“…2021) involves the Kolmogorov length scale , with considered sufficiently resolved, where is the maximum resolved wavenumber. For the present simulations, for , at , this corresponds to , respectively, which satisfies the criterion; it is similar to the resolution used in DNS of bubble deformation in turbulence (Farsoiya, Popinet & Deike 2021). For details, see the supplementary materials.…”
Section: Energetics and Transition To 3-d Turbulent Flowmentioning
We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number (Re, wave inertia relative to viscous effects) and Bond number (Bo, wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo, and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value
$Re_\lambda \sim 100$
, consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. (J. Fluid Mech., vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale,
$r_H$
. We confirm two regimes in the bubble size distribution,
$N(r/r_H)\propto (r/r_H)^{-10/3}$
for
$r>r_H$
, and
$\propto (r/r_H)^{-3/2}$
for
$r<r_H$
. Bubbles are resolved up to one order of magnitude below
$r_H$
, and we observe a good collapse of the numerical data compared to laboratory breaking waves (Deane & Stokes, Nature, vol. 418 (6900), 2002, pp. 839–844). We resolve droplet statistics at high Bo in good agreement with recent experiments (Erinin et al., Geophys. Res. Lett., vol. 46 (14), 2019, pp. 8244–8251), with a distribution shape close to
$N_d(r_d)\propto r_d^{-2}$
. The evolution of the droplet statistics appears controlled by the details of the impact process and subsequent splash-up. We discuss velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process.
“…2021) involves the Kolmogorov length scale , with considered sufficiently resolved, where is the maximum resolved wavenumber. For the present simulations, for , at , this corresponds to , respectively, which satisfies the criterion; it is similar to the resolution used in DNS of bubble deformation in turbulence (Farsoiya, Popinet & Deike 2021). For details, see the supplementary materials.…”
Section: Energetics and Transition To 3-d Turbulent Flowmentioning
We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number (Re, wave inertia relative to viscous effects) and Bond number (Bo, wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo, and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value
$Re_\lambda \sim 100$
, consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. (J. Fluid Mech., vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale,
$r_H$
. We confirm two regimes in the bubble size distribution,
$N(r/r_H)\propto (r/r_H)^{-10/3}$
for
$r>r_H$
, and
$\propto (r/r_H)^{-3/2}$
for
$r<r_H$
. Bubbles are resolved up to one order of magnitude below
$r_H$
, and we observe a good collapse of the numerical data compared to laboratory breaking waves (Deane & Stokes, Nature, vol. 418 (6900), 2002, pp. 839–844). We resolve droplet statistics at high Bo in good agreement with recent experiments (Erinin et al., Geophys. Res. Lett., vol. 46 (14), 2019, pp. 8244–8251), with a distribution shape close to
$N_d(r_d)\propto r_d^{-2}$
. The evolution of the droplet statistics appears controlled by the details of the impact process and subsequent splash-up. We discuss velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process.
“…2021; Perrard et al. 2021; Farsoiya, Popinet & Deike 2021) and atmospheric turbulent boundary layers (van Hooft et al. 2018).…”
Section: The Dns Of Fully Coupled Wind and Wavesmentioning
confidence: 99%
“…(2021) and Farsoiya et al. (2021) have used AMR for a homogeneous and isotropic turbulence box and demonstrated the accuracy of the methods by considering the second-order structure function scaling. Figure 18.A slice of the field showing the adaptive mesh for the case.…”
Section: Figure 16mentioning
confidence: 99%
“…We use adaptive mesh refinement (AMR) which allows us to reduce the computational cost when solving such a multiscale problem. The methods have been extensively validated and applied to wave breaking (Deike, Popinet & Melville 2015;Deike, Melville & Popinet 2016;Mostert & Deike 2020;Mostert, Popinet & Deike 2022), two-phase turbulent flow (Rivière et al 2021;Perrard et al 2021;Farsoiya, Popinet & Deike 2021) and atmospheric turbulent boundary layers (van Hooft et al 2018).…”
Section: The Dns Of Fully Coupled Wind and Wavesmentioning
We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. We consider the ratio of the wave speed
$c$
to the wind friction velocity
$u_*$
from
$c/u_*= 2$
to 8, i.e. in the slow to intermediate wave regime; and initial wave steepness
$ak$
from 0.1 to 0.3; the two being varied independently. The turbulent wind and the travelling, nearly monochromatic waves are fully coupled without any subgrid-scale models. The wall friction Reynolds number is 720. The novel fully coupled approach captures the simultaneous evolution of the wave amplitude and shape, together with the underwater boundary layer (drift current), up to wave breaking. The wave energy growth computed from the time-dependent surface elevation is in quantitative agreement with that computed from the surface pressure distribution, which confirms the leading role of the pressure forcing for finite amplitude gravity waves. The phase shift and the amplitude of the principal mode of surface pressure distribution are systematically reported, to provide direct evidence for possible wind wave growth theories. Intermittent and localised airflow separation is observed for steep waves with small wave age, but its effect on setting the phase-averaged pressure distribution is not drastically different from that of non-separated sheltering. We find that the wave form drag force is not a strong function of wave age but closely related to wave steepness. In addition, the history of wind wave coupling can affect the wave form drag, due to the wave crest shape and other complex coupling effects. The normalised wave growth rate we obtain agrees with previous studies. We make an effort to clarify various commonly adopted underlying assumptions, and to reconcile the scattering of the data between different previous theoretical, numerical and experimental results, as we revisit this longstanding problem with new numerical evidence.
“…As our theory neglects the outer fluid, the ratios and have both been chosen to be quite small to minimise the dynamics of the outer fluid. Basilisk is based on the volume-of-fluid algorithm and the solver has been extensively benchmarked for unsteady two-phase flows (Farsoiya, Mayya & Dasgupta 2017; Singh, Farsoiya & Dasgupta 2019; Mostert & Deike 2020; Basak, Farsoiya & Dasgupta 2021; Farsoiya, Popinet & Deike 2021; Ramadugu, Perlekar & Govindarajan 2022). A comprehensive list of publications based on the Basilisk solver is provided in Popinet (2014).…”
We demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh–Plateau (RP) instability on a liquid cylinder by subjecting it to a radial oscillatory body force. Viscosity is found to play a crucial role in this stabilisation. Linear stability predictions are obtained via Floquet analysis demonstrating that RP unstable modes can be stabilised using radial forcing. We also solve the linearised, viscous initial-value problem for free-surface deformation obtaining an equation governing the amplitude of a three-dimensional Fourier mode. This equation generalizes the Mathieu equation governing Faraday waves on a cylinder derived earlier in Patankar et al. (J. Fluid Mech., vol. 857, 2018, pp. 80–110), is non-local in time and represents the cylindrical analogue of its Cartesian counterpart (Beyer & Friedrich, Phys. Rev. E, vol. 51, issue 2, 1995, p. 1162). The memory term in this equation is physically interpreted and it is shown that, for highly viscous fluids, its contribution can be sizeable. Predictions from the numerical solution to this equation demonstrate the predicted RP mode stabilisation and are in excellent agreement with simulations of the incompressible Navier–Stokes equations (up to the simulation time of several hundred forcing cycles).
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