise and vertical vortices in the shear layers is the vortex generation on the wall first and then dominant vortex induction just near the wall. The entire process of the formation and shedding of vortices with three components of vorticity is first and completely illustrated. Other characteristics of the evolution of mode B are presented in detail.

Numerical analysis of effects of fins and conductive walls on heat transfer in side heated cavities — Onset of three-dimensional phenomena in natural convection

In the present study, we analyse individual and combined effects of conductive horizontal walls and conductive fins on the natural convection of air in side heated cavities (SHC). The flow and heat transfer are studied for Rayleigh numbers in the range of 104−109: Direct Numerical Simulation (DNS) is conducted for the lower and Large Eddy Simulation (LES) for the higher Rayleigh numbers (>108). Thermally conductive walls destabilize the flow yielding an earlier transition to turbulence and expedite the decay in boundary layer thickness with increase in Rayleigh number. The preheating/precooling along the conductive walls reduces the actual heat transfer at the vertical walls. Above the fin, instabilities are only marginally enhanced for adiabatic horizontal walls, whereas for conductive horizontal walls, plumes erupt from the fin. This localized Rayleigh-Bénard-like effect triggers 3D instabilities in the entire flow field and yields a steeper slope in Nusselt-Rayleigh diagram. The presence of a fin increases the integral heat transfer by 18% for adiabatic and 21% for conductive horizontal walls. We show that 2D and 3D simulations are similar for the smooth cases (i.e., without fin), but differ by 4% and 13% for the adiabatic and conductive fin cases respectively. The local heat transfer characteristics even deviates up to 50%, therefore a 2D simplification should be avoided.

Existence of dual solutions and three-dimensional instability in helical pipe flow

Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9]) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.

3D Instability of a Toroidal Flow in the Liquid Partially Covered by a Solid Film

The structure of a steady radial thermocapillary flow from the local heat source in cylindrical geometry has been studied numerically. The up boundary of the liquid was partially covered by the stationary film of an insoluble surfactant, pushed to the wall of the cavity. The calculations are fulfilled on the base of interfacial hydrodynamics equations by using mathematical package “Comsol Multiphysics”. It is shown that the effect of a radial flow symmetry breakdown appears as a result of convective instability, so that the initial poloidal rotation of the liquid transforms into the azimuthal plane. The system of inclined steady volumetric vortices is formed under the film of surfactant. The inclination angle of the plane of rotation in dependence on the intensity of radial thermocapillary flow is studied. It is shown that the azimuthal vorticity can be regulated by the power of point-heat source and by free surface area. The increase of heating intensity leads to the growth of the azimuthal vorticity. Thus, the initially radially symmetric toroidal flow is divided into two parts with the origination of vortices in the azimuthal plane under the film.

Tridimensional nonhydrostatic transient rip currents in a wave-resolving model

Flash rips and surf eddies are transient horizontal structures of the order of 10 to 100 m, which can be generated in the surfzone in the absence of bathymetric irregularities. They are traditionally evaluated in a depth averaged setting which involves intrinsic horizontal shear instabilities and the direct generation of vorticity by short-crested waves. In this article, we revisit the processes of surf eddy generation with a new three-dimensional wave resolution model (CROCO) and provide a plausible demonstration of new 3D non-hydrostatic instability and turbulent cascade. We first present a quick overview of a compressible free surface approach suitable for nearshore dynamics. Its ability to simulate the propagation of surface gravity waves and nearshore wave-driven circulation is validated by two laboratory experiments. Next, we present a real world application from Grand Popo Beach, Benin, forced by waves with frequency and directional spreading. The generation of surf eddies by the 3D model differs from depth-averaged models, due to the vertical shear associated with shallow breaking waves. In this case, the generation of eddies from both horizontal shear instability and the breaking of short-crested waves is hampered, the former by stretching the alongshore current and the latter by inhibiting the inverse energy cascade. Instead, the vertical shear flow is subjected to forced wave group variability and Kelvin–Helmholtz type instability at an inflection point. Primary and secondary instabilities generate spanwise and streamwise vorticity connecting small-scale eddies to larger horizontal surfzone structures. Streamwise filaments, appearing as 5 m wide ribs or mini-rips, can extend beyond the surfzone but with moderate energy. These results appear consistent with the velocity spectra and observed patterns of tracers and suspended sediments at Grand Popo Beach. The timescale associated with the mean shear-induced turbulence is several times the wave period and suggests an intermediate range between breaker-induced turbulence and large-scale surf eddies.