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Using the energy‐conserved quantity method developed by Arnol’d [Dokl. Mat. Nauk 162, 773 (1965); Am. Math. Soc. Trans. 19, 267 (1969)] a study was made of the nonlinear stability of two inviscid fluid flows in three dimensions: (1) flow of a homogeneous fluid and (2) flow of a fluid whose energy density depends on the mass density alone (a so‐called barotropic fluid). In order to implement the Arnol’d technique one must identify the quantities conserved by the flow in addition to the total energy. In the case of the two flows considered, the conserved quantities cannot be expressed in terms of the usual Eulerian variables—fluid velocity and mass density—alone. Instead the introduction of the Lagrangian labels of the fluid elements is required. A complete description of these conserved quantities, in both Eulerian and Lagrangian specifications of the fluid, is provided. The phase space of the flow is the entire Hamiltonian phase space expressed in either canonical or noncanonical variables. The nature of ...

Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations, especially in dealing with atmosphere and ocean dynamics, where viscous and diffusive dissipation effects are negligible. This paper derives a family of three different types of stochastic parameterisations for the classical Euler-Boussinesq (EBC) equations for a buoyant incompressible fluid flowing under gravity in a vertical plane. These three stochastic models are inspired by earlier work on the effects of stochastic fluctuations on transport, see, e.g., Kraichnan [1968, 1994] and Doering et al. [1994]. They are derived here from variants of Hamilton's principle for the deterministic case when Stratonovich noise is introduced. The three models possess different variants of their corresponding Hamiltonian structures. One variant (SALT) introduces stochastic transport. Another variant (SFLT) introduces stochastic \emph{forcing}, rather than stochastic \emph{transport}. The third variant (LA SALT) introduces nonlocality in its stochastic transport, in the probabilistic sense of McKean [1966]., Comment: 24 pages, 10 figures

This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose results lead to new perspectives on thin-film behavior. The new perspectives in large-scale droplet-spreading dynamics are elucidated by comparing numerical-simulation results for the solution properties of the current model with corresponding known properties of three different alternative models. The three specific comparisons in solution behavior are made with the slip model, the precursor-film method and the diffuse-interface model., 20 pages, 11 figures