To understand the self-sustenance of subcritical turbulence in spectrally stable shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain and analyzed the dynamical processes in Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of perturbation harmonics due to the shear flow non-normality. This non-normality-induced, or nonmodal growth is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space appears to be the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade that exemplifies a well-known bypass scenario of subcritical turbulence. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process varies, but always remains quite large. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

We present a Bayesian earthquake location framework that couples a Deep Learning Surrogate with Gibbs sampling to enable uncertainty-aware hypocenter estimation. The surrogate model is trained to reproduce the three-dimensional first-arrival travel-time field by enforcing the Eikonal equation, thereby removing the need for computationally intensive ray tracing. Within a fully probabilistic formulation, Gibbs sampling is used to explore the posterior distribution of source parameters, yielding comprehensive uncertainty quantification. Application to the 2021 Luding aftershock sequence shows that the proposed approach attains location accuracy comparable to that of NonLinLoc while reducing computational cost by more than an order of magnitude. In addition, it produces detailed posterior probability maps that explicitly characterize spatial uncertainty. This integration of physics-informed learning and Bayesian inference provides a scalable, physically consistent, and computationally efficient solution for real-time earthquake location in complex velocity structures.