GAMM2025

Session

PP05: Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness

PP05

8 Apr 2025, 14:00

Lecture and Conference Centre

Conveners

PP05: Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness: PP05.01

• Christian Rohde
• Qian Huang

743. Anomalous dissipation in compressible and incompressible flow

Georgy Zinchenko

08/04/2025, 14:00

The dissipative anomaly, known as the zeroth law of turbulence, states that the rescaled mean kinetic energy dissipation rate ⟨ε⟩ L/Urms³ remains constant in the bulk of a turbulent flow away from surfaces when the kinematic viscosity ν approaches zero. Here, L is a characteristic outer scale of the flow and Urms is the root mean square velocity.

The framework first suggested by Duchon and...

744. Multi-point probability density hierarchy for homogeneous isotropic turbulence

Simon Görtz

08/04/2025, 14:30

We analyze Lundgren's infinite multipoint hierarchy of probability density functions (PDFs) in the context of homogeneous isotropic turbulence (HIT). To account for the physical properties of HIT, we express the PDF in terms of the scalar invariants under the SO(3) group of rotations, yielding new coordinates for a homogeneous isotropic PDF and leading to a dimensional reduction of the...

745. Statistical conservation laws for the scalar and Navier-Stokes equations

Qian Huang

08/04/2025, 15:00

The statistical behaviors of hyperbolic conversation laws with random initial data and/or stochastic forcing terms are crucial for uncertainty quantification and deeper insights into turbulent flows. We start from derivations of known hierarchies governing the evolution of probability distribution functions f, and propose a new set of hierarchies relating locally higher-order spatial...

746. Toward machine-learned implicit large-eddy simulations of compressible turbulence

Deniz A. Bezgin

08/04/2025, 15:30

Flows with high Mach and Reynolds numbers exhibit pronounced multi-scale features due to turbulence and compressibility effects. Implicit large-eddy simulation (ILES) models for such flows require numerical discretizations with tailored truncation error properties, enabling coarse-resolution simulations to closely approximate low-pass filtered direct numerical simulation (DNS) data. These ILES...