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Power-law decay of homogeneous turbulence at low Reynolds numbers. (English) Zbl 0832.76031
Summary: The decay of nominally isotropic, homogeneous incompressible turbulence is studied by direct numerical simulations for \(\text{Re}_\lambda\) in the range (5-50) with \(256^3\) spectral coefficients. A power-law decay of the turbulent energy is observed with exponents approximately equal to 1.5 and 1.25, apparently dependent on \(\text{Re}_\lambda\). A new complete similarity form for the double and triple velocity correlation functions, \(f(r,t)\) and \(k(r,t)\), is proposed for low to intermediate \(\text{Re}_\lambda\) that is consistent with the Kármán-Howarth equation and the results of the numerical experiments. The results are also consistent with Saffman’s proposed asymptotic behavior of \(f(r,t)\) for large separation \(r\) for runs with a decay exponent of 1.5. The so- called final period of decay is not observed.

MSC:
76F05 Isotropic turbulence; homogeneous turbulence
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[1] DOI: 10.1098/rspa.1947.0095 · doi:10.1098/rspa.1947.0095
[2] DOI: 10.1098/rspa.1948.0061 · Zbl 0030.37704 · doi:10.1098/rspa.1948.0061
[3] DOI: 10.1098/rspa.1948.0095 · Zbl 0032.22602 · doi:10.1098/rspa.1948.0095
[4] DOI: 10.1252/jcej.16.273 · doi:10.1252/jcej.16.273
[5] DOI: 10.1103/PhysRevLett.71.2583 · doi:10.1103/PhysRevLett.71.2583
[6] DOI: 10.1063/1.868319 · Zbl 0825.76278 · doi:10.1063/1.868319
[7] DOI: 10.1017/S0022112082001049 · Zbl 0483.76057 · doi:10.1017/S0022112082001049
[8] DOI: 10.1098/rspa.1938.0013 · Zbl 0018.15805 · doi:10.1098/rspa.1938.0013
[9] DOI: 10.1017/S0022112092002180 · Zbl 0756.76030 · doi:10.1017/S0022112092002180
[10] Batchelor G. K., Q. of Appl. Math. 6 pp 97– (1948) · Zbl 0035.25604 · doi:10.1090/qam/28162
[11] DOI: 10.1017/S0022112067000552 · Zbl 0148.22403 · doi:10.1017/S0022112067000552
[12] Batchelor G. K., Proc. R. Soc. London Ser. A 248 pp 369– (1956)
[13] DOI: 10.1098/rspa.1934.0091 · JFM 60.0739.01 · doi:10.1098/rspa.1934.0091
[14] DOI: 10.1017/S0022112066001071 · doi:10.1017/S0022112066001071
[15] DOI: 10.1017/S0022112066000338 · doi:10.1017/S0022112066000338
[16] DOI: 10.1063/1.858423 · Zbl 0754.76042 · doi:10.1063/1.858423
[17] Barenblatt G. J., Sov. Phys. JETP 38 pp 399– (1974)
[18] DOI: 10.1002/sapm1971504293 · Zbl 0237.76012 · doi:10.1002/sapm1971504293
[19] DOI: 10.1016/0021-9991(88)90022-8 · Zbl 0655.76042 · doi:10.1016/0021-9991(88)90022-8
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