Effects of Numerical Resolution on Simulated Cloud-Wind Interactions

Mixing by hydrodynamical instabilities plays a key role in cloud-wind interactions, causing cloud destruction in the adiabatic limit and facilitating cloud survival with efficient radiative cooling. However, the rate of mixing in numerical simulations is sensitive to the smallest resolved scale, and the relationship between resolution and cloud evolution is under-explored. Using a set of cloud-crushing simulations, we investigate the effects of numerical resolution on cloud survival and acceleration. Modeling both adiabatic and radiative cases, in a subsonic and supersonic wind, we find that cloud survival and velocity does depend on the numerical resolution, however, no single resolution requirement can be applied to all scenarios. In the radiative subsonic case, we find that mass growth and acceleration appear converged at only 4 cells per cloud radius. Conversely, in the supersonic regime, we see a clear dependence of cloud destruction and velocity on resolution that is not converged even at 48 cells per cloud radius, implying that accurately capturing cloud destruction may require higher resolution than capturing growth. We also present a simple model illustrating how ram pressure accelerates cool clouds at early times before mixing kicks in as an acceleration mechanism.

💡 Research Summary

This paper investigates how numerical resolution influences the evolution of cold clouds embedded in hot galactic winds, focusing on both cloud survival (mass retention) and acceleration. The authors perform a suite of idealized “wind‑tunnel” simulations using the Cholla hydrodynamics code, varying the number of cells per cloud radius (R = 4, 8, 16, 32, 48). Four physical setups are explored: adiabatic subsonic (a100), adiabatic supersonic (a1000), radiative cooling subsonic (r100), and radiative cooling supersonic (r1000). All clouds have a radius of 50 pc, a density contrast χ = 10², and are initially in pressure equilibrium with a wind of n_w = 0.01 cm⁻³, T_w = 10⁶ K. The wind speeds are 100 km s⁻¹ (Mach 0.66) and 1000 km s⁻¹ (Mach 6.6).

Key diagnostics are the cloud mass fraction M_cl/M₀ and the mass‑weighted mean velocity ⟨v_x⟩/v_w, measured for cells with density ≥ (1/3) ρ_cl,init. The authors also compare early‑time acceleration to a simple ram‑pressure model (dv/dt ≈ ρ_w v_w² / (ρ_cl R_cl)).

Results show a stark contrast between regimes. In the radiative subsonic case (r100), cloud mass growth and acceleration converge already at the lowest resolution (4 cells R⁻¹). The mixed gas cools rapidly (t_cool,mix ≈ 0.002 t_cc), condenses onto the cloud, and the cloud survives for many crushing times. By contrast, the radiative supersonic case (r1000) exhibits strong resolution dependence: even at 48 cells R⁻¹ the cloud destruction time and terminal velocity have not converged, and intermediate resolution (R = 16) oddly retains more mass than both lower and higher resolutions. This reflects the heightened role of shock‑induced Kelvin‑Helmholtz and Rayleigh‑Taylor instabilities, whose growth rates are highly sensitive to the smallest resolved scale.

Adiabatic runs display non‑monotonic trends. The lowest resolution clouds are destroyed quickly, but the R = 16 case retains mass longer than both R = 8 and R = 48, suggesting that numerical diffusion and artificial viscosity affect mixing in competing ways.

Early in the simulations (t ≲ 2 t_cc) all models follow the ram‑pressure acceleration curve closely, confirming that ram pressure dominates the initial momentum transfer. At later times, mixing‑driven acceleration becomes important, and the measured velocities fall below the ram‑pressure prediction because a fraction of the mixed gas is excluded by the density threshold, biasing the average toward denser, slower material.

The authors discuss implications for cosmological galaxy‑formation simulations. For subsonic, radiatively cooling winds, a modest resolution of ~4 cells per cloud radius suffices to capture the essential physics, offering substantial computational savings. However, for supersonic winds—common in starburst‑driven outflows—current typical resolutions (≤ 48 cells R⁻¹) are insufficient to achieve convergence in cloud destruction or acceleration. Consequently, sub‑grid models that encapsulate unresolved mixing and cooling processes are likely required, or simulations must aim for much higher resolution (≥ 100 cells R⁻¹).

Overall, the study provides a quantitative benchmark for the resolution needed to model cloud‑wind interactions across different physical regimes, clarifies the transition from ram‑pressure‑dominated to mixing‑dominated acceleration, and highlights the necessity of careful resolution choices or sub‑grid prescriptions in large‑scale galaxy evolution models.