## Research Experience

Thermodynamics of moist Rayleigh-Benard convection (2017-)

Advisor: Yihua Lin

Moist Rayleigh-Benard convection model reproduces various tropical atmosphere phenomenon, and could serve as a simplified version of RCE. However, there had not been a clear definition of its simplified buoyancy, and the thermodynamic framework is loose. I linked temperature with buoyancy directly, and proved that the "moist buoyancy" variable is more like wet bulb potential temperature than the previously-assumed equivalent potential temperature. With a clearer thermodynamics, I included rain in the previously nonprecipitating model.

Vorticity-velocity formulation DNS code (2014-)

Advisor: Yihua Lin & Yuan Wang & Bowen Zhou

I made a vorticity-velocity formulation DNS model by discretizing vorticity equation. It's potentially useful to study the vortex dynamics in Rayleigh-Benard convection. Velocity is found from vorticity inverting a costly vector-Poisson equation at each time step. The divergence-free constraint of velocity precludes many pre-existing numerical methods. Enlightend by the fact that divergence-free is preserved by shrinking a cell, I derived a simple but efficient geometric multigrid method. I also proved its fast convergence rate with Fourier analysis.

Cloud self-aggregation in moist Rayleigh-Benard convection, mid-level vertical velocity

Vortex interaction in rotating convection (2013-2016)

Student collaborator: Shiwei Sun

When Rayleigh-Benard convection is conducted on a rotating table, convective columnar vortices dominate the flow. In 1986, Boubnov has observed (with aluminum powder) that two adjacent vortices sometimes counter-rotate and entangle into a double-helix structure. We studied transient vortex interaction events with self-made rotating tank and PIV system. We observed that lower and upper parts tend to move synchronously before merging, and two vortices tend to collide into each other straightly without obvious counter-rotation. Though preliminary, our work at least indicate that vortex merge in versatile ways.

Experimental setup and vorticity field measured by PIV

Shallow water equation code of spectral method (2016-)

I am developing a flexible Fortran code to cover all kinds of equations in large scale dynamics. It helps me review the GFD and CFD courses. I have finished the one layer shallow water equation(SWE) and quasi-geostrophic equation version. The model uses spectral method, and runs on either spherical or cartesian coordinate, depending on the orthogonal function we use to expand the variables. I once used the barotropic vorticity equation version to simulate free-decaying 2D turbulence on f and beta plane, to help me understand energy cascade and jet formation, see below.

A snapshot of vorticity field in 2D turbulence on f and beta plane

Student GFD lab of Nanjing University (2013-)

Student collaborator: Shiwei Sun, Yunjiao Pu, Mingrui Liu, Zhiming Feng

In my bachelor years, I lead a student research project to build a rotating table to study rotating Rayleigh-Benard convection. There had not been a geophysical fluid dynamics lab before, and our project dramatically evolved into a student lab. Ever since then, nine projects have been conducted by students, including Taylor column, Rossby wave and density current etc. The lab also gives demonstrative experiments for undergraduate courses like fluid dynamics and dynamic meteorology.