The structure of turbulent shear-induced countercurrent flow

Abstract

Countercurrent flow is a generalized plane Couette flow in which a shear-induced drift current is opposed by a pressure-driven return flow such that the resulting mass flux is zero. This type of flow is encountered in both environmental fluid mechanics and tribology. Measurements are described that were undertaken in steady turbulent countercurrent flow, generated in a novel type of apparatus between smooth walls, at Reynolds numbers, expressed in terms of surface velocity and depth of the flow, from 200 to 20000; the critical Reynolds number of laminar to turbulent transition as determined herein is approximately 1750. The laboratory facility is explained, and experimental data are presented on mean velocities, pressure gradient, turbulence intensities, Reynolds stresses, and energy spectra. It is found that the velocity distributions follow the universal law of the wall in the drift current, but that the flow is undeveloped in the return portion of the flow. The non-dimensional longitudinal pressure gradient increases with Reynolds number, and a semi-empirical law of resistance is proposed and experimentally verified. Turbulence intensities in the drift current increase toward the shearing surface but are essentially constant in the opposing pressure-driven flow. The distribution of the Reynolds stress is found to be consistent with previous measurements obtained in this type of flow using different apparatus, but only approximately follows the theoretically linear distribution. Energy spectra in the shear-induced portion of the flow involve higher frequencies closer to the shearing surface than in the return current. There, the spectral energy is essentially the same throughout the flow, reflecting the constancy of turbulent intensity in this region.

An engineering model for countercurrent flow under wind-induced waves and current

“…is a constant used to characterize the intensity of the turbulence. According to Tsanis [16] and Wu and Tsanis [21], z s / h = 2.2 × 10 −4 and z b / h = 1.4 × 10 −4 for fully-turbulent countercurrent flow conditions. In addition, was estimated to be between 0.2 and 0.5 with an average value of about 0.35 for surface Reynolds numbers (Re) ranging from 10 3 to 10 5 [16].…”

“…Velocity profiles and bed shear stresses under deep-water conditions are well-described using the turbulent countercurrent model developed by Tsanis [16] and Wu and Tsanis [21], since the influence of surface waves is insignificant in most of the flow field. Under intermediate and shallow water conditions, however, where the flow structure is (strongly) influenced by the surface waves, the Wu and Tsanis [21] model does not accurately describe the resulting velocity field.…”

“…To obtain a solution for the velocity, an expression for the turbulent eddy viscosity is required. Tsanis [16] suggested a parabolic expression of the form: Fig. 1 Schematic of geometry under consideration on the assumption that a linear shear stress distribution exists.…”

“…Later, Koutitas and O'Connor [8], Goossens et al [3], Tsuruya et al [17], Tsanis and Leutheusser [15], Tsanis [16] and Wu [21] made progress in examining the countercurrent (water) flow induced by pure surface shear stress (without waves). Tsanis [16] proposed a double logarithmic law for the mean velocity field for this countercurrent flow, which was then improved by Wu and Tsanis [21]. The model was based on the flow motion driven by a flat, translating wall and therefore free surface effects were not accounted for.…”

Using inverse modeling to estimate parameter values for three dimensional transport of contaminants in Lake Ontario

“…Close to the surface the thickness is smaller to ensure appropriate conditions between the wind and water surface. The vertical average current profile is logarithmic with the larger gradient close to the surface and lower gradient close to the bottom (Tsanis et al, 1988) where the water intakes reside in the bottom of the lake few kilometres from shore at depths 12 m to 21 m. For the study described herein the model was setup on a Cartesian x-y grid at a resolution of 500 m with open boundaries to the east, west and south. The north was bounded by the shoreline.…”