Advances in Turbulence VI pp 149-152 | Cite as

# Vortex Quadrupoles and Propagation of Grid Turbulence

## Abstract

The purpose of this communication is to present the results of experiments dealing with the propagation of turbulent fronts induced by oscillating grids in homogeneous fluids and to explane the experimental results theoretically. In most of the previous experiments grids made with large square bars were used to study a variety of problems ranging from velocity decay law to mixing across density interfaces (e.g., see Fernando, 1991). Barenblatt (1977) modeled the grid forcing by a source of turbulent kinetic energy distributed homogeneously in the grid’s plane and analyzed the propagation of a turbulent front. Voropayev *et al*. (1980) demonstrated experimentally that this modeling leads to the conclusion that the turbulent kinetic energy flux from the grid, oscillating with constant frequency and amplitude, rapidly decreases with time, which seems unrealistic (also see Barenblatt and Voropayev, 1983; Benilov *et al*. ,1983). Dickinson and Long (1978) studied the propagation of a turbulent layer by employing a fine grid with small mesh and bar diameter. Considering such a grid, it is possible to simplify the problem and develop an idealized model to describe the grid forcing on the fluid by using some singularities distributed in the grid’s plane. Such an attempt was made by Long (1978), who modeled the flow near the grid by a system of point source sink doublets. An essential shortcoming of this model is the absence of vorticity in the flow, and in a recent paper Long (1995) attempted to modify this model because the source-sink doublets produce no vorticity — “the *sine qua non* of turbulence”.

## Keywords

Turbulent Kinetic Energy Stokes Number Grid Element Turbulent Layer Homogeneous Fluid## Preview

Unable to display preview. Download preview PDF.

## References

- Barenblatt G.I. (1977) Strong interaction of gravity waves and t urbulence
*Izvestiya*, Atmos.*Oceanic Phys*.**8**, 581–583Google Scholar - Barenblatt, G.I. and Voropayev, S.I. (1983) A contribution to the theory of a steady-state turbulent layer
*Izvestiya*, Atmos.*Oceanic Phys***19**, 126–129Google Scholar - Benilov A.Yu., Voropayev, S.I. and Zhmur, V.V (1983) Modeling the evolution of the upper turbulent layer of the ocean during heating
*Izvestiya*, Atmos.*Oceanic Phys***19**, 130–136Google Scholar - Dickinson, S.C. and Long, R.R. (1978) Laboratory study of the growth of turbulent layer of fluid
*Phys. Fluids***21**, 1698–1701ADSCrossRefGoogle Scholar - Fernando, H.J.S. (1991) Turbulent mixing in a stratified fluid
*Ann. Rev. Fluid Meek***23**, 455–493ADSCrossRefGoogle Scholar - Long, R.R. (1978) Theory of turbulence in a homogeneous fluid induced by an oscillating grid
*Phys. Fluids*,**21**, 1887–1888ADSzbMATHCrossRefGoogle Scholar - Long, R.R. (1995) A theory of grid turbulence in a homogeneous fluid, to be submittedGoogle Scholar
- Stokes, G.G.(1966) On the effect of the internal friction of fluids on the motion of pendulumst
*Mathematical and Physical Papers***3**(33),1–141Google Scholar - Tatsumo, M and Bearman, P.W. (1990) A visual study of the flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers and low Stokes numbers
*J. Fluid Mech*.,**211**, 157–173ADSCrossRefGoogle Scholar - Voropayev, S.I., Afanasyev, Ya. D. and van Heijst, G.J.F. (1995) Two-dimensional flows with zero net momentum: evolution of vortex quadrupoles and oscillating grid turbulence
*J. Fluid. Mech***282**, 21–44MathSciNetADSzbMATHCrossRefGoogle Scholar - Voropayev, S.I. Gavrilin, B.L., Zatsepin, A.G. and Fedorov, K.N (1980) A laboratory study of the deepening of a mixed layer in a homogeneous liquid
*Izvestiya*, Atmos.*Oceanic Phys*.,**16**126–128Google Scholar - Voropayev, S.I. and Fernando, H.J.S. (1996) Propagation of grid turbulence in homogeneous fluids
*Phys. Fluids*in pressGoogle Scholar - Voropayev, S.I., Fernando H.J.S. and Wu, P.C. (1996) Starting and steady quadrupolar flow
*Phys. Fluids*,**8**, 384–396MathSciNetADSzbMATHCrossRefGoogle Scholar