4 results
The turbulent/non-turbulent interface in an inclined dense gravity current
- Dominik Krug, Markus Holzner, Beat Lüthi, Marc Wolf, Wolfgang Kinzelbach, Arkady Tsinober
-
- Journal:
- Journal of Fluid Mechanics / Volume 765 / 25 February 2015
- Published online by Cambridge University Press:
- 20 January 2015, pp. 303-324
-
- Article
- Export citation
-
We present an experimental investigation of entrainment and the dynamics near the turbulent/non-turbulent interface in a dense gravity current. The main goal of the study is to investigate changes in the interfacial physics due to the presence of stratification and to examine their impact on the entrainment rate. To this end, three-dimensional data sets of the density and the velocity fields are obtained through a combined scanning particle tracking velocimetry/laser-induced fluorescence approach for two different stratification levels with inflow Richardson numbers of $\mathit{Ri}_{0}=0.23$ and $\mathit{Ri}_{0}=0.46$, respectively, at a Reynolds number around $\mathit{Re}_{0}=3700$. An analysis conditioned on the instantaneous position of the turbulent/non-turbulent interface as defined by a threshold on enstrophy reveals an interfacial region that is in many aspects independent of the initial level of stratification. This is reflected most prominently in matching peaks of the gradient Richardson number $\mathit{Ri}_{g}\approx 0.1$ located approximately $10{\it\eta}$ from the position of the interface inside the turbulent region, where ${\it\eta}=({\it\nu}^{3}/{\it\epsilon})^{1/4}$ is the Kolmogorov scale, and ${\it\nu}$ and ${\it\epsilon}$ denote the kinematic viscosity and the rate of turbulent dissipation, respectively. A possible explanation for this finding is offered in terms of a cyclic evolution in the interaction of stratification and shear involving the buildup of density and velocity gradients through inviscid amplification and their subsequent depletion through molecular effects and pressure. In accordance with the close agreement of the interfacial properties for the two cases, no significant differences were found for the local entrainment velocity, $v_{n}$ (defined as the propagation velocity of an enstrophy isosurface relative to the fluid), at different initial stratification levels. Moreover, we find that the baroclinic torque does not contribute significantly to the local entrainment velocity. Comparing results for the surface area of the convoluted interface to estimates from fractal scaling theory, we identify differences in the interface geometry as the major factor in the reduction of the entrainment rate due to density stratification.
An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number
- MICHELE GUALA, ALEXANDER LIBERZON, ARKADY TSINOBER, WOLFGANG KINZELBACH
-
- Journal:
- Journal of Fluid Mechanics / Volume 574 / 10 March 2007
- Published online by Cambridge University Press:
- 15 February 2007, pp. 405-427
-
- Article
- Export citation
-
Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.
On the evolution of material lines and vorticity in homogeneous turbulence
- MICHELE GUALA, BEAT LÜTHI, ALEXANDER LIBERZON, ARKADY TSINOBER, WOLFGANG KINZELBACH
-
- Journal:
- Journal of Fluid Mechanics / Volume 533 / 25 June 2005
- Published online by Cambridge University Press:
- 15 June 2005, pp. 339-359
-
- Article
- Export citation
-
The evolution of material lines, $l$, and vorticity, $\omega$, is investigated experimentally through three-dimensional particle-tracking velocimetry (3D-PTV) in quasi-homogeneous isotropic turbulence at $Re_{\lambda }\,{=}\,50$. Through 3D-PTV data the full set of velocity derivatives, $\partial u_{i}/\partial x_{j}$, is accessible. This allows us to monitor the evolution of various turbulent quantities along fluid particle trajectories. The main emphasis of the present work is on the physical mechanisms that govern the Lagrangian evolution of $l$ and $\omega$ and the essential differences inherent in these two processes. For example, we show that vortex stretching is smaller than material lines stretching, i.e. $\langle\omega_{i}\omega_{j}s_{ij}/\omega^{2}\rangle \,{<}\,\langle l_{i}l_{j}s_{ij}/l^{2}\rangle$, and expand on how this issue is closely related to the predominant alignment of $\omega$ and the intermediate principal strain eigenvector $\lambda_{2}$ of the rate of strain tensor, $s_{ij}$. By focusing on Lagrangian quantities we discern whether these alignments are driven and maintained mainly by vorticity or by strain. In this context, the tilting of $\omega$ and the rotation of the eigenframe $\lambda_{i}$ of the rate of strain tensor $s_{ij}$ are investigated systematically conditioned on different magnitudes of strain, $s^{2}$, and enstrophy, $\omega^{2}$. Further, we infer that viscosity contributes through the term $\nu\omega_{i}\nabla^2\omega_{i}$ to ${\rm D}\omega^{2}/{\rm D}t$, whereas ${\rm D}l^{2}/{\rm D}t$ has no diffusive term. This difference plays a key role in defining the mutual orientation between $\omega$ and $\lambda_{i}$. Viscosity thus contributes significantly to the difference in growth rates of $\langle\omega_{i}\omega_{j}s_{ij}\rangle$ and $\langle l_{i}l_{j}s_{ij}\rangle$.
Lagrangian measurement of vorticity dynamics in turbulent flow
- BEAT LÜTHI, ARKADY TSINOBER, WOLFGANG KINZELBACH
-
- Journal:
- Journal of Fluid Mechanics / Volume 528 / 10 April 2005
- Published online by Cambridge University Press:
- 24 March 2005, pp. 87-118
-
- Article
- Export citation
-
The full set of velocity derivatives, $\partial u_{i}/\partial x_{j}$, is measured experimentally in a Lagrangian way in quasi-homogeneous isotropic turbulence. This is achieved by applying the three-dimensional particle tracking velocimetry (3D-PTV) technique to an electromagnetically forced flow with $\hbox{\it Re}_{\lambda}\,{\thickapprox}\,50$. Checks based on precise kinematic relations show that the technique presented measures the velocity derivatives with good accuracy. In a study on vorticity, characteristic properties of turbulent flows known from direct numerical simulations are reproduced. These are the positive skewness of the intermediate eigenvalue of the rate of strain tensor, $s_{ij}$, $\langle \Lambda_{2}\rangle \,{>}\,0$, the predominance of vortex stretching over vortex compression, $\langle \omega_{i}\omega_{j}s_{ij}\rangle \,{>}\,0$ and the predominant alignment of vorticity, ${\bm \omega}$, with the intermediate principal axis of strain, ${\bm \lambda}_{2}$. Results on the evolution in time of material lines, ${\bm l}$, compared to vortex lines, ${\bm \omega}$, are presented. They show that the nonlinear interaction of vorticity with the surrounding flow assists viscosity in maintaining this predominant ${\bm \lambda}_{2}$-alignment of vorticity. Lagrangian measurements of enstrophy budget terms suggest that there is no pointwise balancing of production and viscous reduction of enstrophy and that the role played by viscosity is of great importance.