Autoencoder-Based Analysis of Roughness Effects on Heat-Momentum Dissimilarity

Surface roughness strongly alters wall-bounded turbulence, breaking the Reynolds analogy between momentum and heat transfer. Although the resulting dissimilarity is well documented, the geometric features that drive it remain hidden within complex roughness topographies. We address this gap with a convolutional autoencoder (CNN-AE) that learns nonlinear, low-dimensional representations of instantaneous velocity and temperature fields. Instantaneous co-located streamwise velocity $u_1(x,t)$ and temperature $\theta(x,t)$ are extracted as two-dimensional windows from a DNS dataset of channel flow at friction Reynolds number $Re_\tau \approx 800$ over a wide range of pseudo-random rough surfaces. The windows serve as separate single-channel inputs to a shared CNN-AE. An auxiliary multilayer perceptron is attached to the latent space to classify each embedding as belonging to velocity or passive scalar, encouraging disentanglement of momentum and heat representations. The network is trained jointly with a loss that balances reconstruction error and classification accuracy. At a compression factor of $16$ the model reconstructs both $u_1$ and $\theta$ with a global error below $6\%$, while the MLP head yields a latent space in which velocity and temperature embeddings are clearly separated, as confirmed by principal-component analysis. ... mehrDistances between co-located latent vectors are then correlated with precise quantitative measures of heat-momentum dissimilarity and roughness variation.