Location
MC 5479
Candidate
Kwan Tsaan (Donald) Lai | Applied Mathematics, University of Waterloo
Title
Kinetic Energy Spectra, Backscatter, and Subgrid Parameterization Analysis in Radiative-Convective Equilibrium
Abstract
The kinetic energy spectra, subfilter energy transfer, and subgrid parameterization are studied in idealized radiative-convective equilibrium (RCE) simulations. Aggregation creates a convective system that is more energetic on the large scales. The horizontal kinetic energy spectrum in the aggregated simulation resembles closer to the -5/3 spectrum when compares the non-aggregated simulation in the upper troposphere. In the upper troposphere, energy is mainly gained by buoyancy flux and lost by vertical energy flux. There is a direct energy cascade in the upper troposphere. Energy is transferred from large scales to small scales, in which the energy is dissipated by the dissipation. In the lower stratosphere, the energy is mainly gained by vertical flux and lost by the transfer term, the buoyancy flux, and the dissipation. There is an inverse energy transfer in the lower stratosphere, which may be explained by wave-mean-flow-interaction according to an Eliassen-Palm analysis.
Subfilter energy transfer analysis at a filter scale of 4 km is performed on an idealized RCE simulation. A 1-km horizontal resolution simulation is filtered to a horizontal scale of 4 km to perform a priori analysis of subfilter energy transfer. The net subfilter energy transfer rate is dissipative in the upper troposphere and backscattering in the lower stratosphere. The net subfilter energy transfer rate is the sum of a large amount of dissipation and backscatter in both the upper troposphere and lower stratosphere. The subfilter energy transfer rate is dominated by the vertical components in the upper troposphere and dominated by the shear components in the lower stratosphere. The filter type has a significant effect on the magnitude of the subfilter energy transfer rate but not its overall dependence on space and time. The box filter and the Gaussian give almost identical results. The use of the spectral cutoff filter results in significantly stronger dissipation and backscatter than the box filter and the Gaussian filter. The kinetic energy spectrum resembles the -5/3 spectrum in both the upper troposphere and lower stratosphere. In the upper troposphere, the energy gain in buoyancy flux is balanced by the energy loss in the vertical flux. In the lower stratosphere, the energy gain in vertical flux is balanced by the energy loss in the transfer term. There is direct energy transfer in the upper troposphere and inverse energy transfer in the lower stratosphere.
The stochastic backscatter TKE scheme, a stochastic backscatter-allowing subgrid turbulence scheme created by adding a zero-mean stochastic forcing to the eddy viscosity of the TKE scheme, is proposed and tested on idealized RCE simulations. The stochastic kinetic energy backscatter scheme (SKEBS) will also be used to compare against the stochastic backscatter TKE schemes. The addition of stochastic and backscatter elements in the stochastic backscatter TKE scheme has improved the commonly-used purely-dissipative TKE scheme when compared to the distribution of the subfilter energy transfer rate of the high-resolution 1-km simulation. The net subgrid energy transfer rate of the stochastic backscatter TKE simulations is similar to the TKE simulation. In the stochastic backscatter TKE scheme, backscatter is weak relative to dissipation. The kinetic energy spectra and spectral energy budget of the stochastic backscatter TKE simulations and TKE simulations are similar in the upper troposphere. In the lower stratosphere, the horizontal kinetic energy spectrum of the stochastic backscatter TKE scheme resembles closer to the -5/3 spectrum when compared to the TKE simulations. The horizontal energy spectrum of the SKEBS simulation resembles the -5/3 spectrum, likely due to the fact that SKEBS injects energy into the atmosphere with the designated -5/3 spectrum.