An efficient geometric method for incompressible hydrodynamics on the sphere

Article Mechanics

Two-dimensional turbulence on a sphere

Erik Lindborg et al.

Summary: This study conducts a spectral analysis of a non-divergent flow on a sphere based on Fjortoft's method. It demonstrates that the spherical harmonic energy spectrum remains invariant under rotations of the polar axis, and derives the spectral energy equation and energy transfer relations. The importance of exploring two-dimensional turbulence through simulations using spherical geometry is highlighted, based on the explanation of relevant theories and hypotheses.

JOURNAL OF FLUID MECHANICS (2022)

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Article Mechanics

Canonical scale separation in two-dimensional incompressible hydrodynamics

Klas Modin et al.

Summary: Understanding the behavior of two-dimensional inviscid incompressible fluids is a complex problem. By studying the intrinsic splitting of Euler's equations, we can gain insights into scale separation and the formation of coherent vortex structures.

JOURNAL OF FLUID MECHANICS (2022)

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Article Physics, Fluids & Plasmas

Casimir preserving spectrum of two-dimensional turbulence

Paolo Cifani et al.

Summary: This study presents predictions of the energy spectrum of forced two-dimensional turbulence and constructs a finite-mode approximation of the Navier-Stokes equations. It provides robust evidence for the existence of double energy cascade.

PHYSICAL REVIEW FLUIDS (2022)

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Article Computer Science, Theory & Methods