Mixing induced by oscillatory stratified flow past a right-circular cylinder

1995 ◽  
Vol 284 ◽  
pp. 1-21 ◽  
Author(s):  
M. J. A. M. Perera ◽  
H. J. S. Fernando ◽  
D. L. Boyer
Keyword(s):  
Circular Cylinder ◽  
Potential Energy ◽  
Stratified Flow ◽  
Stratified Fluid ◽  
Rate Of Change ◽  
Buoyancy Flux ◽  
Eddy Diffusivities ◽  
Flow Past ◽  
Rectangular Basin ◽  
Good Agreement

A series of laboratory experiments was performed to investigate the overall mixing characteristics of oscillatory stratified flow past an isolated topography. The experiments were conducted by oscillating a right-circular cylinder in an otherwise quiescent linearly stratified fluid contained in a rectangular basin. The mixing was largely confined to the turbulent ‘core’ region around the cylinder. This mixed fluid was then injected into the fluid interior of the basin by numerous intrusive tongues. These intrusions were accompanied by return currents of unmixed stratified fluid into the turbulent core. The overall effect of this mixing process was to increase the potential energy of the fluid in the basin. An expression is derived to relate the rate of change of potential energy of the system to the basin-averaged buoyancy flux. This formula was then used to calculate the mean buoyancy flux from measurements of the rate of change of potential energy of the fluid system. Basin-averaged diapycnal eddy diffusivities for the experiments were evaluated and the results were found to be in good agreement with the predictions of a heuristic model based on the energetics of the mixing. Observations on the spreading of intrusions and the evolution of the density field are also presented.

scholarly journals The spin-up of a linearly stratified fluid in a sliced, circular cylinder

2016 ◽  
Vol 806 ◽  
pp. 254-303
Author(s):  
R. J. Munro ◽  
M. R. Foster
Keyword(s):  
Circular Cylinder ◽  
Rossby Waves ◽  
Rotation Axis ◽  
A Priori ◽  
Propagation Speed ◽  
Stratified Fluid ◽  
Decay Rates ◽  
The Waves ◽  
Western Half ◽  
Good Agreement

A linearly stratified fluid contained in a circular cylinder with a linearly sloped base, whose axis is aligned with the rotation axis, is spun-up from a rotation rate $\unicode[STIX]{x1D6FA}-\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}$ to $\unicode[STIX]{x1D6FA}$ (with $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}\ll \unicode[STIX]{x1D6FA}$) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number $S$ is not small, then that spin-up looks quite different from that reported by Pedlosky & Greenspan (J. Fluid Mech., vol. 27, 1967, pp. 291–304) for $S=0$. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height $S^{-1/2}$ above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al.Phys. Fluids A, vol. 2, 1990, pp. 150–159 and Munro & Foster Phys. Fluids, vol. 26, 2014, 026603, for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom $S^{-1/2}$ region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with $S$ as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large $S$, and vertical vortices are found to occur only for Rossby numbers comparable to $E^{1/2}$, where $E$ is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

A linear analysis of rotating stratified flow past a circular cylinder on an f-plane

1985 ◽  
Vol 157 ◽  
pp. 501-518 ◽  
Author(s):  
Lee-Or Merkine
Keyword(s):  
Circular Cylinder ◽  
Stratified Flow ◽  
Linear Analysis ◽  
Vertical Shear ◽  
Horizontal Scale ◽  
Reversed Flow ◽  
Ekman Number ◽  
Striking Result ◽  
Vertical Boundary ◽  
Flow Past

A linear analysis of rotating stratified flow past a circular cylinder on an f-plane is made for moderate and strong stratification, i.e. for σS = O(E½) and σS = O(1) respectively. E is the Ekman number and σS is the product of the Prandtl number and the inverse rotational Froude number. The most striking result is that, for oncoming flows that are of one sign and possess vertical shear, reversed-flow regions can exist next to the cylinder. Depending on the degree of stratification, these backflow regions can occupy the inner part of the vertical boundary layer or can extend horizontally across distances comparable to the horizontal scale of the cylinder.

Flow past an impulsively started circular cylinder

1973 ◽  
Vol 60 (1) ◽  
pp. 105-127 ◽  
Author(s):  
W. M. Collins ◽  
S. C. R. Dennis
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Accurate Method ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Secondary Vortex ◽  
Flow Past ◽  
Dependent Flow ◽  
Good Agreement

An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated forR= 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder forR= 500 is also found to be in reasonable agreement with experimental measurements for the caseR= 560.For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. ForR> 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the caseR= 500, but for higher Reynolds numbers, including the caseR= ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.

Stability analysis of cross buoyancy flow past a circular cylinder using OpenFOAM

2020 ◽  
Vol 28 ◽  
pp. 2057-2061
Author(s):  
Sartaj Tanweer ◽  
Anupam Dewan ◽  
Sanjeev Sanghi ◽  
Anuj Kumar Shukla
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Buoyancy Flow ◽  
Flow Past
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