Population Distribution in the Wake of a Sphere

Abstract

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.

Supersaturation in the Wake of a Precipitating Hydrometeor and Its Impact on Aerosol Activation

“…The statistics of the bright-colored supersaturated region in Figure 1a shows the evolution ∝S −2 in Figure 1b. This scaling in the distribution of the samples follows a Cauchy-Lorentz function, which is detailed in Bhowmick et al (2020), and appears as a typical feature in the spatial distribution of the momentum and the transported scalars in the steady wake regime due to the balance between the advection and the diffusion. This trend of S −2 ceases around S ≥ 0.13, which is the highest magnitude of S reached within the boundary layer and in the recirculating zone behind the hydrometeor in Figure 1a.…”

“…The surface of the hydrometeor is no‐slip at zero velocity and with a constant temperature T p and water vapor density , which is saturated at T p according to Maxwell diffusion model. The transport of momentum and scalars in the steady wake of a sphere is discussed in Bhowmick et al (2020) using the same numerical method.…”

Laminar supersonic sphere wake unstable bifurcations

“…The incompressible behavior of the space-time dynamics of a flow past a sphere has been well documented in the past both experimentally [1][2][3][4][5] and numerically. [6][7][8][9][10][11][12][13][14] While the interest of the scientific community for the incompressible regime is still very high and numerous studies have been recently done, [15][16][17][18][19][20] very limited information exists regarding the effects of compressibility, especially at supersonic speeds.…”