We conduct long simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experiments. The observed results are in excellent agreement with theoretical models, as well as the continuum statistical mechanica...

We derive boundary conditions for the vorticity equation with solid wall boundaries. The formulation uses a Dirichlet condition for the normal component of vorticity, and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e. it is enforced by a right-hand side functional and does not impose a boundary constraint on ...

Barotropic f -plane dipolar vortices were generated in a rotating fluid and a comparison was made with the so-called supersmooth f -plane solution which—in contrast to the classical Lamb–Chaplygin solution—is marked by an elliptical separatrix and a doubly continuously differentiable vorticity field. Dyevisualization and high-resolution particle-tracking techniques revealed that the observed di...

We investigate feature detection schemes used to guide appropriate mesh resolution for CFD calculations with adaptive mesh refinement (AMR). Methods based on eigenvalues of the velocity gradient, difference between vorticity and strain rate magnitudes, and eigenvalues of the vorticity vector are investigated and compared to traditional vorticity-based detection schemes such as the Q-criterion. ...

We analyze the dynamics of a perfectly flexible string with a constant length and a vanishing inner friction. The local angular velocity of line elements in this seemingly simple mechanical system is shown to have many mathematical and physical properties in common with vorticity in the three-dimensional incompressible Euler equation. It is demonstrated that initially smooth vorticity fields lo...

Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulae are derived that quantify the spontaneous generation of such waves by unsteady vorticity as well as the scattering of surface waves by vorticity. In a first Born approximation the radiated surface elevation is linearly related to the Fourier transform of ...

Acoustic field generated by a single vortex approaching a hydrofoil is studied. A combined vortex/RANS simulation for the near–field unsteady vorticity is developed to include effects from RANS Reynolds stresses. The far-field acoustics is calculated using a vortex sound formula with the near-field vorticity as the source. The results show that at a higher incident angle when the RANS shows a s...

In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as...

The nonlinear Schrödinger (NLS) equation describing the propagation of weakly rotational wave packets in an infinitely deep fluid in Lagrangian coordinates has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. The vorticity effects manifest themselves in a shift of the wave number...