Turbulent flows have historically presented formidable challenges to
predictive computational modeling. Traditional numerical simulations often
require vast computational resources, making them infeasible for numerous
engineering applications. As an alternative, deep learning-based surrogate
models have emerged, offering data-drive solutions. However, these are
typically constructed within deterministic settings, leading to shortfall in
capturing the innate chaotic and stochastic behaviors of turbulent dynamics. We
introduce a novel generative framework grounded in probabilistic diffusion
models for versatile generation of spatiotemporal turbulence. Our method
unifies both unconditional and conditional sampling strategies within a
Bayesian framework, which can accommodate diverse conditioning scenarios,
including those with a direct differentiable link between specified conditions
and generated unsteady flow outcomes, and scenarios lacking such explicit
correlations. A notable feature of our approach is the method proposed for
long-span flow sequence generation, which is based on autoregressive
gradient-based conditional sampling, eliminating the need for cumbersome
retraining processes. We showcase the versatile turbulence generation
capability of our framework through a suite of numerical experiments,
including: 1) the synthesis of LES simulated instantaneous flow sequences from
URANS inputs; 2) holistic generation of inhomogeneous, anisotropic wall-bounded
turbulence, whether from given initial conditions, prescribed turbulence
statistics, or entirely from scratch; 3) super-resolved generation of
high-speed turbulent boundary layer flows from low-resolution data across a
range of input resolutions. Collectively, our numerical experiments highlight
the merit and transformative potential of the proposed methods, making a
significant advance in the field of turbulence generation.

我们介绍了一种基于概率扩散模型的新型生成框架，用于多样化生成时空湍流。我们的方法在贝叶斯框架内统一了无条件和条件抽样策略，并能适应各种条件情景，包括指定条件与生成的非稳定流动结果之间具有直接可微分链接的情况以及缺乏明确相关性的情况。我们的方法的一个显著特点是基于自回归梯度条件抽样的长时跨度流动序列生成方法，在没有繁琐的重新训练过程的情况下完成。通过一系列数值实验展示了我们框架的多样化湍流生成能力，包括：1）从 URANS 输入合成 LES 模拟的瞬态流动序列；2）从给定的初始条件、规定的湍流统计数据或完全从头开始生成非均匀的、各向异性的壁面湍流；3）从不同输入分辨率的低分辨率数据中实现高速湍流边界层流动的超分辨生成。综合而言，我们的数值实验突显了所提方法的优点和变革潜力，在湍流生成领域取得了重大进展。