Roshko number#

Named after: Anatol Roshko (1923-2017).

$$\text{Ro}_s \stackrel{\text{def}}{=} \frac{f L^{2}}{\nu} \sim \frac{\text{vortex shedding}}{\text{viscous diffusion}}$$

Measures vortex-shedding frequency relative to viscous diffusion. It combines Strouhal and Reynolds effects for wake oscillations.

Name	Symbol	SI units	Dimension
frequency	$f$	$\mathrm{Hz}$	$\text T^{-1}$
characteristic length	$L$	$\mathrm{m}$	$\text L$
kinematic viscosity	$\nu$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$

Wake oscillations

Range	Regime	Description
0 – 1	viscous wake	Viscous diffusion is fast relative to the shedding time scale, suppressing organized vortex formation.
1 – 10	periodic shedding	Unsteady shedding and viscous diffusion are comparable, supporting coherent periodic wakes.
10 – ∞	high frequency shedding	Shedding is rapid compared with viscous diffusion and wake dynamics are dominated by inertia.

Name	Symbol	SI units	Dimension
frequency	\(f\)	\(\mathrm{Hz}\)	\(\text T^{-1}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
kinematic viscosity	\(\nu\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)