scholarly journals Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

2008 ◽  
Vol 65 (6) ◽  
pp. 1955-1966 ◽  
Author(s):  
J. B. Marston ◽  
E. Conover ◽  
Tapio Schneider
Keyword(s):  
Numerical Simulations ◽  
Relaxation Times ◽  
Direct Numerical Simulations ◽  
Linear Relaxation ◽  
Critical Layer ◽  
Cumulant Expansion ◽  
Rotating Sphere ◽  
Equal Time ◽  
Barotropic Flow ◽  
Turbulent Statistics

Abstract Low-order equal-time statistics of a barotropic flow on a rotating sphere are investigated. The flow is driven by linear relaxation toward an unstable zonal jet. For relatively short relaxation times, the flow is dominated by critical-layer waves. For sufficiently long relaxation times, the flow is turbulent. Statistics obtained from a second-order cumulant expansion are compared to those accumulated in direct numerical simulations, revealing the strengths and limitations of the expansion for different relaxation times.

Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4

2007 ◽  
Vol 586 ◽  
pp. 259-293 ◽  
Author(s):  
F. X. TRIAS ◽  
M. SORIA ◽  
A. OLIVA ◽  
C. D. PÉREZ-SEGARRA
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Two Dimensional ◽  
Turbulent Statistics ◽  
Large Eddies ◽  
Three Dimensional Simulations

A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

scholarly journals Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re = 30 000

2013 ◽  
Vol 718 ◽  
pp. 398-427 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt
Keyword(s):  
Numerical Simulations ◽  
Outer Cylinder ◽  
Outer Region ◽  
Direct Numerical Simulations ◽  
Taylor Vortex ◽  
Scaling Exponent ◽  
Transverse Current ◽  
Counter Rotation ◽  
Turbulent Statistics ◽  
Taylor Couette

AbstractThe torque in turbulent Taylor–Couette flows for shear Reynolds numbers $R{e}_{S} $ up to $3\times 1{0}^{4} $ at various mean rotations is studied by means of direct numerical simulations for a radius ratio of $\eta = 0. 71$. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of $\Gamma = 2$, close to the torque maximum. The local transport resulting in the torque is investigated via the transverse current ${J}^{\omega } $ which measures the transport of angular momentum and can be computed from the velocity field. The typical spatial distribution of the individual convective and viscous contributions to the local torque is analysed for a turbulent flow case. To characterize the turbulent statistics of the transport, probability density functions (p.d.f.s) of local current fluctuations are compared with experimental wall shear stress measurements. P.d.f.s of instantaneous torques reveal a fluctuation enhancement in the outer region for strong counter-rotation. Moreover, we find for simulations realizing the same shear $R{e}_{S} \geq 2\times 1{0}^{4} $ the formation of a torque maximum for moderate counter-rotation with angular velocities ${\omega }_{o} \approx - 0. 4\hspace{0.167em} {\omega }_{i} $. In contrast, for $R{e}_{S} \leq 4\times 1{0}^{3} $ the torque features a maximum for a stationary outer cylinder. In addition, the effective torque scaling exponent is shown to also depend on the mean rotation state. Finally, we evaluate a close connection between boundary-layer thicknesses and the torque.

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