Testing the role of radiation in determining tropical cloud top temperature

Tropical anvil clouds that detrain near the mixing barrier near 13km in the tropics have a strong effect on the longwave and shortwave energy budgets of Earth. A cloud-resolving model is used to test the Fixed Anvil Temperature (FAT) Hypothesis proposed by Hartmann and Larson (2002). Results show that the radiative cooling, primarily due to water vapor, is the strongest control of the anvil cloud detrainment temperature. Water vapor concentrations are largely controlled by temperature, so, following the FAT hypothesis, the cloud detrainment should follow a fixed temperature. The results also show, however, that ozone contributes a significant heating rate in the upper tropical troposphere. If ozone is fixed as a function of pressure as the SST is warmed, anvil clouds warm and their fractional coverage decreases. The presence of a fixed ozone profile in our model can be thought of as a pressure dependent contribution to stability that inhibits convection from rising to the level of diminished water vapor cooling. This suggests that to model the response of tropical anvil clouds to climate change, one must also predict ozone in the upper tropical troposphere and TTL region, where ozone concentrations are also influenced by convection, forming a strong interaction between ozone and cold clouds in the tropics. Broader implications of the influence of the TTL on the detrainment temperature of tropical anvils include the modification of the longwave cloud radiative effect and the net radiative energy budget effect of tropical deep convective systems

Vortex filament solutions of the Navier-Stokes equations

We consider solutions of the Navier-Stokes equations in $3d$ with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth curve. First, we prove global well-posedness for perturbations of the Oseen vortex column in scaling-critical spaces. Second, we prove local well-posedness (in a sense to be made precise) when the filament is a smooth, closed, non-self-intersecting curve. Besides their physical interest, these results are the first to give well-posedness in a neighborhood of large self-similar solutions of $3d$ Navier-Stokes, as well as solutions which are locally approximately self-similar.Comment: 89 page

Finite depth gravity water waves in holomorphic coordinates

In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second, we consider the small data problem and establish cubic lifespan bounds for the solutions. Our results are uniform in the infinite depth limit, and match the earlier infinite depth result of Hunter-Ifrim-Tataru.Comment: 82 pages, 1 figur

The lifespan of small data solutions to the KP-I

We show that for small, localized initial data there exists a global solution to the KP-I equation in a Galilean-invariant space using the method of testing by wave packets.Comment: 20 pages, minor update