中文摘要：

采用数值模拟方法，研究了高度和宽度比为1：10的狭长矩形腔内的水平自然热对流．根据对瑞利数（Rayleigh数）Ra在10^4〈Ra〈10^11内情形的计算结果，将流动分为三个不同的区间：线性区、连续过渡区、1，5次幂律区．虽然流量和努塞尔数（Nusselt数）Nu随瑞利数的变化都包括了三个参数演化区间，但从一个区间到另外一个参数区间的转变时并不是同步的，其中努塞尔数的转变总是超前流量的转变．对比前人的研究发现，流量1／3次幂律的结果是由于瑞利数不够高所致．此外，模拟结果也表明Siggers等的理论分析过高估计了热通量强度，实际的温度边界层内努塞尔数和瑞利数为1／5次幂律关系．

英文摘要：

The horizontal convection at high Rayleigh number （ Ra ） in a rectangle cavity with aspect ratio of 1 ： 10 is numerically simulated. The horizontal convection is an important model to understand the ocean circulation and the power laws of the flow are the most concerned. According to the results within the regime of 10^4 〈 Rα 〈 10^11 , three continuous regimes are obtained： the linear regime （ 10^4 〈 Rα 〈 10^6 ）, the transition regime （ 10^6 〈 Rα 〈 10^8 ） and the 1/5-power law regime （ 10^8 〈 Rα 〈 10^11 ）. For the flow strength, a 1/3-power law of Ra is fitted when Ra is not high enough （10^7 〈 Rα 〈 10^8）. However, a 1/5-power law is obtained when Ra is high enough （ 10^8 〈 Rα 〈 10^11 ）. The 1/5-pewer law confirms the analysis of Rossby and implies that 1/3- power law of Ra for Nusseh number by Siggers et al. is an over estimation.