Logarithmic Mean Velocity Profile Research Articles

Vertical variability and effect of stability on turbulence characteristics down to the floor of a pine forest

Among the fundamental problems in canopy turbulence, particularly near the forest floor, remain the local diabatic effects and linkages between turbulent length scales and the canopy morphology. To progress on these problems, mean and higher order turbulence statistics are collected in a uniform pine forest across a wide range of atmospheric stability conditions using five 3-D anemometers in the subcanopy. The main novelties from this experiment are: (1) the agreement between second-order closure model results and measurements suggest that diabatic states in the layer above the canopy explain much of the modulations of the key velocity statistics inside the canopy except in the immediate vicinity of the trunk space and for very stable conditions. (2) The dimensionless turbulent kinetic energy in the trunk space is large due to a large longitudinal velocity variance but it is inactive and contributes little to momentum fluxes. (3) Near the floor layer, a logarithmic mean velocity profile is formed and vertical eddies are strongly suppressed modifying all power spectra. (4) A spectral peak in the vertical velocity near the ground commensurate with the trunk diameter emerged at a moderate element Reynolds number consistent with Strouhal instabilities describing wake production.

Reynolds number effects in a turbulent pipe flow for low to moderate Re

We present in this paper high resolution, two-dimensional LDV measurements in a turbulent pipe flow of water over the Reynolds number range 5000–25000. Results for the turbulence statistics up to the fourth moment are presented, as well as power spectra in the near-wall region. These results clearly show that the turbulence statistics scaled on inner variables are Reynolds-number dependent in the aforementioned range of Reynolds numbers. For example, the constants in the dimensionless logarithmic mean-velocity profile are shown to vary with Reynolds number. Our conclusion that turbulence statistics depend on the Reynolds number is consistent with results found in other flow configurations, e.g., a channel flow. Our results for the pipe flow, however, lead nevertheless to quite different tendencies.

A wind-tunnel boundary-layer study of the effects of a surface roughness change: Rough to smooth

The changes imposed on mean velocities and turbulence statistics in the lower atmosphere by an abrupt change in surface roughness, from very rough to smooth, were modelled in a wind tunnel. The influence of a change in the effective surface level, which often accompanies such a variation in surface roughness, was also studied. A deep, turbulent flow was generated upstream of the change, which had a logarithmic mean velocity profile and constant shear-stress for approximately 200 mm above the floor, except for a region near the surface which was influenced by the three-dimensional nature of the random rough surface.

Remarks on the Equilibrium Turbulent Boundary Layer

Two similarity laws are known for the mean-velocity profile in a turbulent boundary layer with constant pressure. These are Prandtl's law of the wall and Karman's momentum-defect law. The first law has recently been generalized empirically to flows with arbitrary pressure gradient by Ludwieg and Tillmann, and the second law to a certain class of equilibrium flows by F. Clauser. In the present paper it is shown that the pressure distribution corresponding to a given equilibrium flow cam be computed by assuming that a certain parameter D = (τ_w/q)dq/dτ_w is constant, where q and τ_w are the dynamic pressure in the free stream and the shearing stress at the wall, respectively. The hypothesis D = constant is suggested by a study of the integrated continuity equation and is supported by a rigorous analogy between the class of equilibrium flows defined by Clauser and the class of laminar flows studied by Falkner and Skan. The hypothesis D = constant is also verified using experimental data for several equilibrium turbulent flows and is interpreted physically from a kinematic point of view. Two hypothetical limiting cases of equilibrium flow are described. At one extreme is the boundary Layer in a sink flow, with a completely logarithmic mean-velocity profile outside the sublayer. At the other extreme is a continuously separating boundary layer in a dimensionless pressure gradient (x/q)dq/dx approximately twice that for the corresponding laminar flow. Typical shearing-stress profiles are computed for several equilibrium turbulent flows, including the two limiting cases.