Anomalous dissipation in a stochastic inviscid dyadic model

Uniqueness for an inviscid stochastic dyadic model on a tree

In this paper we prove that the lack of uniqueness for solutions of the tree dyadic model of turbulence is overcome with the introduction of a suitable noise. The uniqueness is a weak probabilistic uniqueness for all l-initial conditions and is proven using a technique relying on the properties of the q-matrix associated to a continuous time Markov chain.

Anomalous Dissipation and Energy Cascade in 3D Inviscid Flows

Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flows, it is shown that the anomalous dissipation is – in the case of decaying turbulence – indeed capable of triggering the cascade which then continues ad infinitum, confirming Onsager’s predictions.

1 1 N ov 2 00 8 Energy dissipation and self - similar solutions for an unforced inviscid dyadic model

A shell-type model of an inviscid fluid, previously considered in the literature, is investigated in absence of external force. Energy dis-sipation of positive solutions is proved and decay of energy like t −2 is established. Self-similar decaying positive solutions are introduced and proved to exist and classified. Coalescence and blow-up are obtained as a consequence, in the class of arbitrar...

Bounding dissipation in stochastic models

We generalize to stochastic dynamics the exact expression for average dissipation along an arbitrary non-equilibrium process, given in Phys. Rev. Lett. 98, 080602 (2007). We then derive lower bounds by various coarse-graining procedures and illustrate how, when and where the information on the dissipation is captured in models of overand underdamped Brownian particles. PACS numbers: 05.70.Ln, 0...

A Stochastic Optimization Model for Groundwater Management