High-resolution large-eddy simulations of turbulent mixing at the inner surface of a dense shell which undergoes forced compression by a spherically imploding shock wave are presented. Perturbations on the inner surface grow as a result of Richtmyer-Meshkov and Rayleigh-Taylor instabilities and effects related to geometric convergence and compressibility. Three different cases with different initial surface perturbations, one broadband and two narrowband, are considered. The perturbation power spectrum is related to the mode number via Pℓ ∝ ℓn, where the case with broadband perturbations has n = −2, and modes in the range ℓ = 6–200. The narrowband perturbations have n = 0 and modes in the range ℓ = 50–100 and ℓ = 100–200. The simulations are carried out in spherical coordinates using the PLUTO hydrodynamics code. Results on the mix layer width, molecular mix, and turbulent kinetic energy distribution are presented, demonstrating clearly the impact of the amplitude and spectral form of the initial perturbation on the evolution of integral properties. A recently developed model predicting the growth of single mode perturbations in spherical implosions including shock waves is extended to predict mix layer amplitudes for broadband and narrowband cases, along with a model proposed by Mikaelian [“Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells,” Phys. Rev. A 42, 3400–3420 (1990)]. The resultant layer amplitude predictions from the new model are in good agreement with the numerical results while the longest wavelengths are not yet saturated, while Mikaelian’s model agrees well where the initial modes are saturated.

High-resolution three-dimensional implicit large eddy simulations of implosion in spherical geometries are presented. The growth of perturbations is due to Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and also to geometric convergence and compression effects. RM and RT instabilities have been studied extensively in planar configurations, but there are comparatively few studies on spherical geometries. Planar geometries lack the effect of convergence that changes the morphology and growth of perturbations in spherical geometries. This paper presents a study of turbulent mixing in spherical geometries considering different narrowband (NB) and broadband multimode initial perturbations and examines several quantities including the evolution of the integral mixing layer width and integral bubble and spike heights using novel integral definitions. The growth of the bubble and spike is modeled using a Buoyancy–Drag (BD) approach that is based on simple ordinary differential equations to model the growth of the turbulent mixing layer. In a recent study, Youngs and Thornber [“Buoyancy-drag modelling of bubble and spike distances for single-shock Richtmyer-Meshkov mixing,” Physica D 410, 132517 (2020)] constructed modifications to the BD equations to take into account the early stages of the mixing process that are dependent on the initial conditions. Those modifications are shown to be important to obtain correct results. The current study adopted the same modifications and adapted the BD equations to the spherical implosion case. The results of the BD model are compared with those of different initial NB cases that include different initial amplitudes and wavelengths of the perturbations, for validation purposes. The predictions from the new BD model are in very good agreement with the numerical results; however, there exist some limitations in the accuracy of the model, in particular the use of the interface position and fluid velocity from one-dimensional data.

Abstract:The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier-Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor-Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a k −4 spectrum at t * = 4, and near the dissipation peak, all methods were capable of predicting the k −5/3 slope accurately when refining the mesh.

Extreme wind gusts cause major socioeconomic damage, and the rarity and localised nature of those events make their analysis challenging by either modelling or empirical approaches. A 23-year long data record from 29 automatic weather stations located in New South Wales (eastern Australia) is used to study the distribution, frequency and average recurrence intervals (ARIs) of extreme gusts via a peaks-over-threshold approach. We distinguish between gust events generated by synoptic phenomena (e.g. cyclones and frontal systems), hereafter called “synoptic events”, and convective phenomena (i.e. thunderstorms), hereafter called “convective events”, using the wind time series. For synoptic events the frequency of gusts $$>25$$ > 25 m/s decreases systematically inland from the coast, in contrast to convective gusts which are more uniformly distributed geographically and occur more often than synoptic gusts at nearly all inland locations. At inland locations the most extreme wind gusts are likewise dominated by convective events, whereas at coastal stations both gust types have similar intensities at low ARIs but convective events again dominate at the highest ARIs. Extreme gust directions were found to be predominantly westerly at inland locations and southerly at coastal ones, with more variable direction for convective than synoptic events. This study confirms the dominant role of thunderstorms in producing the most extreme gusts in the region, and shows that wind risk varies strongly with distance from the coast.

No abstract