Attached flow structure and streamwise energy spectra in a turbulent boundary layer

Area of Science:

• Fluid dynamics
• Turbulence research
• Wall-bounded flows

Background:

• Turbulent boundary layers are crucial in many engineering applications.
• Understanding energy spectra in these layers is key to predicting drag and heat transfer.
• Existing models, like the Townsend-Perry attached eddy model, offer theoretical frameworks for spectral behavior.

Purpose of the Study:

• To investigate the scaling laws of the streamwise energy spectrum in turbulent boundary layers.
• To compare experimental findings with predictions from the Townsend-Perry attached eddy model.
• To determine the influence of wall-attached eddies on spectral characteristics near the wall.

Main Methods:

• Utilizing particle image velocimetry (PIV) for high-resolution, large-field-of-view turbulent boundary layer data.
• Employing a mathematical relationship connecting energy spectra to modeled flow structures.
• Analyzing data across a range of Reynolds numbers (Reτ) from 10³ to 10⁴.

Main Results:

• The streamwise energy spectrum E₁₁(kₓ) scaling near the wall is governed by wall-attached eddies.
• The observed scaling E₁₁(kₓ)∼kₓ⁻¹⁻ᵖ deviates from the Townsend-Perry model's predictions.
• The exponent p varies with wall-normal distance, exhibiting negative values in the buffer layer and positive values in the inertial layer.

Conclusions:

• Wall-attached eddies, not the Townsend-Perry model, determine near-wall energy spectrum scaling.
• The exponent p quantifies turbulence within streaky structures, dependent on their length.
• Skin friction velocity alone cannot adequately scale the energy spectrum in regions influenced by the wall.