We study the Casimir force on a single surface immersed in an inhomoge-neous medium. Specifically we study the vacuum fluctuations of a scalar field with a spatially varying squared mass, m 2 + λ∆(x − a) + V (x), where V is a smooth potential and ∆(x) is a unit-area function sharply peaked around x = 0. ∆(x − a) represents a semi-penetrable thin plate placed at x = a. In the limits {∆(x−a) → δ(...

A fundamental problem in heat transfer is the convective cooling of the heated walls of a channel. We find steady two-dimensional (2D) flows that maximize the heat removed from fixed-temperature walls for a given rate of energy used to drive the flow, Pe (Pe is the Peclet number, a dimensionless flow speed). For parabolic (Poiseuille) flow, the heat transfer scales as Pe. Starting from Poiseuil...

We analyze the effective diffusivity of a passive scalar in a two-dimensional, steady, incompressible random flow that has mean zero and a stationary stream function. We show that in the limit of small diffusivity or large Peclet number, with convection dominating, there is substantial enhancement of the effective diffusivity. Our analysis is based on some new variational principles for convect...

Radiatively inefficient accretion flows onto black holes are unstable due to both an outwardly decreasing entropy (“convection”) and an outwardly decreasing rotation rate (the “magnetorotational instability”, MRI). Using a linear magnetohydrodynamic stability analysis, we show that long-wavelength modes with λ/H ≫ β are primarily destabilized by the entropy gradient and that such “convective” m...

Recent work has produced a theory for tropical convective available potential energy (CAPE) that highlights the Clausius-Clapeyron (CC) scaling of the atmosphere’s saturation deficit as a driver of increases in CAPE with warming. Here we test this so-called “zero-buoyancy” theory for CAPE by modulating the saturation deficit of cloud-resolving simulations of radiative-convective equilibrium in ...

Numerical simulations of laminar, forced convection heat transfer for reciprocating, twodimensional channel flows are performed as a function of the penetration length, Womersley (a) and Prandtl (Pr) numbers. The numerical algorithm is based on a spectral element formulation, which enables high-order spatial resolution with exponential decay of discretization errors, and second-order time-accur...

Numerical simulations have by now revealed that the fine scale structure of the penumbra in general and the Evershed effect in particular is due to overturning convection, mainly confined to gaps with strongly reduced magnetic field strength. The Evershed flow is the radial component of the overturning convective flow visible at the surface. It is directed outwards – away from the umbra – becau...

We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing length formalism. We seek self-similar solutions in which the angular velocity and sound speed scale as R, where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one...