Direct numerical simulations of stratified open channel flows subject to a varying surface heat flux are performed. The influence of the diurnal heating time on the spatial and temporal variation of mixing in the flow and the characteristics of the mean flow state are examined. The control parameters are the bulk stability parameter \(\lambda_{B}\), defined through the ratio of the channel height \(\delta\) and a bulk Obukhov length scale \(\mathscr{L}_{B}\), and the diurnal time scale \(\hat{t}\), defined as the ratio of the heating time to an eddy turnover time. The Prandtl number Pr and Reynolds number \(Re_{\tau}\) have values of 1 and 400. Simulations are performed over \(\hat{t} = 1\) to 24 and \(\lambda_{B} = 0.6\) to 26. Two key flow features are used to classify the flow regimes observed, namely the laminar layer depth (LLD) and stratified layer depth (SLD) where the LLD is defined as the depth from the free surface when the buoyancy Reynolds number \(Re_{B} \approx 7\) and the SLD is the depth from the free surface when the turbulent Froude number \(Fr \approx 1\). This study attempts to characterise how these length scales vary across the diel cycle. The LLD is a viscous length scale and a regime map of a viscous parameter, the bulk Obhukov Reynolds number \(Re_\mathscr{L}\), and \(\hat{t}\) is presented to classify the LLD behaviour. A regime map of \(\lambda _{B}\) and \(\hat{t}\) is presented to classify the behaviour of the SLD. Three classifications for each layer depth behaviour within a diel cycle form the basis of the regime maps for this paper: a neutral flow where the LLD or SLD does not exist (denoted by NL and NS), a stratified flow where the LLD or SLD are diurnally varying (denoted as DL and DS) and a persistent layer of the LLD or SLD (denoted as PL and PS). The transition between the NL to DL is \(\hat{t} \propto Re_{\mathscr{L}}^{4.5}\), DL to PL is \(\hat{t} \propto Re_{\mathscr{L}}^{- 0.5}\), NS to DS is \(\hat{t} \propto \lambda _{B}^{0}\) and DS to PS is \(\hat{t} \propto \lambda _{B}^{1}\). The regime maps may be used as a predictive tool to determine when suppressed mixing regimes occur in rivers. At each flow depth, the flow sweeps though a range of mixing states across the diel cycle. The local mixing efficiency are briefly assessed and found to scale well with the instantaneous \(Fr\) number according to the regimes proposed by Garanaik and Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323-333).

对受不同表面热通量影响的分层明渠流进行直接数值模拟。研究了昼夜加热时间对流动混合时空变化的影响以及平均流动状态的特征。控制参数是体积稳定性参数\(\lambda_{B}\)，通过通道高度\(\delta\)和体积 Obukhov 长度尺度\(\mathscr{L}_{B}\ )，以及昼夜时间尺度\(\hat{t}\)，定义为加热时间与涡流周转时间的比率。普朗特数Pr和雷诺数\(Re_{\tau}\)的值为 1 和 400。模拟执行超过\(\hat{t} = 1\)到 24 和\(\lambda_{B} = 0.6\)到 26。两个关键的流动特征用于对观察到的流动状态进行分类，即层流层深度 (LLD) 和分层深度（SLD），其中LLD定义为当浮力雷诺数\(Re_{B}\approx 7\)时距自由表面的深度，SLD是当湍流弗劳德数\时距自由表面的深度（Fr \约1 \）。这项研究试图描述这些长度尺度在昼夜循环中如何变化。LLD 是粘性长度尺度和粘性参数的状态图，大块 Obhukov 雷诺数\(Re_\mathscr{L}\)和\(\hat{t}\)用于对 LLD 行为进行分类。政权地图提出\(\lambda _{B}\)和\(\hat{t}\)对 SLD 的行为进行分类。昼夜循环内每层深度行为的三种分类构成了本文的状态图的基础：不存在 LLD 或 SLD 的中性流（用 NL 和 NS 表示）、LLD 或 SLD 存在的分层流昼夜变化（表示为 DL 和 DS）和持久层 LLD 或 SLD（表示为 PL 和 PS）。NL 到 DL 之间的转换为\(\hat{t} \propto Re_{\mathscr{L}}^{4.5}\)，DL 到 PL 为\(\hat{t} \propto Re_{\mathscr{ L}}^{- 0.5}\)，NS 到 DS 是\(\hat{t} \propto \lambda _{B}^{0}\)， DS 到 PS 是\(\hat{t} \propto \lambda _{B}^{1}\)。状态图可以用作预测工具来确定河流中何时出现抑制混合状态。在每个流动深度，流动会在整个昼夜循环中经历一系列混合状态。 根据 Garanaik 和 Venayagamoorthy 提出的方案（J. Fluid Mech.，第 867 卷，2019 年，第 323-333 页），对局部混合效率进行了简要评估，发现其与瞬时\(Fr\)数很好地缩放。