Vortex Quadrupoles and Propagation of Grid Turbulence
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”.
KeywordsTurbulent Kinetic Energy Stokes Number Grid Element Turbulent Layer Homogeneous Fluid
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- 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
- 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 pendulumstMathematical and Physical Papers 3(33),1–141Google 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