Turbulence dynamics in separated flows: the generalised Kolmogorov equation for inhomogeneous anisotropic conditions

Abstract

The generalised Kolmogorov equation is used to describe the scale-by-scale turbulence dynamics in the shear layer and in the separation bubble generated by a bulge at one of the walls in a turbulent channel flow. The second-order structure function, which is the basis of such an equation, is used as a proxy to define a scale-energy content, that is an interpretation of the energy associated with a given scale. Production and dissipation regions and the flux interchange between them, in both physical and separation space, are identified. Results show how the generalised Kolmogorov equation, a five-dimensional equation in our anisotropic and strongly inhomogeneous flow, can describe the turbulent flow behaviour and related energy mechanisms. Such complex statistical observables are linked to a visual inspection of instantaneous turbulent structures detected by means of the Q-criterion. Part of these turbulent structures are trapped in the recirculation where they undergo a pseudo-cyclic process of disruption and reformation. The rest are convected downstream, grow and tend to larger streamwise scales in an inverse cascade. The classical picture of homogeneous isotropic turbulence in which energy is fed at large scales and transferred to dissipate at small scales does not simply apply to this flow where the energy dynamics strongly depends on position, orientation and length scale.

Investigation of the dynamics in separated turbulent flow

“…11 for Re τ = 125, the propagating vortices are nearly circular with a radius of approximately H/2 stretching into elliptical shapes further downstream. This phenomenon is also previously observed by Mollicone et al [10]. The fluctuating spanwise vorticity field, shown in Fig.…”

“…Many research activities have been focused on relatively simple academic configurations such as a rounded ramp [5], a bump [6], a wall-mounted bump [7][8][9][10], a backward facing step [11] or a thick flat plate [12,13].…”

“…The anisotropy of the different scales are also highlighted through the deviatoric components of the Reynolds stresses aiming to improve turbulence modeling for separated flows. Mollicone et al [10] expanded these analyses by trying to identify the link with coherent structures through the generalized Kolmogorov equation (GKE). However, a further understanding onto the role of coherent vortical motion and flow unsteadiness are not discussed by Mollicone et al [9] and Mollicone et al [10].…”

Liquid transport in scale space

“…As per Mollicone et al (2018), it is convenient to introduce the flux convection velocities in either the r-or X-space…”

Analyzing the spectral energy cascade in turbulent channel flow

“…In a recent important study, Mollicone et al 21 have contributed a study of energy cascades in physical space using a generalised Kolmogorov equation. They extended the comprehension of the production and transfer of turbulent kinetic energy (TKE) in the combined position/scale spaces for a more complex geometry, a separation bubble generated by a bulge at a turbulent plane channel flow.…”