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This numerical study investigates steady separated flow past a grooved circular cylinder within the Reynolds number range $7.5\le R{e}_D\le 30$, comprising variations in groove depth ($h$) and spacing ($\beta$). The groove width ($w$) is kept constant, while h/w varies across four levels ($0.5\le h/w\le 2$) and $\beta$ across five angles ($10°\le \beta \le 45°$). The results exhibit strong agreement with unbounded flow data, confirming blockage independence across the examined regime. Detailed analysis shows that $\beta$ has a stronger influence than $h/w$ on surface-pressure-dependent variables ($C_{p,0}$, $C_{p,b}$, $C_D$, ${\theta }_{sep}$) and wake-defining parameters ($L_w$, $W_w$, $\xi$, $\eta$), underscoring the dominant role of $\beta$ in rectilinear groove aerodynamics. In this regard, a critical spacing of $\beta =20°$ is observed, beyond which the sensitivity of the parameters toward the cylinder configuration decreases. Thus, significant flow control and drag reduction are attained for $R{e}_D=7.5$ at the lowest spacing $\beta =10°$, regardless of the groove’s $h/w$. Among these, the streamwise-oriented variables, $C_{p,0}$, $C_D$, $L_w$, $\xi$, and $u_{min}$, exhibit monotonic trend with respect to $\beta$ and are modeled using power-law relations. The models for $C_{p,0}$ and $C_D$ exhibit significant accuracy with $R^2\approx 0.999$ across all $\beta$ values considered, while it is 0.89–0.98 for $L_w$, $\xi$, and $u_{min}$, depending on $R{e}_D$. Transverse-oriented parameters ($W_w\mathrm{a}\mathrm{n}\mathrm{d}\eta$) vary non-monotonically. In addition, it is found that the streamwise locations of maximum wake width ($x_{w,max}$) and minimum velocity ($x_{u,min}$) are unaffected by the grooved cylinder configuration. Full article

The physics of heat and mass transfer from an object in its wake has significant importance in natural phenomena as well as across many engineering applications. Here, we report numerical results on the population density of the spatial distribution of fluid velocity, pressure, scalar concentration, and scalar fluxes of a wake flow past a sphere in the steady wake regime (Reynolds number 25 to 285). Our findings show that the spatial population distributions of the fluid and the transported scalar quantities in the wake follow a Cauchy-Lorentz or Lorentzian trend, indicating a variation in its sample number density inversely proportional to the squared of its magnitude. We observe this universal form of population distribution both in the symmetric wake regime and in the more complex three dimensional wake structure of the steady oblique regime with Reynolds number larger than 225. The population density distribution identifies the increase in dimensionless kinetic energy and scalar fluxes with the increase in Reynolds number, whereas the dimensionless scalar population density shows negligible variation with the Reynolds number. Descriptive statistics in the form of population density distribution of the spatial distribution of the fluid velocity and the transported scalar quantities is important for understanding the transport and local reaction processes in specific regions of the wake, which can be used e.g., for understanding the microphysics of cloud droplets and aerosol interactions, or in the technical flows where droplets interact physically or chemically with the environment. Full article