Systematic parameter-space characterization of turbulent wake dynamics

Determine how vortex shedding, self-similar scaling exponents, drag force, and the transition between laminar and turbulent wake dynamics depend on the boosted black-brane velocity and temperature, Gaussian source amplitude, widths and activation timescales, domain sizes, and spatial resolution, and establish whether an effective Reynolds-like number controls this transition.

Background

The simulations explore only a reference configuration and a limited set of variations in the background velocity, source amplitude, and source widths. Although the broad wake phenomenology appears stable, the paper does not systematically determine when vortex shedding begins, how the scaling laws and drag change across regimes, or whether the dynamics can be organized by a Reynolds-like control parameter. The authors identify the source and background parameters, as well as the domain and resolution, as relevant variables for such a study.

References

A systematic study is left for future work. The relevant parameters are: the background velocity $U_x$ and temperature $T$ of the boosted black brane, which together characterise the unperturbed flow; the amplitude $A$, characteristic widths $\sigma_x$, $\sigma_y$, and activation timescales $v_0$ and $\tau$ of the Gaussian source, which determine the strength and geometry of the tidal deformation; and the longitudinal and transverse domain sizes $L_x$ and $L_y$ together with the spatial resolution, which set the range of scales available to the wake. A full exploration of this parameter space would in particular aim to identify the onset of vortex shedding as a function of these parameters, to characterise how the self-similar scaling exponents and the drag force vary across the turbulent regime, and to determine whether an effective Reynolds-like number can be constructed that controls the transition between laminar and turbulent wake dynamics, for instance, a heuristic combination of $U_x$, a characteristic length scale such as $\sigma_x$ or $L_y$, and an effective viscosity estimated from the dual CFT via $\eta/s = 1/4\pi$, which could at least order the scan even in the absence of a rigorously defined holographic Reynolds number.

— Turbulent gravitational waves  (2609.18295 - Taiocchi et al., 16 Sep 2026) in Section 4, Results, final paragraph of the parameter-space discussion

This condition is not satisfied in our reference simulation, and we therefore defer a quantitative determination of the drag to future work with larger domains. A full exploration of how $F_d$ depends on background velocity, source amplitude, and obstacle size, and in particular whether it exhibits signatures distinguishing turbulent from laminar wakes, would also be of great interest.

— Turbulent gravitational waves  (2609.18295 - Taiocchi et al., 16 Sep 2026) in Section Discussion, paragraph beginning “A natural quantity to compute is the drag force”

We note that the convergence study presented above is performed at the level of the qualitative flow structure rather than the fitted self-similar exponent $a$ itself; a dedicated convergence study of the fitted scaling exponents is left for future work, together with the systematic parameter-space exploration discussed in Section 4.

— Turbulent gravitational waves  (2609.18295 - Taiocchi et al., 16 Sep 2026) in Appendix, Section “Turbulent wake: convergence test”, final paragraph