Jonas Boschung

The local topology of stream- and vortex lines in turbulent flows

Tangent lines to a given vector field, such as streamlines or vortex lines, define a local unit vector t that points everywhere in the lines direction. The local behavior of the lines is characterized by the eigenvalues of the tensor T=∇·t. In case of real eigenvalues, t can be interpreted as a normal vector to a surface element, whose shape is defined by the eigenvalues of T. These eigenvalues can be used to define the mean curvature −H and the Gaussian curvature K of the surface. The mean curvature −H describes the relative change of the area of the surface element along the field line and is a measure for the local relative convergence or divergence of the lines. Different values of (H, K) determine whether field lines converge or diverge (elliptic concave or elliptic convex surface element, stable/unstable nodes), converge in one principal direction and diverge in another (saddle) or spiral inwards or outwards (stable/unstable focus). In turbulent flows, a plethora of local field line topologies are ...

Exact relations between the moments of dissipation and longitudinal velocity derivatives in turbulent flows.

Following an approach by Siggia, we present coefficients C(n) relating the moments of the dissipation of kinetic energy 〈ɛ〉 and the longitudinal velocity gradient 〈∂u(1)/∂x(1)〉 under the assumption of isotropy and continuity. Particularly, we find that the moment 〈ɛ(n)〉 of order n is completely determined by 〈(∂u(1)/∂x(1))(2n)〉 and an order- (and viscosity-) dependent coefficient for all n under the assumption of (local) isotropy. This implies that all theories which specify 〈ɛ(n)〉 also implicitly determine 〈(∂u(1)/∂x(1))(2n)〉 and vice versa. As a corollary to the direct connection between the moments of the dissipation and the longitudinal velocity gradient, the even standardized moments of order 2n of ∂u(1)/∂x(1) (flatness, hyperflatness, and so on) are directly related to the ratio of the moments 〈ɛ(n)〉/〈ɛ〉(n). We compare the theoretical values of the coefficients C(n) up to n=6 with homogeneous isotropic DNS data ranging from Re(λ)=88 to Re(λ)=529.

Analysis of structure function equations up to the seventh order

ABSTRACTWe examine balances of structure function equations up to the seventh order N = 7 for longitudinal, mixed and transverse components. Similarly, we examine the traces of the structure function equations, which are of interest because they contain invariant scaling parameters. The trace equations are found to be qualitatively similar to the individual components equations. In the even-order equations, the source terms proportional to the correlation between velocity increments and the pseudo-dissipation tensor are significant, while for odd N, source terms proportional to the correlation of velocity increments and pressure gradients are dominant. Regarding the component equations, one finds under the inertial range assumptions as many equations as unknown structure functions for even N, i.e. can solve for them as function of the source terms. On the other hand, there are more structure functions than equations for odd N under the inertial range assumptions. Similarly, there are not enough linearly ...

Statistical Description of Streamline Segments in a Turbulent Channel Flow with a Wavy Wall

In this study we investigate the statistical properties of so called streamline segments in a turbulent channel flow with one plane and one wavy wall. We give a short overview of the concept of streamline segments and recent results in description and modeling in this field. We find that streamline segments in the vicinity of the wavy wall are significantly smaller on average than in the core region. However, normalizing the length distribution with the mean segment length leads to an almost perfect collapse of the pdfs. This quasi-universal behavior is further highlighted by the comparison to statistics of streamline segments in homogeneous isotropic turbulence. Finally, we investigate the kinematic behavior of streamline segments by means of conditional moments and show differences in scaling behavior compared to the classical structure function analysis.

Streamlines in stationary homogeneous isotropic turbulence and fractal-generated turbulence

We compare streamline statistics in stationary homogeneous isotropic turbulence and in turbulence generated by a fractal square grid. We examine streamline segments characterised by the velocity difference and the distance l between extremum points. We find close agreement between the stationary homogeneous isotropic turbulence and the decay region of the fractal-generated turbulence as well as the production region of the fractal flow for small segments. The statistics of larger segments are very similar for the isotropic turbulence and the decay region, but differ for the production region. Specifically, we examine the first, second and third conditional mean . Noticeably, non-vanishing for are due to an asymmetry of positive and negative segments, i.e. those for which and , respectively. This asymmetry is not only kinematic, but is also due to dissipative effects and therefore contains cascade information.