Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 94

The variance in wall pressure, in relation to the inner
scales, increases slightly in a logarithmic fashion with
increasing , in accordance with what is shown by

Bradshaw [BRA 67]. The dotted line shows the empirical
result

Re
τ

p 0 p 0
ρ

= 6.5 Re

τ <

333

2

u

τ

⎛ ⎝ ⎞

p 0 p 0
ρ

Re
τ
333

= 6.5 +1.86ln Re

τ >

333

⎜ ⎟

2

⎠

u

τ

obtained by Farabee and Casarella [FAR 91a] by integrating
the spectral density in different regions of the Fourier space,
as we will discuss later on. We can see a close
corresponden ce with the experimental results and the
relationship p 0 p 0 ∝

()

, in spite of certain differences, in
particular when the value of the Reynolds number is high.

ln Re

Figure 2.15. Quadratic mean value of the pressure at the wall in mixed
scales as a function of the Reynolds number. For the key, see Figure 2.14

The pressure is an integral quantity, and depends on the
whole of the flow. The intensity of the fluctuations in w al l
pressure is rendered dimensionless by the mixed scale u τ U ex ρ