This paper presents a method for computing the time-dependent three-dimensional propagation of high-energy laser beams through the atmosphere, including the effects of horizontal wind and turbulence. The method uses a discrete Fourier transform to solve the Maxwell wave equation in the Fresnel approximation, which is effective for diffraction problems. It also applies discrete Fourier transforms to solve hydrodynamic equations. Turbulence is modeled using random phase screens generated at each step along the propagation path, which can either move with the wind or be regenerated at each time step. The paper discusses several high-energy laser propagation problems, including propagation in the presence of transonic and supersonic winds due to beam slewing, propagation through dead zones where wind velocity is zero, and multi-pulse propagation. For steady-state conditions and wind velocities below sound speed, a simple isobaric approximation to the linearized hydrodynamic equations is accurate. However, when wind velocities approach or exceed sound speed, the isobaric approximation is no longer valid, and the full hydrodynamic equations must be solved. For transonic winds, a weak shock wave develops, increasing the sound speed in the heated medium, which keeps the Mach number below 1. When the wind speed exceeds sound speed, the shock disappears, and the sound speed returns to ambient levels, making the Mach number greater than 1. In such cases, the linearized hydrodynamic equations still govern the steady-state solution, provided the correct Mach number is known. The paper describes a general "Four-D" code capable of handling these problems, including modeling atmospheric turbulence with random phase screens. The code is used to simulate multi-pulse propagation, where the time-dependent isobaric approximation is adequate for describing the influence of one pulse on subsequent pulses, but more accurate acoustic equations are needed for self-blooming effects. The code also allows for the study of long-time averages of turbulence effects on beam propagation. The Four-D code is a versatile tool for simulating various high-energy laser propagation scenarios.This paper presents a method for computing the time-dependent three-dimensional propagation of high-energy laser beams through the atmosphere, including the effects of horizontal wind and turbulence. The method uses a discrete Fourier transform to solve the Maxwell wave equation in the Fresnel approximation, which is effective for diffraction problems. It also applies discrete Fourier transforms to solve hydrodynamic equations. Turbulence is modeled using random phase screens generated at each step along the propagation path, which can either move with the wind or be regenerated at each time step. The paper discusses several high-energy laser propagation problems, including propagation in the presence of transonic and supersonic winds due to beam slewing, propagation through dead zones where wind velocity is zero, and multi-pulse propagation. For steady-state conditions and wind velocities below sound speed, a simple isobaric approximation to the linearized hydrodynamic equations is accurate. However, when wind velocities approach or exceed sound speed, the isobaric approximation is no longer valid, and the full hydrodynamic equations must be solved. For transonic winds, a weak shock wave develops, increasing the sound speed in the heated medium, which keeps the Mach number below 1. When the wind speed exceeds sound speed, the shock disappears, and the sound speed returns to ambient levels, making the Mach number greater than 1. In such cases, the linearized hydrodynamic equations still govern the steady-state solution, provided the correct Mach number is known. The paper describes a general "Four-D" code capable of handling these problems, including modeling atmospheric turbulence with random phase screens. The code is used to simulate multi-pulse propagation, where the time-dependent isobaric approximation is adequate for describing the influence of one pulse on subsequent pulses, but more accurate acoustic equations are needed for self-blooming effects. The code also allows for the study of long-time averages of turbulence effects on beam propagation. The Four-D code is a versatile tool for simulating various high-energy laser propagation scenarios.