Two-way coupled long-wave isentropic ocean-atmosphere dynamics

The events following the 15 January 2022 explosions of the Hunga Tonga-Hunga Ha'apai volcano highlighted the need for a better understanding of ocean-atmosphere interactions when large amounts of energy are locally injected into one (or both). Starting from the compressible Euler equations, a two-way coupled (TWC) system is derived governing the long-wave behaviour of the ocean and atmosphere under isentropic constraint. Bathymetry and topography are accounted for along with three-dimensional atmospheric non-uniformities through their depth average over a spherical shell. A linear analysis, yielding two pairs of gravito-acoustic waves, offers explanations for phenomena observed during the Tonga event. A continuous transcritical regime (in terms of water depth) is identified as the source of large wave generation in deep water bodies, removing the singularity-driven Proudman-type resonance observed in one-way coupled models. The refractive properties, governing the interaction of the atmospheric wave with step changes in water depth, are derived to comment on mode-to-mode energy transfer. Two-dimensional global simulations modelling the propagation of the atmospheric wave (under realistic conditions on the day) and its worldwide effect on oceans are presented. Local maxima of water-height disturbance in the farfield from the volcano, linked to the atmospheric wave deformation (in agreement with observations), are identified, emphasising the importance of the TWC model for any daylong predictions. The proposed framework can be extended to include additional layers and physics, e.g. ocean and atmosphere stratification. With the aim of contributing to warning system improvement, the code necessary to simulate the event with the proposed model is made available.journal articl

Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions

A combined numerical and analytical approach is used to study the low-frequencyshock motions observed in shock/turbulent-boundary-layer interactions in theparticular case of a shock-reflection configuration. Starting from an exact formof the momentum integral equation and guided by data from large-eddy simulations,a stochastic ordinary differential equation for the reflected-shock-foot low-frequencymotions is derived. During the derivation a similarity hypothesis is verified for thestreamwise evolution of boundary-layer thickness measures in the interaction zone. Inits simplest form, the derived governing equation is mathematically equivalent to thatpostulated without proof by Plotkin (AIAA J., vol. 13, 1975, p. 1036). In the presentcontribution, all the terms in the equation are modelled, leading to a closed form ofthe system, which is then applied to a wide range of input parameters. The resultingmap of the most energetic low-frequency motions is presented. It is found that whilethe mean boundary-layer properties are important in controlling the interaction size,they do not contribute significantly to the dynamics. Moreover, the frequency of themost energetic fluctuations is shown to be a robust feature, in agreement with earlierexperimental observations. The model is proved capable of reproducing available lowfrequencyexperimental and numerical wall-pressure spectra. The coupling betweenthe shock and the boundary layer is found to be mathematically equivalent to afirst-order low-pass filter. It is argued that the observed low-frequency unsteadinessin such interactions is not necessarily a property of the forcing, either from upstreamor downstream of the shock, but an intrinsic property of the coupled system, whoseresponse to white-noise forcing is in excellent agreement with actual spectra

Meteotsunamis in Japan associated with the Tonga Eruption in January 2022

Large-amplitude meteotsunamis were observed in many areas in Japan, following the arrival of barometric Lamb waves emitted by an underwater volcanic eruption of Hunga Tonga-Hunga Ha‘apai in January 2022. We modeled the power spectra of the tidal level data obtained from 12 tide stations of the Geospatial Information Authority of Japan, based on a method of transfer function which converts the barometric pressure pulse spectra into the meteotsunami spectra. The obtained transfer functions are similar at 12 stations. The pressure pulse spectra are obtained from the ensemble average of ∼1500 Soratena weather sensors of Weathernews Inc. distributed over Japan. The observed meteotsunami spectra can be characterized by the enhanced seiche eigenmodes at each station excited by the mesoscale pressure pulse within the amplitude error of 50%, which contributes for accumulating the necessary knowledge to understand the potential dangers in various different areas over Japan

Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble

The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. We present here a large-eddy simulation investigation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer. Contrary to past large-eddy simulation investigations on shock/turbulent boundary layer interactions, we have used an inflow technique which does not introduce any energetically significant low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system. The large-eddy simulation has been run for much longer times than previous computational studies making a Fourier analysis of the low frequency possible. The broadband and energetic low-frequency component found in the interaction is in excellent agreement with the experimental findings. Furthermore, a linear stability analysis of the mean flow was performed and a stationary unstable global mode was found. The long-run large-eddy simulation data were analyzed and a phase change in the wall pressure fluctuations was related to the global-mode structure, leading to a possible driving mechanism for the observed low-frequency motions

Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at Re-tau=1000

A direct-numerical-simulation-based study is presented, which focuses on the response of near-wall turbulence and skin friction to the imposition of an oscillatory spanwise wall motion in channel flow. One point of contrast to earlier studies is the relatively high Reynolds number of the flow, namely Reτ=1000 in the unforced baseline flow. Another is the focus on transients in the drag that are in the form of moderate oscillatory variations in the skin friction and near-wall turbulence around the low-drag state at a sub-optimal actuation period. These conditions allow phase-averaged statistics to be extracted, during the periodic drag decrease and rise, that shed light on the interaction between turbulence and the unsteady Stokes strain. Results are presented for, among others, the phase-averaged second moments of stochastic fluctuations and their budgets, enstrophy components and joint probability density functions. The study identifies velocity skewness – the wall-normal derivative of the angle of the velocity vector – as playing a significant role in the streak-damping process during the drag-reduction phase. Furthermore, the phase-wise asymmetry in the skewness is identified as the source of a distinctive hysteresis in all properties, wherein the drag decrease progresses over a longer proportion of the actuation cycle than the drag increase. This feature, coupled with the fact that the streak-generation time scale limits the ability of the streaks to re-establish themselves during the low-skewness phase when the actuation period is sufficiently short, is proposed to drive the drag-reduction process. The observations in the study thus augment a previously identified mechanism proposed by two of the present authors, in which the drag-reduction process was linked to the rate of change in the Stokes strain in the upper region of the viscous sublayer where the streaks are strongest. Furthermore, an examination of the stochastic-stress budgets and the enstrophy lead to conclusions contrasting with those recently proposed by other authors, according to which the drag-reduction process is linked to increases in enstrophy and turbulence-energy dissipation. It is shown, both for the transient drag-reduction phase and the periodic drag fluctuations around the low-drag state, that the drag decrease/increase phases are correlated with decreases/increases in both enstrophy and dissipation

Small-scale two-dimensional turbulence shaped by bulk viscosity

Bulk-to-shear viscosity ratios of three orders of magnitude are often reported in carbon dioxide but are always neglected when predicting aerothermal loads in external (Mars exploration) or internal (turbomachinery, heat exchanger) turbulent flows. The recent (and first) numerical investigations of that matter suggest that the solenoidal turbulence kinetic energy is in fact well predicted despite this seemingly arbitrary simplification. The present work argues that such a conclusion may reflect limitations from the choice of configuration rather than provide a definite statement on the robustness of kineticenergy transfers to the use of Stokes’ hypothesis. Two distinct asymptotic regimes (Euler– Landau and Stokes–Newton) in the eigenmodes of the Navier–Stokes equations are identified. In the Euler–Landau regime, the one captured by earlier studies, acoustic and entropy waves are damped by transport coefficients and the dilatational kinetic energy is dissipated, even more rapidly for high bulk-viscosity fluids and/or forcing frequencies. If the kinetic energy is initially or constantly injected through solenoidal motions, effects on the turbulence kinetic energy remain minor. However, in the Stokes–Newton regime, diffused bulk compressions and advected isothermal compressions are found to prevail and promote small-scale enstrophy via vorticity-dilatation correlations. In the absence of bulk viscosity, the transition to the Stokes–Newton regime occurs within the dissipative scales and is not observed in practice. In contrast, at high bulk viscosities, the Stokes– Newton regime can be made to overlap with the inertial range and disrupt the enstrophy at small scales, which is then dissipated by friction. Thus, flows with substantial inertial ranges and large bulk-to-shear viscosity ratios should experience enhanced transfers to small-scale solenoidal kinetic energy, and therefore faster dissipation rates leading to modifications of the heat-transfer properties. Observing numerically such transfers is still prohibitively expensive, and the present simulations are restricted to two-dimensional turbulence. However, the theory laid here offers useful guidelines to design experimental studies to track the Stokes–Newton regime and associated modifications of the turbulence kinetic energy, which are expected to persist in three dimensional turbulence

Shock-induced energy conversion of entropy in non-ideal fluids

From shaping cosmic structures in space to producing intense sounds in aircraft engines, shock waves in fluids ineluctably convert entropy fluctuations into swirling motions and sound waves. Studies of the corresponding conversion from internal energy to kinetic energy have so far been restricted to ideal (or idealised) fluids. Yet, many substances do not obey the ideal-gas law (including those in the above two examples). The present work demonstrates that non-ideal thermodynamic properties provide a remarkable degree of control over the conversion to solenoidal and dilatational kinetic energies. Of particular interest is the ability to suppress much of the emitted acoustic field whilst promoting mixing downstream of the shock. This is made possible by exploiting the convexity (or lack thereof) of the shock adiabats. Whilst illustrated here using dense vapours near the thermodynamic critical point, this ability to design and control specific shock-induced energy transfers extends beyond near-critical-point phenomena; e.g. shocked mixtures (high-speed dusty flows on Mars, nanoparticle formation in supersonic expanders for drug manufacturing), reacting fronts (supersonic combustion, rocket propulsion), ionising shocks (reentry systems, inertial confinement fusion) or fronts in active fluids (bacterial and crowd flows). This theoretical work, which demonstrates the predictive capabilities of linear theory, lays the foundation for future experimental investigations ultimately aimed at delivering novel shock-based flow-control strategies exploiting the thermodynamic properties of the fluid