Fluid equations, for instance Euler equations, are on the one hand equations that are hard to study, as they tend to have highly nonlinear terms as well as several interacting scales. On the other hand, however, some fluid-type equations have a strong geometric structure which makes them amenable to simulation by structure-preserving numerics. This allows for reliable numerics for the study of physical phenomena such as turbulence or blow-up phenomena, i.e., where the fluid breaks down. For instance, a wave may become infinitely high or a vortex spin infinitely fast. With this project, we intend to study four different problems: 1. Blow-up in the 3D axisymmetric Euler equations: how to capture this with structure-preserving numerics, and how to use this to guide analytical results? 2. Structure-preserving simulations for averaged Navier--Stokes turbulence with viscosity dissipation: We are currently interested in the filtered 2D Navier--Stokes equations and how this affects scaling laws observed in turbulence (Kraichnan type inverse cascade/forward cascade scalings). We have theoretical results, but future reviews may require large-scale simulations to verify the theoretical results. 3. Turbulence by selective disspation: This is alternative type of disspiation. Also used to study disspiation. We intend to study this type of disspiation to see how it affects scaling laws in magnetohydrodynamics, all with structure-preseving simulation. 4. Regularization by noise: It is proven, as a purely theoretical result, that the Navier--Stokes equations in the limit of vanishing viscosity may be regularized by adding structured noise. We want to investigate if this theoretical work can be captured in structure-preserving numeris, and this requires large-scale simulations.