The coastal ocean may experience periods of fluctuating along-shelf wind direction, causing shifts between upwelling and downwelling conditions with responses that are not symmetric. We seek to understand these asymmetries and their implications on the Eulerian and Lagrangian flows. We use a two-dimensional (variations across-shelf and with depth; uniformity along-shelf) primitive equation nume...

L∞ SOLUTIONS FOR A MODEL OF NONISOTHERMAL POLYTROPIC GAS FLOW∗ HERMANO FRID† , HELGE HOLDEN‡ , AND KENNETH H. KARLSEN‡ Abstract. We establish the global existence of L∞ solutions for a model of polytropic gas flow with varying temperature governed by a Fourier equation in the Lagrangian coordinates. The result is obtained by showing the convergence of a class of finite difference schemes, which...

In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between the local homogeneity of Frisch and global homogeneity. It is sho...

In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between the local homogeneity of Frisch and global homogeneity. It is sho...

The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic eld embedded in a conducting ow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian ow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrang...

This paper presents an adaptive multigrid approach, combining adaptive local grid refinement and multigrid methods, in conjunction with the Lagrangian–Eulerian finite element method to simulate contaminant transport in the 3D subsurface. Adaptive local grid refinement can improve solution accuracy without sacrificing computational efficiency because computer efforts are focused on the rough reg...

We design an Eulerian Gaussian beam summation method for solving Helmholtz equations in the high-frequency regime. The traditional Gaussian beam summation method is based on Lagrangian ray tracing and local ray-centered coordinates. We propose a new Eulerian formulation of Gaussian beam theory which adopts global Cartesian coordinates, level sets, and Liouville equations, yielding uniformly dis...

Relative dispersion in fully developed turbulence is investigated by means of direct numerical simulations. Lagrangian statistics is found to be compatible with Richardson description although small systematic deviations are found. The value of the Richardson constant is estimated as C2 approximately equal to 0.55, in a close agreement with recent experimental findings [S. Ott and J. Mann, J. F...