## Graduate Student

**Junyi Chai** (Email: junyic@ NOSPAM princeton.edu)

**2007-2011**: BS in Physics, Peking University, China

**2011-Now**: PhD candidate in Atmospheric and Oceanic Sciences, Princeton University, USA

**Advisors**: Isaac Held, Geoffrey Vallis

**Research Interest**

I am interested in geophysical fluid dynamics for various flows in terrestrial and planetary atmospheres, and in Earth's oceans. Particularly, I focus on building theoretical understandings. Following Isaac's approach, I try to build such an understanding by two steps: first, use simple theories to understand idealized model simulations; and second, use more comprehensive model simulations to understand observations. Currently, my strength is within the first step. My toolkit includes idealized models such as pseudo-spectral models for solving primitive equations and quasi-geostrophic equations, and theories such as linear instability theory, wave-mean flow interaction theory, and various theories on two-dimensional turbulence. Eventually, I will move on to the second step, familiarizing myself with more comprehensive general circulation models and observations.

#### Past and ongoing projects

**Extratropical eddy scale**: Baroclinic eddies largely control the day-to-day weathers and large scale circulations in mid-latitudes. The eddy scale is important in understanding many properties of the eddies. For example, a scaling for eddy diffusivity can be U*L, where U is a velocity scale and L is a length scale for eddies. We studies the relationship between eddy scale and criticality, which is a non-dimensional parameter relating together horizontal temperature gradient and vertical stability. When criticality varies near one, we show that there exists a weakly nonlinear regime in which the eddy scale increases with criticality without involving an inverse cascade. The quasi-geostrophic instability of Charney problem is revisited. It is demonstrated that both the horizontal and vertical scales of the most unstable wave depend on criticality, and simple estimates for the two scales are obtained. This leads to a new estimate for eddy scale.

**Circulation on gas giants**: A school of thoughts often regard the dynamics of the upper atmosphere in Jovian planet to be similar as that of Earth. One key difference is that the large scale drag felt by the Jovian atmosphere may be extremely small due to the lack of a rigid bottom. However, due to inverse energy cascade, two-dimensional turbulence often need the large scale drag to remove energy from the largest scales. We find that there is another way for baroclinic turbulence to reach equilibrium in the limit of vanishing bottom drag through a "energy-recycling" mechanism: kinetic energy is generated by baroclinic instability near the deformation radius, then it is inversely cascade to larger and larger scales until gets converted into potential energy again by circulations at the largest scale; eventually, potential energy is dissipated by radiative damping.

**Geostrophic turbulence**: We found a new regime for beta-plane turbulence and a corresponding new scaling of eddy diffusivity.

#### Some Recent Publications:

Chai, J. and Vallis, G. K. 2014. The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM, JAS [pdf]

Chai, J., Jansen, M., and Vallis, G. 2016: Equilibration of a baroclinic planetary atmosphere toward the limit of vanishing bottom friction, accepted by JAS [pdf]

Chai, J., Jansen, M., and Held, I. M. 2016: The role of forcing scale on the beta-plane turbulence. Part I: jet formation, in preparation

Chai, J., Jansen, M., and Held, I. M. 2016: The role of forcing scale on the beta-plane turbulence. Part II: eddy diffusion, in preparation