A multifractal model for the momentum transfer process in wall-bounded flows.

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Multifractal Analysis

Background:

• Turbulent kinetic energy cascades are modeled as multiplicative processes using multifractal formalism.
• The behavior of momentum cascades in wall-bounded turbulent flows remains less understood.
• Existing models often focus on energy transfer, not momentum dynamics in confined flows.

Purpose of the Study:

• To investigate the applicability of multifractal formalism to momentum cascading in wall-bounded turbulence.
• To propose and validate a multifractal model for streamwise wall-shear stress fluctuations.
• To characterize the momentum cascade as either multiplicative or additive.

Main Methods:

• Applied multifractal formalism to analyze the momentum cascade process.
• Developed a model for low-pass filtered streamwise wall-shear stress fluctuations (${\tau }_l^{\text{'}}$).
• Utilized direct numerical simulation (DNS) data of channel flow at $R{e}_{\tau }$ = 4200 for validation.

Main Results:

• The momentum cascade in wall-bounded flows is demonstrated to be an additive process.
• The proposed multifractal model accurately describes flow kinematics.
• Key scaling laws were identified: $〈{\tau }^{\text{'}2}〉~\text{log}\left(R{e}_{\tau }\right)$ and $〈\text{exp}\left(p{\tau }_l^{\text{'}}\right)〉~{(L/l)}^{{\zeta }_p}$ in the log-region.

Conclusions:

• Multifractal formalism is a viable tool for modeling momentum cascades in wall-bounded turbulence.
• The additive nature of the momentum cascade distinguishes it from kinetic energy cascades.
• The findings provide new insights into the scaling and statistical properties of wall-bounded turbulence.