scholarly journals Rotations of small, inertialess triaxial ellipsoids in isotropic turbulence

2017 ◽  
Vol 821 ◽  
pp. 517-538 ◽  
Author(s):  
Nimish Pujara ◽  
Evan A. Variano
Keyword(s):  
Angular Velocity ◽  
Strain Rate ◽  
Rotational Motion ◽  
Isotropic Turbulence ◽  
Direct Numerical Simulations ◽  
Homogeneous Isotropic Turbulence ◽  
Particle Rotation ◽  
Principal Axes ◽  
Total Particle ◽  
Angular Velocities

The statistics of rotational motion of small, inertialess triaxial ellipsoids are computed along Lagrangian trajectories extracted from direct numerical simulations of homogeneous isotropic turbulence. The total particle angular velocity and its components along the three principal axes of the particle are considered, expanding on the results of Chevillard & Meneveau (J. Fluid Mech., vol. 737, 2013, pp. 571–596) who showed results of the rotation rate of the particle’s principal axes. The variance of the particle angular velocity, referred to as the particle enstrophy, is found to increase as particles become elongated, regardless of whether they are axisymmetric. This trend is explained by considering the contributions of vorticity and strain rate to particle rotation. It is found that the majority of particle enstrophy is due to fluid vorticity. Strain-rate-induced rotations, which are sensitive to shape, are mostly cancelled by strain–vorticity interactions. The remainder of the strain-rate-induced rotations are responsible for weak variations in particle enstrophy. For particles of all shapes, the majority of the enstrophy is in rotations about the longest axis, which is due to alignment between the longest axis and fluid vorticity. The integral time scale for particle angular velocities about different axes reveals that rotations are most persistent about the longest axis, but that a full revolution is rare.

The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence

1998 ◽  
Vol 377 ◽  
pp. 65-97 ◽  
Author(s):  
KEIKO K. NOMURA ◽  
GARY K. POST
Keyword(s):  
Isotropic Turbulence ◽  
High Amplitude ◽  
Direct Numerical Simulations ◽  
Principal Strain ◽  
Homogeneous Isotropic Turbulence ◽  
Physical Processes ◽  
Structure And Dynamics ◽  
Principal Axes ◽  
Non Local ◽  
Burgers Vortices

The structure and dynamics of vorticity ω and rate of strain S are studied using direct numerical simulations (DNS) of incompressible homogeneous isotropic turbulence. In particular, characteristics of the pressure Hessian Π, which describe non-local interaction of ω and S, are presented. Conditional Lagrangian statistics which distinguish high-amplitude events in both space and time are used to investigate the physical processes associated with their evolution. The dynamics are examined on the principal strain basis which distinguishes vortex stretching and induced rotation of the principal axes of S. The latter mechanism is associated with misaligned ω with respect to S, a condition which predominates in isotropic turbulence and is dynamically significant, particularly in rotation-dominated regions of the flow. Locally-induced rotation of the principal axes acts to orient ω towards the direction of either the intermediate or most compressive principal strain. The tendency towards compressive straining of ω is manifested at the termini of the high-amplitude tube-like structures in the flow. Non-locally-induced rotation, associated with Π, tends to counteract the locally-induced rotation. This is due to the strong alignment between ω and the eigenvector of Π corresponding to its smallest eigenvalue and is indicative of the controlling influence of the proximate structure on the dynamics. High-amplitude rotation-dominated regions deviate from Burgers vortices due to the misalignment of ω. Although high-amplitude strain-dominated regions are promoted primarily by local dynamics, the associated spatial structure is less organized and more discontinuous than that of rotation-dominated regions.

Non-Gaussianity in turbulent relative dispersion

2019 ◽  
Vol 867 ◽  
pp. 877-905
Author(s):  
B. J. Devenish ◽  
D. J. Thomson
Keyword(s):  
Stochastic Model ◽  
Velocity Distribution ◽  
Relative Velocity ◽  
Isotropic Turbulence ◽  
Dispersion Model ◽  
Original Model ◽  
Direct Numerical Simulations ◽  
Relative Dispersion ◽  
Lagrangian Stochastic Model ◽  
Homogeneous Isotropic Turbulence

We present an extension of Thomson’s (J. Fluid Mech., vol. 210, 1990, pp. 113–153) two-particle Lagrangian stochastic model that is constructed to be consistent with the $4/5$ law of turbulence. The rate of separation in the new model is reduced relative to the original model with zero skewness in the Eulerian longitudinal relative velocity distribution and is close to recent measurements from direct numerical simulations of homogeneous isotropic turbulence. The rate of separation in the equivalent backwards dispersion model is approximately a factor of 2.9 larger than the forwards dispersion model, a result that is consistent with previous work.

scholarly journals Angular velocity of rotation of extended bodies in general relativity

1996 ◽  
Vol 172 ◽  
pp. 309-320
Author(s):  
S.A. Klioner
Keyword(s):  
General Relativity ◽  
Angular Velocity ◽  
Rigid Body ◽  
Rotational Motion ◽  
The Body ◽  
Astronomical Observations ◽  
Newtonian Approximation ◽  
Accurate Definition ◽  
Principal Axes ◽  
Definition Of

We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

Direct Numerical Simulations of Colliding Particles Suspended in Homogeneous Isotropic Turbulence

2009 ◽  
Author(s):  
M. Ernst ◽  
M. Sommerfeld
Keyword(s):  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Stokes Number ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Collision Rate ◽  
Homogeneous Isotropic Turbulence ◽  
And Performance ◽  
Fluid Behaviour

Direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed to characterize the collision rate as a function of different particle properties. The fluid behaviour is computed using a three-dimensional Lattice Boltzmann Method including a spectral forcing scheme to generate the turbulence field. Under assumption of mass points, the transport of spherical particles is modelled in a Lagrangian frame of reference. In the simulations the influence of the particle phase on the fluid flow is neglected. The detection and performance of inelastic interparticle collisions are based on a deterministic collision model. Different studies with monodisperse particles are considered. According to the executed simulations, particles with small Stokes number possess a collision rate similar to the prediction of Saffman and Turner [1], whereas particles with larger Stokes numbers behave similarly to the theory of Abrahamson [2].

Evolution of enstrophy in shock/homogeneous turbulence interaction

2012 ◽  
Vol 707 ◽  
pp. 74-110 ◽  
Author(s):  
Krishnendu Sinha
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Interaction Analysis ◽  
Direct Numerical Simulations ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Flow ◽  
Linear Interaction

AbstractInteraction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier–Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of$k$–$\epsilon $equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock–boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

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