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Energy spectra and passive tracer cascades in turbulent flows
Michael Jolly, Djoko Wirosoetisno
We study the influence of the energy spectrum on the extent of the cascade range of a passive tracer in turbulent flows. The interesting cases are when there are two different spec…
Navier-Stokes equations on a rapidly rotating sphere
Djoko Wirosoetisno
We extend our earlier β-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes eq…
Navier-Stokes equations on the -plane
Mustafa Al-Jaboori, Djoko Wirosoetisno
We show that, given a sufficiently regular forcing, the solution of the two-dimensional Navier--Stokes equations on the periodic -plane (i.e.\ with the Coriolis force varying as…
Stability of the slow manifold in the primitive equations
R. Temam, D. Wirosoetisno
We show that, under reasonably mild hypotheses, the solution of the forced--dissipative rotating primitive equations of the ocean loses most of its fast, inertia--gravity, componen…
Two-dimensional Euler flows in slowly deforming domains
J. Vanneste, D. Wirosoetisno
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially st…
Exponential approximations for the primitive equations of the ocean
R. Temam, D. Wirosoetisno
We show that in the limit of small Rossby number $\eps$, the primitive equations of the ocean (OPEs) can be approximated by ``higher-order quasi-geostrophic equations'' up to an ex…