Modeling of atmospheric temperature fluctuations by translations of oscillatory random processes with application to spacecraft atmospheric re-entry

The presence of random fluctuations of air temperature within the Earth’s atmosphere is a well-documented phenomenon. During the past seventy years there have been numerous experimental efforts to accurately measure air temperature as a function of altitude and, through careful data analysis, provide statistics describing these fluctuations and the associated fluctuations in temperature gradients. In addition, several researchers suggest the presence of atmospheric layers or “sheets” where the statistics describing fluctuations in air temperature can vary significantly from layer to layer. Herein, we propose a model to represent fluctuations of air temperature within a layered atmosphere. The model is a special type of inhomogeneous non-Gaussian differentiable random process and can be calibrated to available data on the marginal statistics and spectral content of the fluctuating temperature field, as well as the associated first derivative of the process representing fluctuations in temperature gradients. Properties of the proposed model are presented, and statistical realizations of the fluctuating temperature field and its gradient are computed and presented for illustration. The random vibration response of a spacecraft falling to Earth through these fluctuating conditions is then considered to demonstrate the usefulness of the proposed model.