Eddy Length Scale Response to Static Stability Change in an Idealized Dry Atmosphere: A Linear Response Function Approach*

The response of mid-latitude equilibrated eddy length scale to static stability has long been questioned but not investigated in well-controlled experiments with unchanged mean zonal wind and meridional temperature gradient. With iterative use of the linear response function of an idealized dry atmosphere, we obtain a time-invariant and zonally-uniform forcing to decrease the near-surface temperature by over 2 K while keeping the change in zonal wind negligible (within 0.2m s−1). In such experiments of increased static stability, energy-containing zonal scale decreases by 3–4%, which matches with Rhines scale decrease near the jet core. Changes in Rossby radius (+2%), maximum baroclinic growth scale (-1%) and Kuo scale (0%) fail to match this change in zonal scale. These findings and well-controlled experiments help with better understanding of eddy–mean flow interactions and hence the mid-latitude circulation and its response to climate change.

A Review Of The Linear Response Function In Condensed Matter Physics And Their Application In Some Elementary Processes

Linear response theory in quantum theory with its linear response function and its quantization process has been formulated. The relation between the linear response function with its generalized susceptibility, its symmetry properties, and its analyticity has been studied. These properties produce the dispersion relation or Kramers-Kronig relation. The explicit form of the quantum response function and generalized susceptibility also been reviewed. Applications of linear response functions have been described for three elementary processes. The process discussed is the magnetic field disturbance in the magnetic system that generates magnetic susceptibility, and the electric field disturbance in the electrical system that generates electrical conductivity tensor and the ferromagnet Heisenberg that generates its generalized susceptibility.

Macroturbulence Response to Vertical Stratification Change Using Linear Response Function of an Idealized Dry Atmosphere

<p>Rossby radius and Rhines scale are two popular scaling arguments for eddy length scale. They have not been tested in a well-controlled experiment with increased vertical stratification and unchanged jet. This is done using the linear response function of an idealized dry atmosphere calculated by Hassanzadeh and Kuang (2016). The resulting change in zonal wind is mostly less than 0.2m/s when temperature near surface is cooled by more than 2K. In such experiment, energy-containing zonal scale decreases, which is against the prediction of Rossby radius but consistent with the prediction of Rhines scale. Eddy kinetic energy decreases for all wavenumbers and latitudes, but eddy momentum flux strengthens locally around zonal wavenumber 8 and 40°S. This local strengthening is associated with a stronger Pearson correlation between u and v.</p>

Dielectric Characteristics Analysis of Aluminum Electrolytic Capacitors Based on Linear Response Function

The electrical characteristics of Aluminum Electrolytic Capacitors are usually measured in frequency domain. The measured data of capacitance and dissipation or equivalent series resistance (ESR) has been treated individually for each frequency, and the “LCR” model has been developed by utilizing the measurement data in frequency domain. Therefore, these models don't show any relation between capacitance and dissipation which should follow the Kramers-Kronig relations. In this paper, we discuss the dielectric characteristics of Aluminum Electrolytic Capacitors based on the linear response theory. The complex dielectric formula based on this study can explain both the frequency and the temperature characteristic of capacitance of Aluminum Electrolytic Capacitor, and the relation between the frequency dependency of capacitance and the dissipation factor. This study is based on the hypothesis that the linear response function of the dielectric of Aluminum Electrolytic Capacitor should be expressed as the -nth powers of the ratio of time to the relaxation saturation time τdi. Only the two parameters: 1- n and τdi can give the exact calculation formula to both the capacitance and the dissipation factor of the dielectric behavior of Aluminum Electrolytic Capacitors.