Effects of Adverse Pressure Gradients on Mean Flows and Turbulence Statistics in a Boundary Layer

  • Y. Nagano
  • M. Tagawa
  • T. Tsuji


Measurements in boundary layers with ‘moderate’ to ‘strong’ adverse pressure gradients are presented and discussed. With increasing adverse pressure gradients, the velocity profile in \( {\overline U ^ + } \sim {y^ + }\) coordinates lies below the standard log law, thus indicating a reduction in the thickness of the sublayer. Correspondingly, the turbulence energy components as well as the Reynolds shear stress peak in the outer region of the boundary layer. Higher-order moments of velocity fluctuations are also seriously affected by the adverse pressure gradient. In strong adverse-pressure-gradient flows, the triple products of velocity have completely opposite signs to those in zero-pressure-gradient flows over most of the boundary layer.


Boundary Layer Wall Shear Stress Turbulent Boundary Layer Friction Velocity Reynolds Shear Stress 
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wall static pressure coefficient, =\( \left( {\overline P - {{\overline P }_{ref}}} \right)/\left( {\rho {{\overline {\text{U}} }^2}_{{\text{ref}}}/2} \right) \)


shape factor, = δ * /θ

\( \overline P \)

mean pressure


dimensionless pressure gradient parameter, = \( v\left( {d\overline {P/dx} } \right)/\rho u_T^3 \)


Reynolds number based on momentum thickness, = \( {\bar U_e}\theta /v \)


skewness factor of x, =\( {\overline X ^3}/{\left( {\overline {{X^2}} } \right)^{3/2}} \)

\( \overline U \)

mean velocity in x direction

\( \overline {{U_e}} \)

free stream velocity


friction velocity, = \( \sqrt {{T_w}/\rho } \)

u, v, w

fluctuating velocity components in x, y and z directions


distance from tripping plate

x, y, z

streamwise, wall-normal and lateral coordinates


dimensionless distance from wall, = u τ y/v


Clauser pressure gradient parameter, = \( \left( {{\delta ^*}/{\tau _w}} \right)d\overline P /dx \)


boundary layer thickness

δ*, θ

displacement and momentum thicknesses


kinematic viscosity




wall shear stress


time mean value


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Y. Nagano
    • 1
  • M. Tagawa
    • 1
  • T. Tsuji
    • 1
  1. 1.Department of Mechanical EngineeringNagoya Institute of TechnologyShowa-ku, Nagoya 466Japan

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