Aerodynamic sound generation by turbulence
in shear flows
G. Khujadze
1,3
, G. Chagelishvili
2,3
, M. Oberlack
1
, A. Tevzadze
3
and
G. Bodo
4
1
Chair of Fluid Dynamics, Technische Universit¨at Darmstadt, Germany
khujadze@fdy.tu-darmstadt.de
2
M. Nodia institute of Geophysics, Tbilisi, Georgia,
3
E. Kharadze Georgian National Astrophysical Observatory, Tbilisi, Georgia
4
Osservatorio Astronomico di Torino, Pino Torinese, Italy
The nonlinear aerodynamic sound generation by turbulence has been long
analyzed since the foundation of the theory of aerodynamic sound in pioneer-
ing paper by Lighthill [1]. Also, it was Lighthill [2] who noted that velocity
shear can increase the acoustic wave emission in the aerodynamic situation
due to the existence of linear terms in the inhomogeneous part of the analogy
equations (second derivative of the Reynolds stress). In [3] it was disclosed
and described a linear aerodynamic sound generation mechanism. Specifically,
it was shown that the flow non-normality induced linear phenomenon of the
conversion of vortex mode into the acoustic wave mode is the only contributor
to the acoustic wave production of the unbounded shear flows in the linear
regime. From the physical point of view the potential vorticity was identified
as the linear source of acoustic waves in shear flows.
We perform comparative analysis of linear and nonlinear aerodynamic
sound generation by turbulent perturbations in constant shear flows and study
numerically the generation of acoustic waves by stochastic/turbulent pertur-
uniform background density and pressure ( U
0
(Ay, 0); A, ρ
0
,P
0
= const). The
governing hydrodynamic equations of the considered 2D compressible flow are:
∂ρ
∂t
+
∂ (ρU
x
)
∂x
+
∂ (ρU
y
)
∂y
=0, (1)
∂U
x
∂t
+U
x
∂U
x
∂x
+U
y
∂U
x
∂y
= −
1
ρ
∂P
∂x
,
∂U
y
∂t
+U
x
∂U
y
∂x
+U
y
∂U
y
∂y
= −
1
ρ
∂P
∂y
, (2)
∂
∂t
+ U
x
∂
∂x
+ U
y
∂
∂y
P = −
γP
ρ
∂
∂t
+ U
x
∂
∂x
+ U
y
∂
∂y
ρ, (3)
where γ – adiabatic index, c
2
s
≡ γP
0
/ρ
0
– sound speed. The potential vorticity
is defined as: W = [curlU]
z
/ρ.
B. Eckhardt (ed.), Advances in Turbulence XII, Springer Proceedings in Physics 132,
© Springer-Verlag Berlin Heidelberg 2009
867
bations embedded in 2D planar unbounded inviscid constant shear flow with
DOI 10.1007/978-3-642-03085-7_208,