Leon Lpj Kamp

The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer

Many experiments have been performed in electromagnetically driven shallow fluid layers to study quasi-two-dimensional (Q2D) turbulence, the shallowness of the layer commonly is assumed to ensure Q2D dynamics. In this paper, however, we demonstrate that shallow fluid flows exhibit complex three-dimensional (3D) structures. For this purpose we study one of the elementary vortex structures in Q2D turbulence, the dipolar vortex, in a shallow fluid layer. The flow evolution is studied both experimentally and by numerical simulations. Experimentally, stereoscopic particle image velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane, and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. It is found that significant and complex 3D structures and vertical motions occur throughout the flow evolution, i.e., during and after the forcing phase. We conclude that the bottom friction is not the main mechanism l...

Intrinsic three-dimensionality in electromagnetically driven shallow flows

The canonical laboratory set-up to study two-dimensional turbulence is the electromagnetically driven shallow one- or two-layer fluid. Stereo-Particle-Image-Velocimetry measurements in such driven shallow flows revealed strong deviations from quasi–two-dimensionality, which are attributed to the inhomogeneity of the magnetic field and, in contrast to what has been believed so far, the impermeability condition at the bottom and top boundaries. These conjectures have been confirmed by numerical simulations of shallow flows without surface deformation, both in one- and two-layer fluids. The flow simulations reveal that the observed three-dimensional structures are in fact intrinsic to flows in shallow fluids because they do not result primarily from shear at a no-slip boundary: they are a direct consequence of the vertical confinement of the flow.

A model‐independent algorithm for ionospheric tomography: 1. Theory and tests

This paper presents a model-independent algorithm for tomography of the ionosphere. Prior knowledge consists of the following pieces of information: electron density cannot be negative, the ionosphere is basically smooth and stratified, and electron density is low at high (≳700 km) and low (≲100 km) altitudes. Tests based on simulated measurements show that the method recovers the latitudinal structure well, whereas the vertical structure is recovered with moderate success: the estimated height of the layer of maximum electron density may be as much as 90 km in error. Because of the imposed smoothness the method tends to underestimate the peak in electron density by as much as one third in unfavorable cases.

An algorithm for quadratic optimization with one quadratic constraint and bounds on the variables

This paper presents an efficient algorithm to solve a constrained optimization problem with a quadratic object function, one quadratic constraint and (positivity) bounds on the variables. Against little computational cost, the algorithm allows for the inclusion of positivity of the solution as prior knowledge. This is very useful for the solution of those (linear) inverse problems where negative solutions are unphysical. The algorithm rewrites the solution as a function of the Lagrange multipliers, which is achieved with the help of the generalized eigenvectors, or equivalently, the generalized singular value decomposition. The next step is to find the Lagrange multipliers. The multiplier corresponding to the quadratic constraint, which is known to be active, is easy to find. The Lagrange multipliers corresponding to the positivity constraints are found with an iterative method that can be likened to the active set methods from quadratic programming.

Toroidal flows in resistive magnetohydrodynamic steady states

Ideal magnetohydrodynamics (MHD) still provides the mathematical framework and the textbook vocabulary in which the possible states of a toroidal plasma are discussed, generally regarded as static equilibria. This is so, despite the increasing realization that virtually all toroidal magnetofluids have nontrivial fluid flows (finite velocity fields) in them. A very different perspective results from nonideal MHD, including both resistivity and viscosity and invoking nonideal boundary conditions. There, it has been shown that if Ohm’s law and Faraday’s law are given equal importance with force balance, flows are an inevitable consequence of the assumptions of time independence and axisymmetry. Previous treatments of the toroidal steady states for such systems have been based on perturbation theory in which the flow velocity was assumed small, as a consequence of high viscosity (or in dimensionless terms, low Hartmann number H). Here, recently newly available numerical programs are used to lift this limitati...

Meandering streams in a shallow fluid layer

Decaying turbulence in a shallow flow is shown to be characterized by the emergence of long-lived meandering currents, which are closely related to pronounced vertical flows inside the shallow layer. These vertical flows are concentrated in regions that are dominated either by vorticity or by strain of the flow field. Upwelling of fluid is observed in patch-like domains near elliptic points. Downward flow takes place close to hyperbolic points where the hyperbolic nature of the streamlines leads to thin, elongated regions of intense downwelling. The latter results in long, contracting regions in the free-surface flow. Particles that float on the liquid surface will congregate in these strain-dominated regions, thus lining out the large-scale meandering streams.

Toroidal steady states in visco-resistive magnetohydrodynamics

Previous computations concerning the allowed magnetohydrodynamic steady states of a visco-resistive magnetofluid in a toroid are extended. The current is supported by an externally imposed toroidal electric field, and a scalar resistivity and viscosity are assumed. Emphasis is on the character of the necessary velocity fields (mass flows) that toroidal geometry demands. Non-ideal boundary conditions are imposed at the toroidal boundary. One of the more interesting results to emerge is the sensitive dependence of the flow pattern on the shape of the toroidal cross-section boundary: the dipolar poloidal flow that had appeared for cross sections that were symmetric about the midplane is seen to deform continuously into a monopolar pattern for a ‘D-shaped’ cross section as the viscous Lundquist number

Dynamics of plasma vortices : The role of the electron skin depth

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A model‐independent algorithm for ionospheric tomography: 2. Experimental results

is increased. A net toroidal mass flow also develops. A boundary layer whose properties scale with fractional powers of

Vortex dipole collision with a sliding wall

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