5 problems

Let $\psi$ and $\theta$ denote the flow and temperature fields, respectively, and let $(X,Y,Z)$ be the phase-space variables associated with the generalized Lorenz description. A l…

Let the generalized Lorenz equations ({GELE}) retain nonlinear modal interactions among harmonics with indices satisfying $l\leq 10$ and $m\leq 10$, and let the direct numerical si…

Grossmann–Lohse's conjecture. The plume shedding frequency scales as

Kraichnan's conjecture. The thermal flux velocity satisfies $U_{flux}=u_\tau/(2Pe_T)$.

Conjecture on the optimal aspect ratio. The optimal aspect ratio in the fixed-enstrophy transport problem satisfies