Combination Of Direct Numerical Simulations Research Articles

Traveling spiral wave chimeras in coupled oscillator systems: emergence, dynamics, and transitions

Systems of coupled nonlinear oscillators often exhibit states of partial synchrony in which some of the oscillators oscillate coherently while the rest remain incoherent. If such a state emerges spontaneously, in other words, if it cannot be associated with any heterogeneity in the system, it is generally referred to as a chimera state. In planar oscillator arrays, these chimera states can take the form of rotating spiral waves surrounding an incoherent core, resembling those observed in oscillatory or excitable media, and may display complex dynamical behavior. To understand this behavior we study stationary and moving chimera states in planar phase oscillator arrays using a combination of direct numerical simulations and numerical continuation of solutions of the corresponding continuum limit, focusing on the existence and properties of traveling spiral wave chimeras as a function of the system parameters. The oscillators are coupled nonlocally and their frequencies are drawn from a Lorentzian distribution. Two cases are discussed in detail, that of a top-hat coupling function and a two-parameter truncated Fourier approximation to this function in Cartesian coordinates. The latter allows semi-analytical progress, including determination of stability properties, leading to a classification of possible behaviors of both static and moving chimera states. The transition from stationary to moving chimeras is shown to be accompanied by the appearance of complex filamentary structures within the incoherent spiral wave core representing secondary coherence regions associated with temporal resonances. As the parameters are varied the number of such filaments may grow, a process reflected in a series of folds in the corresponding bifurcation diagram showing the drift speed s as a function of the phase-lag parameter α.

Dynamics of a stratified vortex under the complete Coriolis force: two-dimensional three-components evolution

We study the dynamics of an initially axisymmetric and vertical Lamb–Oseen vortex in a stratified-rotating fluid under the complete Coriolis force on the $f$ plane, i.e. in the presence of a background rotation both along the vertical and horizontal directions. By a combination of direct numerical simulations and asymptotic analyses for small horizontal background rotation, we show that a critical layer appears at the radius where the angular velocity of the vortex is equal to the buoyancy frequency when the Froude number is larger than unity. This critical layer generates a vertical velocity that is invariant along the vertical and which first increases linearly with time and then saturates at an amplitude scaling like $Re^{1/3}/\widetilde{Ro}$ , where $Re$ is the Reynolds number and $\widetilde {Ro}$ the non-traditional Rossby number based on the horizontal component of the background rotation. In turn, a quasi-axisymmetric anomaly of vertical vorticity is produced at the critical radius through the non-traditional Coriolis force. Below a critical $\widetilde {Ro}$ depending on $Re$ , the Rayleigh's inflectional criterion is satisfied and a shear instability is subsequently triggered rendering the vertical vorticity fully non-axisymmetric. The decay of the angular velocity is then enhanced until it is everywhere lower than the buoyancy frequency. A theoretical criterion derived from the Rayleigh condition predicts well the instability. It shows that this phenomenon can occur even for a large non-traditional Rossby number $\widetilde {Ro}$ for large $Re$ . Hence, the non-traditional Coriolis force might have much more impact on geophysical vortices than anticipated by considering the order of magnitude of $\widetilde {Ro}$ .

Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers.

In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a set of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echoes of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echoes can successively replace the main pulses, which defines their lifetime. This pulse instability mechanism originates from a global bifurcation of the saddle-node infinite-period type. In addition, we show that, under the influence of noise, the stable pulses exhibit forms of a behavior characteristic of excitable systems. Furthermore, for the harmonic solutions consisting of multiple equispaced pulses per round-trip, we show that if the location of the pulses coincides with the echo of another, the range of stability of these solutions is increased. Finally, it is shown that around these resonances, branches of different solutions are connected by period-doubling bifurcations.

Suppression of internal waves by thermohaline staircases

Abstract

Thermohaline layering on the microscale

A theoretical model is developed which illustrates the dynamics of layering instability, frequently realized in ocean regions with active fingering convection. Thermohaline layering is driven by the interplay between large-scale stratification and primary double-diffusive instabilities operating at the microscale – temporal and spatial scales set by molecular dissipation. This interaction is described by a combination of direct numerical simulations and an asymptotic multiscale model. The multiscale theory is used to formulate explicit and dynamically consistent flux laws, which can be readily implemented in large-scale analytical and numerical models. Most previous theoretical investigations of thermohaline layering were based on the flux-gradient model, which assumes that the vertical transport of density components is uniquely determined by their local background gradients. The key deficiency of this approach is that layering instabilities predicted by the flux-gradient model have unbounded growth rates at high wavenumbers. The resulting ultraviolet catastrophe precludes the analysis of such basic properties of layering instability as its preferred wavelength or the maximal growth rate. The multiscale model, on the other hand, incorporates hyperdiffusion terms that stabilize short layering modes. Overall, the presented theory carries the triple advantage of (i) offering an explicit description of the interaction between microstructure and layering modes, (ii) taking into account the influence of non-uniform stratification on microstructure-driven mixing, and (iii) avoiding unphysical behaviour of the flux-gradient laws at small scales. While the multiscale approach to the parametrization of time-dependent small-scale processes is illustrated here on the example of fingering convection, we expect the proposed technique to be readily adaptable to a wide range of applications.

Effects of weak planetary rotation on the stability and dynamics of internal stratified jets

This study explores the stability characteristics and nonlinear evolution of internal jets in rotating stratified fluids using a combination of direct numerical simulations and linear instability analyses. Our ultimate goal is the assessment of the potential impact of the Earth’s rotation on relatively small-scale structures, exemplified by turbulent wakes generated by propagating bluff objects in the ocean. We question the popular notion that ascribes a secondary role to the Coriolis effects in large Rossby number (Ro) systems. It is shown that the Earth’s rotation can substantially influence circulation patterns with Rossby numbers as high as Ro ∼ 103. Therefore, such effects must be taken into account in the numerical and theoretical models of finescale (∼10–100 m) processes in the ocean. We present a series of examples in which planetary rotation controls flows with large but finite values of Ro through centrifugal destabilization. These calculations reveal that centrifugal instabilities can affect fluid motion either directly, by modifying the basic state, or indirectly, by preferentially eliminating anticyclonic coherent vortices that form in the course of dynamic destabilization of jets. The results of this study have potentially significant geophysical implications in terms of elucidating mechanisms of energy cascade to progressively smaller scales. In the naval context, we anticipate that our investigation could influence the development of algorithms for detection and analysis of late wakes, generated by propagating submersibles in the ocean.

A computationally light data-driven approach for heat transfer and hydraulic characteristics modeling of supercritical fluids: From DNS to DNN

Power cycles with supercritical fluids show high thermal efficiency and are widely applicable. For instance, supercritical carbon dioxide (sCO2) is proposed to be deployed in various energy conversion cycles, such as solar thermal, geothermal and nuclear. However, heat transfer deterioration of supercritical fluids in the near-critical region reduces the thermal efficiency and presents a threat to the safety of the system. Therefore, prior identification of such heat transfer deterioration is practically very useful. In addition, hydraulic characteristics (such as wall shear stress) are important for determining pressure drop and the corresponding head loss in designing heat transfer equipment. In the past decade, direct numerical simulation (DNS) has become an important approach to study the heat transfer and hydraulic characteristics of supercritical fluids at moderate Reynolds numbers. The main downside is the extremely high computational burden. In this work, we construct a database including 35 operational conditions (characterized by pipe diameter, inlet pressure, heat flux, and inlet temperature) on sCO2. Both the wall temperature and the wall shear stress are generated from DNS, dependent on the bulk specific enthalpy. 80% of the data are randomly selected to train a deep neural network (DNN), which fits the training data very well. The rest of the data (20%) are used for validation (strictly separated from training). The DNN fits the validation data even better, demonstrating successful counter-overfitting and the general applicability of the DNN under the operational conditions covered by the database. Training of the DNN takes minutes on a regular computer. Evaluating the wall temperature and the wall shear stress with a given operational condition and bulk specific enthalpy takes negligible time. This shows that DNN is a computationally light approach for heat transfer and hydraulic characteristics modeling of supercritical fluids. Furthermore, we test the trained DNN on an operational condition not considered in the database. The DNN still closely follows the results generated by the DNS. Therefore, a combination of DNS and DNN is able to maintain the modeling accuracy that DNS alone has, and significantly reduce the computational load.

Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics

Three-dimensional doubly diffusive convection in a closed vertically extended container driven by competing horizontal temperature and concentration gradients is studied by a combination of direct numerical simulation and linear stability analysis. No-slip boundary conditions are imposed on all six container walls. The buoyancy number $N$ is taken to be $-1$ to ensure the presence of a conduction state. The primary instability is subcritical and generates two families of spatially localized steady states known as convectons. The convectons bifurcate directly from the conduction state and are organized in a pair of primary branches that snake within a well-defined range of Rayleigh numbers as the convectons grow in length. Secondary instabilities generating twist result in secondary snaking branches of twisted convectons. These destabilize the primary convectons and are responsible for the absence of stable steady states, localized or otherwise, in the subcritical regime. Thus all initial conditions in this regime collapse to the conduction state. As a result, once the Rayleigh number for the primary instability of the conduction state is exceeded, the system exhibits an abrupt transition to large-amplitude relaxation oscillations resembling bursts with no hysteresis. These numerical results are confirmed here by determining the stability properties of both convecton types as well as the domain-filling states. The number of unstable modes of both primary and secondary convectons of different lengths follows a pattern that allows the prediction of their stability properties based on their length alone. The instability of the convectons also results in a dramatic change in the dynamics of the system outside the snaking region that arises when the twist instability operates on a time scale faster than the time scale on which new rolls are nucleated. The results obtained are expected to be applicable in various pattern-forming systems exhibiting localized structures, including convection and shear flows.

On the Topographic Modulation of Large-Scale Eddying Flows

AbstractThe modulation of large-scale eddying flows by gentle variation in topography is examined using a combination of direct numerical simulations and theoretical arguments. The basic state is represented by a laterally uniform zonal current that is restricted to the upper layer of a baroclinically unstable quasigeostrophic two-layer system. Therefore, the observed topographically induced generation of large-scale patterns is attributed entirely to the action of mesoscale eddies. The parameter regime investigated in this study is not conducive to the spontaneous formation of stationary zonal jets. The interaction between the large-scale current, eddies, and topography is described using an asymptotic multiscale model. The ability of the model to explicitly represent the interaction between distinct flow components makes it possible to unambiguously interpret the essential dynamics of the topographic/eddy-induced modulation. The multiscale solutions obtained reflect the balance between the modification of the meridional fluxes of potential vorticity (PV) due to the variation in topography and the corresponding modification of PV fluxes due to the induced large-scale circulation. The predictions of the asymptotic theory are successfully tested by comparing to the ones obtained by direct numerical simulations.

Direct numerical simulation of the turbulent premixed flame propagation with radiation effects

This paper investigates the effects of turbulence on radiative heat transfer in premixed flame propagation using a combination of direct numerical simulation (DNS) and the discrete ordinates method (DOM). The DNS code has been validated and established in previous research, and the newly written DOM code is validated by solving a sample radiative heat transfer problem. The DOM code is explicitly combined with the DNS code using the 3rd-order Runge–Kutta scheme. In the numerical experiments, an initially flat laminar premixed flame interacts with imposed turbulent fluctuations and evolves over time. A remarkable increase in the temperature self-correlation factor <T4>/<T>4 is observed in the middle of the reaction. Higher u′ conditions induced faster and more intensive flame wrinkle evolution. However, flow turbulence reduces the radiative heat loss in planar premixed flame due to the flame curvature effects.

The flip-flopping wake pattern behind two side-by-side circular cylinders: A global stability analysis

A global stability analysis is performed for the flip-flopping wake pattern behind two side-by-side cylinders with emphasis on the unstable vorticity field. The combination of direct numerical simulation with the state-of-art lattice Boltzmann method and dynamic mode decomposition is used to analyse such wake pattern for the first time. The vorticity mode of the secondary instability is extracted from the flow. Such mode is found to be symmetrical with respect to the geometric axis of symmetry. Furthermore, a new scenario is found for the high order harmonics that there is a pair of two tertiary modes as a result of nonlinear interaction between the mode related to the secondary instability and the global mode of the in-phase synchronized vortex shedding base flow. Besides, the reason for the Fourier spectra of the lift on the two cylinders being the same is also illustrated for this case.

Generation and maintenance of bulk turbulence by libration-driven elliptical instability

Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

On the appropriate filtering of PIV measurements of turbulent shear flows

The three-dimensional spatial filtering and measurement noise associated with experimental planar and three-dimensional (3D) particle image velocimetry (PIV) measurements is investigated using a combination of direct numerical simulations (DNS) and experimental databases. Spatial filtering velocity fields from a DNS of a zero-pressure-gradient turbulent boundary layer (TBL) at resolutions typical of PIV experiments are shown to underestimate Reynolds stresses by as much as 50 %. Comparison of experimental PIV measurement of a turbulent channel flow and 3D tomographic PIV measurements of a TBL with higher-resolution simulations and hot-wire anemometry measurements show that in real experiments, measurement noise acts to offset this effect. This is shown to produce measurements that appear to provide a good estimate of the turbulent fluctuations in the flow, when in reality the flow is spatially under-resolved and partially contaminated by noise. Means of identifying this noise are demonstrated using the one-dimensional (1D) velocity power spectra and the 1D transfer function between the power spectra of the unfiltered velocity field and the power spectra calculated from the filtered experimental measurement. This 1D transfer function differs from the commonly used sinc transfer function of PIV owing to the integrated effect of filtering in multiple directions. Failure to incorporate this difference is shown to overestimate the maximum resolved wave number in the 3D spectra of the planar PIV by close to 10 %, while conversely underestimating the maximum resolved wave number in the 3D PIV by 50 %. Appropriate spatial filtering of the experimental data is shown to remove the noise-dominated small-scale fluctuations and bring the data inline with that which should be obtained for a noiseless PIV measurement at the corresponding spatial resolution.

Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first break up into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.

Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit.The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure.The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant.

The Efficiency of Mixing in Turbulent Patches: Inferences from Direct Simulations and Microstructure Observations

The time evolution of mixing in turbulent overturns is investigated using a combination of direct numerical simulations (DNS) and microstructure profiles obtained during two field experiments. The focus is on the flux coefficient Γ, the ratio of the turbulent buoyancy flux to the turbulent kinetic energy dissipation rate ϵ. In observational oceanography, a constant value Γ = 0.2 is often used to infer the buoyancy flux and the turbulent diffusivity from measured ϵ. In the simulations, the value of Γ changes by more than an order of magnitude over the life of a turbulent overturn, suggesting that the use of a constant value for Γ is an oversimplification. To account for the time dependence of Γ in the interpretation of ocean turbulence data, a way to assess the evolutionary stage at which a given turbulent event was sampled is required. The ratio of the Ozmidov scale LO to the Thorpe scale LT is found to increase monotonically with time in the simulated flows, and therefore may provide the needed time indicator. From the DNS results, a simple parameterization of Γ in terms of LO/LT is found. Applied to observational data, this parameterization leads to a 50%–60% increase in median estimates of turbulent diffusivity, suggesting a potential reassessment of turbulent diffusivity in weakly and intermittently turbulent regimes such as the ocean interior.

Planform selection in Bénard-Marangoni convection: l hexagons versus g hexagons.

The planform of weakly nonlinear B\'enard-Marangoni convection in a horizontally unbounded layer is analyzed using a combination of direct numerical simulation, amplitude equations, and qualitative discussion. It is demonstrated that there exists a critical Prandtl number ${\mathrm{Pr}}_{\mathit{c}}$ such that in fluids with Pr${\mathrm{Pr}}_{\mathit{c}}$ convection sets in as a pattern of hexagonal cells with downward motion in the center (g hexagons), while for fluids with Prg${\mathrm{Pr}}_{\mathit{c}}$ conventional hexagonal cells with upward motion in the center (l hexagons) appear at the onset of instability. For fluids with Marangoni and Prandtl numbers in the vicinity of the bicritical point (${\mathrm{Ma}}_{\mathit{c}}$,${\mathrm{Pr}}_{\mathit{c}}$) the hexagonal patterns undergo a secondary instability, leading to stationary rolls. The stability domain of stationary rolls increases with the distance from the critical Marangoni number. (c) 1995 The American Physical Society