Helmut Eckelmann

The wall region in turbulent shear flow

Hot-film measurements in a fully developed channel flow have been made in an attempt to gain more insight into the process of Reynolds stress production. The background for this effort is the observation of a certain sequence of events (deceleration, ejection and sweep) in the wall region of turbulent flows by Corino (1965) and Corino & Brodkey (1969). The instantaneous product signal uv was classified according to the sign of its components u and v , and these classified portions were then averaged to obtain their contributions to the Reynolds stress

The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow

-\rho\overline{uv}

Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow

. The signal was classified into four categories; the two main ones were that with u negative and v positive, which can be associated with the ejection-type motion of Corino & Brodkey (1969), and that with u positive and v negative, associated with the sweep-type motion. It was found that over the wall region investigated, 3·5 [les ] y [les ] 100, these two types of motion give rise to a stress considerably greater than the total Reynolds stress. Two other types of motion, (i) u negative, v negative, corresponding to low-speed fluid deflected towards the wall, and (ii) u positive, v positive, corresponding to high-speed fluid reflected outwards from the wall, were found to account for the ‘excess’ stress produced by the first two categories, which give contributions of opposite sign. The autocorrelations of the classified portions of uv were obtained to determine the relative time scales of these four types of motion. The positive stress producing motions ( u v > 0 and u > 0, v u v u > 0, v > 0). It was further surmised that turbulent energy dissipation is associated with the Reynolds stress producing motions, since these result in localized shear regions in which the dissipation is several orders of magnitude greater than the average dissipation at the wall.

On the transition of the cylinder wake

Hot-film anemometer measurements have been carried out in a fully developed turbulent channel flow. An oil channel with a thick viscous sublayer was used, which permitted measurements very close to the wall. In the viscous sublayer between y + ≃ 0·1 and y + = 5, the streamwise velocity fluctuations decreased at a higher rate than the mean velocity; in the region y + [lsim ] 0·1, these fluctuations vanished at the same rate as the mean velocity. The streamwise velocity fluctuations u observed in the viscous sublayer and the fluctuations (∂ u /∂ y ) 0 of the gradient at the wall were almost identical in form, but the fluctuations of the gradient at the wall were found to lag behind the velocity fluctuations with a lag time proportional to the distance from the wall. Probability density distributions of the streamwise velocity fluctuations were measured. Furthermore, measurements of the skewness and flatness factors made by Kreplin (1973) in the same flow channel are discussed. Measurements of the normal velocity fluctuations v at the wall and of the instantaneous Reynolds stress −ρ uv were also made. Periods of quiescence in the − ρ uv signal were observed in the viscous sublayer as well as very active periods where ratios of peak to mean values as high as 30:1 occurred.

The fluctuating wall‐shear stress and the velocity field in the viscous sublayer

Measurements of the three fluctuating components of the velocity and of the two components of the wall shear stress fluctuations have been made in a fully developed turbulent channel flow at Re=7700 using hot‐film probes. These measurements include rms values, skewness and flatness factors, and probability density functions. Although the wall region is emphasized here, information for the whole channel half‐width is also given.

A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47<Re<2×105

The transition of the cylinder wake is investigated experimentally in a water channel and is computed numerically using a finite‐difference scheme. Four physically different instabilities are observed: a local ‘‘vortex‐adhesion mode,’’ and three near‐wake instabilities, which are associated with three different spanwise wavelengths of approximately 1, 2, and 4 diam. All four instability processes can originate in a narrow Reynolds‐number interval between 160 and 230, and may give rise to different transition scenarios. Thus, Williamson’s [Phys. Fluids 31, 3165 (1988)] experimental observation of a hard transition is for the first time numerically reproduced, and is found to be induced by the vortex‐adhesion mode. Without vortex adhesion, a soft onset of three‐dimensionality is numerically and experimentally obtained. A control‐wire technique is proposed, which suppresses transition up to a Reynolds number of 230.

Streamwise vortices associated with the bursting phenomenon

The fluctuating wall‐shear stress was measured with various types of hot‐wire and hot‐film sensors in turbulent boundary‐layer and channel flows. The rms level of the streamwise wall‐shear stress fluctuations was found to be 40% of the mean value, which was substantiated by measurements of the streamwise velocity fluctuations in the viscous sublayer. Heat transfer to the fluid via the probe substrate was found to give significant differences between the static and dynamic response for standard flush‐mounted hot‐film probes with air or oil as the flow medium, whereas measurements in water were shown to be essentially unaffected by this problem.

Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number

Based on experiments a new law is proposed for the vortex shedding from a circular cylinder which describes in a consistent way the Strouhal–Reynolds-number dependency as Sr=Sr*+m/Re from the beginning of the vortex shedding at Re=47 up to the laminar–turbulent transition of the cylinder boundary layer at Re>2×105. The various vortex shedding processes, occurring with increasing Reynolds number, are described by different coefficients Sr* and m.

Some properties of truncated turbulence signals in bounded shear flows

The streamwise and spanwise velocity components and the gradients of these components normal to the wall were examined by using hot-film sensors and flush-mounted wall elements to study the vortex structures associated with the bursting phenomenon. Quadrant probability analysis and conditional sampling techniques indicated that pairs of counter-rotating streamwise vortices occur frequently in the wall region of a bounded turbulent shear flow. A streamwise momentum defect occurred between the vortices as low-speed fluid was ‘pumped’ away from the wall by the vortex pair. The defect region was long and narrow and possibly forms the low-speed streak as observed in visualization studies. The velocity defect was terminated by a strong acceleration followed by a high speed region.

A global stability analysis of the steady and periodic cylinder wake

Based on the observation of vortex splitting in the laminar wake of thin flat plates placed parallel to the flow, an investigation on the consequences of such events for the von Karman vortex street in the wake of circular cylinders was carried out. It was found that a ‘‘design break line’’ of vortex axes can lead to the decoupling of a wake flow from the always present disturbances deriving from the ends. The decoupling gives rise to parallel vortex shedding of a slightly higher frequency, instead of the oblique or slanted vortex shedding at a lower frequency usually observed.