湍流问题一直是物理学中最困难的问题之一，当今对湍流的一个核心理解是能量逐渐由大尺度向小尺度的传递，或从小尺度传向大尺度。与经典流体相比，用超流来研究湍流问题，可以凭借超流无旋、无摩擦的迷人性质，去粗取精地考察湍流中一些基础性的问题。但常用的液氦超流具有非常强的原子间相互作用，对于理论上理解湍流是一个棘手的阻碍。因此，过冷的、只具有弱相互作用的均匀玻色气体成为了研究湍流问题及宏观量子效应的一个非常有前景的介质。 本文简介了玻色-爱因斯坦凝聚的发展史，探讨了冷原子气与液氦超流的凝聚现象，分析了无相互作用的玻色气体的玻色-爱因斯坦凝聚及其热力学性质，引入Gross-Pitaevskii方程考察了弱相互作用玻色气体的玻色-爱因斯坦凝聚在非平衡态的湍流行为，模拟在最大尺度上向一个弱相互作用的量子气体系统中输入能量，观察到系统在周期驱动下发生了非线性响应，形成湍流，出现涡旋，也观察到了能量由大尺度逐渐向小尺度传递的过程。

The turbulence problem has always been one of the most difficult problems in physics. A central concept in the modern understanding of turbulence is the existence of cascade of excitations from large to small length scales, or vice versa. Compared to classical fluids, superfluids possess fascinating features such as irrotational and frictionless flow, which help us reach the fundamental questions about the turbulence penetratingly. However, the strong interactions of liquid helium make theoretical understanding intractable. Hence, the ultracold, weakly interacting uniform Bose gas becomes a promising new medium for investigating many aspects of turbulence, as well as macroscopic quantum phenomena. This thesis provides a brief introduction of the history of Bose-Einstein condensate, as well as the condensates of ultracold gas and superfluid helium-4. We also discuss the thermodynamic quantities of Bose-Einstein condensate of non-interacting Bose gas. In this thesis, we employ the Gross–Pitaevskii equation to describe the dynamics of the condensate of weakly interacting Bose gas, which demonstrates turbulence. By numerical simulation with spectrum method and Runge-Kutta Method, we drive the condensate out of equilibrium with an oscillating force that pumps energy into a weakly interacting quantum gas system at the largest length scales. We also observe turbulence with vortices show up in the condensate and a gradual cascade from large to small length scales.