The paper discusses the time-dependent propagation of high-energy laser beams through the atmosphere, addressing various challenging scenarios such as transonic and supersonic winds, propagation through stagnation zones, and multi-pulse propagation. The authors describe a "four-dimensional" computer code (Four-D) that can handle these complex problems using a discrete Fourier transform method to solve the Maxwell wave equation and hydrodynamic equations. The code models atmospheric turbulence using random phase screens, which can either move with the wind or be regenerated at each time step. The paper provides numerical examples and detailed explanations of the code's capabilities, including its ability to handle steady-state and time-dependent hydrodynamic behaviors, such as thermal blooming and shock wave formation. The Four-D code is designed to be flexible, allowing for different treatments of hydrodynamics based on the specific flow regimes encountered in various propagation scenarios.The paper discusses the time-dependent propagation of high-energy laser beams through the atmosphere, addressing various challenging scenarios such as transonic and supersonic winds, propagation through stagnation zones, and multi-pulse propagation. The authors describe a "four-dimensional" computer code (Four-D) that can handle these complex problems using a discrete Fourier transform method to solve the Maxwell wave equation and hydrodynamic equations. The code models atmospheric turbulence using random phase screens, which can either move with the wind or be regenerated at each time step. The paper provides numerical examples and detailed explanations of the code's capabilities, including its ability to handle steady-state and time-dependent hydrodynamic behaviors, such as thermal blooming and shock wave formation. The Four-D code is designed to be flexible, allowing for different treatments of hydrodynamics based on the specific flow regimes encountered in various propagation scenarios.