Turbulent Energy Balance and Spectra of the Axisymmetric Wake

Abstract

Axisymmetric turbulent wake behind a sphere in an incompressible fluid has been experimentally investigated from 50 to 300 diam downstream from the sphere at Reynolds numbers from 4000 to 150 000. Mean and turbulent velocity measurements show that the region of self-preservation starts 50 sphere diam downstream, and the virtual origin of the wake is 12 sphere diam downstream. Detailed measurements were made in the self-preserving region of the wake. The three components of the turbulent velocity, turbulent shear, and the mean velocity defect were measured across the wake using the hot-wire anemometer. From the measurements the turbulent energy production, dissipation, convection, and diffusion across the wake were determined. The one-dimensional energy spectra of the three components of the turbulent velocity, their dependence on distance along and across the wake and on Reynolds number have been measured. The large scale motion (low wavenumbers) is dynamically similar and the small scale motion (large wavenumbers) exhibits Kolmogoroff's universal equilibrium. The present spectral measurements are compared with other published measurements of the universal equilibrium spectra in various turbulent flows.

Direct numerical simulation of axisymmetric wakes embedded in turbulence

“…Individual profiles were obtained by appropriate circumferential and axial averaging and collapsed quite well for each time within the self-similar period (t > 125), so the profiles shown are those resulting from timeaveraging over that period. They agree qualitatively with previously reported data (for example Uberoi & Freymuth 1970) but, as mentioned in § 1, quantitative agreement might not be expected unless sufficient time has elapsed (or downstream distance is great enough, in the spatial case). In fact, the profiles are quantitatively quite close Finally, once all the wake properties were extracted the TKE balance was calculated using the following equation: Note that the boundary layer approximation has been used and, in computing the dissipation term ( ), local isotropy of the smallest scales of motion was assumed.…”

“…from gradients of triple velocity and pressure-velocity products) were found to be too scattered -an even longer domain would have been required to reduce the scatter. The transport term was therefore deduced as the balance from the other terms, as is often done in experimental studies, for just the same reasons (see Uberoi & Freymuth 1970, for example). Figure 5(b) shows the resulting TKE balance.…”

Interactions between aquatic plants and turbulent flow: a field study using stereoscopic PIV

“…The ratio between the local production and the mean convection terms, 3.8 in the near wake, suggests that the u u field near the shear layer is dominated by local rather than upstream generation processes. This result is consistent with a plane mixing layer (Wygnanski & Fiedler 1970), but differs from many separated flows which feature a region where convection is the dominant gain term, for example the axisymmetric wake (Uberoi & Freymuth 1970) and the wake of a surface-mounted cube (Hussein & Martinuzzi 1996). The turbulent transport term in the u u budget is a loss near the shear layer and a gain at both higher and lower elevations.…”

Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers

“…11 and 22). It is easily observable that our spectral plots mimic those of Uberoi and Freymuth 44 and Gourlay et al 45 where similar effect of the local Reynolds number on the inertial sub-range of turbulent wake flow was reported. In our case, the sub-range with k −5/3 dependence is completely absent for Re h = 1500, until at least x/h ≈ 100 when the local Reynolds number is sufficiently large (i.e., = 16 500 propagated only up to x/h ≈ 30 to develop the k −5/3 zone, which had actually acquired Re y0.5 (x) ≈ 18 000 (Fig.…”