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 -