Benchmark computations of normal and oblique dipole-wall collisions with a no-slip wall

Benchmark results are reported of two separate sets of numerical experiments on the collision of a dipole with a no-slip boundary at several Reynolds numbers. One set of numerical simulations is performed with a finite differences code while the other set concerns simulations conducted with a Chebyshev pseudospectral code. Well-defined initial and boundary conditions are used and the accuracy and convergence of the numerical solutions have been investigated by inspection of several global quantities like the total kinetic energy, the enstrophy and the total angular momentum of the flow, and the vorticity distribution at the no-slip boundaries. It is found that the collision of the dipole with the no-slip wall and the subsequent flow evolution is dramatically influenced by small-scale vorticity produced during and after the collision process. The trajectories of several coherent vortices are tracked during the simulation and show that in particular underresolved high-amplitude vorticity patches near the no-slip walls are potentially responsible for deteriorating accuracy of the computations. Our numerical simulations clearly indicate that it is extremely difficult to obtain mode or grid convergence for this seemingly rather simple two-dimensional vortex-wall interaction problem

Enhanced Vertical Inhomogeneity in Turbulent Rotating Convection

In this Letter we report experimental evidence that rotation enhances vertical inhomogeneity in turbulent convection, in spite of the increased columnar flow ordering under rotation. Measurements using stereoscopic particle image velocimetry have been carried out on turbulent rotating convection in water. At constant Rayleigh number Ra=1.11×109 several rotation rates have been used, so that the Rossby number takes values from Ro=[infinity] (no rotation) to 0.09 (strong rotation). The three-component velocity data, obtained at two vertical positions, are used to investigate the anisotropy of the flow through the invariants of the Reynolds-stress anisotropy tensor and the Lumley triangle, as well as to correlate the vertical velocity and vorticity. In the center plane rotation causes the turbulence to be “rodlike,” while closer to the top plate a trend toward isotropy is observed

Heat transfer in turbulent rotating convection

No abstract

Heat flux intensification by vortical flow localization in rotating convection

The effect of rotation on turbulent convective flow between parallel plates has been assessed with direct numerical simulations. With increasing rotation-rate an interesting transition is observed in the vertical-velocity skewness. This transition indicates a localization of motion directed away from the wall and correlates well with changes observed in the heat flux, as well as in the thermal and viscous boundary layer thicknesses. The formation of localized intense vortical structures provides for intensified vertical heat transport through Ekman pumping. At higher rotation-rates this is counteracted by the inhibition of vertical motion by rotation as expressed in the geostrophic thermal-wind balance

On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z ∝ Re0.8 and P ∝ Re2.25 for 5 × 102 ≤ Re ≤ 2 × 104 and Z ∝ Re0.5 and P ∝ Re1.5 for Re ≥ 2 × 104 (with Re based on the velocity and size of the dipole). A critical Reynolds number Rec(here, Rec ≈ 2 × 104) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z ∝ Re^3/4, P ∝ Re^9/4, and dP/dt ∝ Re11/4 in agreement with the numerically obtained scaling laws. For Re ≥ Rec the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z ∝ Re1/2 and P ∝ Re3/2

Energy spectra for decaying 2D turbulence in a bounded domain

New results are presented for the energy spectra of decaying 2D turbulence in a square container with no-slip walls for integral-scale Reynolds numbers up to 20 000. The one-dimensional energy spectra measured close to the walls reveal a k(-5/3) inertial range, instead of a k(-3) direct enstrophy cascade, due to the production of small-scale vorticity near no-slip boundaries. During the intermediate decay stage a k(-3) spectrum starts to emerge and the change in location of the injection scale of small-scale vorticity is explained in terms of an average boundary-layer thickness

Dissipation of kinetic energy in two-dimensional bounded flows

The role of no-slip boundaries as an enstrophy source in two-dimensional (2D) flows has been investigated for high Reynolds numbers. Numerical simulations of normal and oblique dipole-wall collisions are performed to investigate the dissipation of the kinetic energy E(t), and the evolution of the enstrophy [Omega] (t) and the palinstrophy P(t). It is shown for large Reynolds numbers that dE(t)/dt = ?2 [Omega] (t)/Re [[proportional]] 1/ [sqrt(Re)] instead of the familiar relation dE(t)/dt [[proportional]] 1/Re as found for 2D unbounded flow

The classical dipole-wall collision as a numerical benchmark problem

Abstract only

Quasi-two-dimensional turbulence in shallow fluid layers:The role of bottom friction and fluid layer depth

The numerical and experimental studies of the role of bottom friction and fluid layer depth on decaying quasi-two-dimensional turbulence enable several interesting observations. The numerical simulations showed that the evolution of vortex statistics of decaying 2D turbulence with bottom friction can be described by bottom-friction independent power laws. In the latter regime, the computed data showed a strong bottom-friction dependence and are strongly dominated by lateral diffusion.</p