Buoyancy and velocity scales for dry convection in statistical equilibrium were derived in the early twentieth century by Prandtl, but the scaling of convective velocity and buoyancy, as well as the fractional area coverage of convective clouds, is still unresolved for moist convection. In this paper, high-resolution simulations of an atmosphere in radiative–convective equilibrium are performed...

We present the first global 3D simulations of thermal convection in the oblate envelopes of rapidly-rotating solar-type stars. This has been achieved by exploiting the capabilities of the new Compressible High-ORder Unstructured Spectral difference (CHORUS) code. We consider rotation rates up to 85% of the critical (breakup) rotation rate, which yields an equatorial radius that is up to 17% lar...

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an im...

In this paper, we generalize the theory of invariant subspace method to ( m + 1 ) -dimensional non-linear time-fractional partial differential equations for first time. More specifically, applicability and efficacy have been systematically investigated through 3 generalized diffusion–convection-wave equation along with appropriate initial conditions. This systematic investigation provides an im...

This article is an analysis of fractional nonlinear convection–reaction–diffusion equations involving the Atangana–Baleanu and Caputo derivatives. An efficient Aboodh homotopy perturbation transform method, which combines method with transformation, applied to investigate this fractional-order proposed model, analytically. A modified technique known as formulated approximate these The analytica...