Turbulent Channel Flow (TCF)

The turbulent channel flow describes flow between two parallel infinite plates and is a classic experiment for studying wall-bounded turbulence. Most active flow control strategies aim to reduce wall shear stress via spatially distributed blowing and suction actuators at the walls.

Environment List

Small Channel

Environment ID	Walls	Re_τ
TCFSmall3D-bottom-easy-v0	Bottom	180
TCFSmall3D-bottom-medium-v0	Bottom	330
TCFSmall3D-bottom-hard-v0	Bottom	550
TCFSmall3D-both-easy-v0	Both	180
TCFSmall3D-both-medium-v0	Both	330
TCFSmall3D-both-hard-v0	Both	550

Large Channel

Environment ID	Walls	Re_τ
TCFLarge3D-bottom-easy-v0	Bottom	180
TCFLarge3D-bottom-medium-v0	Bottom	330
TCFLarge3D-bottom-hard-v0	Bottom	550
TCFLarge3D-both-easy-v0	Both	180
TCFLarge3D-both-medium-v0	Both	330
TCFLarge3D-both-hard-v0	Both	550

Reward

The reward is based on the instantaneous reduction of wall shear stress relative to the uncontrolled reference:

\[r_t = 1 - \frac{\tau_{\mathrm{wall}}}{\tau_{\mathrm{wall},\mathrm{ref}}}\]

The wall shear stress is computed as:

\[\tau_{\mathrm{wall}} = \nu \left.\frac{\partial u_x}{\partial y}\right|_{y=0}\]

For single-wall (bottom) actuation, only the bottom wall stress is used; for dual-wall actuation, the stress is averaged across both walls.

Opposition Control Baseline

A pre-computed opposition control baseline is provided. Wall-normal velocity at the wall is prescribed as:

\[v_{\mathrm{wall}}(x,z,t) = -\alpha \, v'(x,y_s,z,t)\]

where \(v'(x,y_s,z,t)\) is the wall-normal velocity fluctuation at the detection plane (\(y^+ = 15\)) and \(\alpha = 1.0\).

Action Space

Control is applied via wall-normal blowing and suction at the boundary using spatially distributed actuators. Zero net-mass-flux is enforced. Boundary velocities are scaled by the friction velocity \(u_+\) as the maximum value.

• Small channel: \(32 \times 32\) actuators per wall.

• Large channel: \(64 \times 64\) actuators per wall.

Two configurations are available: bottom-wall actuation only, or dual-wall actuation (both walls simultaneously).

Observation Space

Observations consist of local velocity fluctuations \(\mathbf{u}' = (u', v')\) defined as deviations from the instantaneous spatial mean:

\[u' = u - \langle u \rangle_V, \qquad v' = v - \langle v \rangle_V\]

where \(\langle \cdot \rangle_V\) denotes volumetric averaging. Fluctuations are sampled at a detection plane located at wall-normal distance \(y^+ = 15\), directly above the corresponding actuator. In the bottom-actuation variant, only observations from the bottom wall are provided.

Difficulty Levels

Difficulty is controlled by the friction Reynolds number \(\mathrm{Re}_\tau\):

Level	Re_τ
Easy	Re_τ = 180
Medium	Re_τ = 330
Hard	Re_τ = 550

Higher friction Reynolds numbers correspond to more intense turbulence, making drag reduction increasingly difficult.

API Reference

fluidgym.envs.tcf.TCF3DBottomEnv(...[, ...])	Environment for turbulent channel flow control.
fluidgym.envs.tcf.TCF3DBothEnv(resolution_y, ...)	Environment for turbulent channel flow control with both walls actuated.