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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - The transition to turbulence in slowly diverging subsonic submerged jets
AU - Landa, P. S.
AU - McClintock, P. V. E.
PY - 2012/3
Y1 - 2012/3
N2 - We address the problem of how turbulence is created in a submerged plane jet, near to the nozzle from which it issues. We do so by making use of a WKB-like asymptotic expansion for approximate solution of a complex, linear, fourth-order differential equation describing small deviations from the steady-state stream function. The result is used as a generating solution for application of the asymptotic Krylov-Bogolyubov method, enabling us to find the spatial and temporal spectra of the turbulence in the first approximation. We have thus been able to find the complex eigenvalues and eigenfunctions, i.e., the natural waves. We show that, for any given set of parameters, there is a continuum of frequencies and, for each frequency, a continuum of phase velocities. Correspondingly, there is an infinite number of wavelengths. It follows that there is no unique dispersion law and, because of perturbations (however, small they may be), a regular temporal spectrum does not exist even in cases where the spatial spectrum is regular. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3693141]
AB - We address the problem of how turbulence is created in a submerged plane jet, near to the nozzle from which it issues. We do so by making use of a WKB-like asymptotic expansion for approximate solution of a complex, linear, fourth-order differential equation describing small deviations from the steady-state stream function. The result is used as a generating solution for application of the asymptotic Krylov-Bogolyubov method, enabling us to find the spatial and temporal spectra of the turbulence in the first approximation. We have thus been able to find the complex eigenvalues and eigenfunctions, i.e., the natural waves. We show that, for any given set of parameters, there is a continuum of frequencies and, for each frequency, a continuum of phase velocities. Correspondingly, there is an infinite number of wavelengths. It follows that there is no unique dispersion law and, because of perturbations (however, small they may be), a regular temporal spectrum does not exist even in cases where the spatial spectrum is regular. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3693141]
KW - differential equations
KW - eigenvalues and eigenfunctions
KW - jets
KW - laminar to turbulent transitions
KW - nozzles
KW - subsonic flow
KW - turbulence
KW - WKB calculations
U2 - 10.1063/1.3693141
DO - 10.1063/1.3693141
M3 - Journal article
VL - 24
JO - Physics of Fluids
JF - Physics of Fluids
SN - 1070-6631
IS - 3
M1 - 035104
ER -