标题： 二维地形湍流中的最小涡量和最大熵平衡态 显示英文标题

标题： Minimum-enstrophy and maximum-entropy equilibrium states in two-dimensional topographic turbulence

摘要： 在二维（2D）地形湍流的近期数值模拟中，由于存在高于地形极值的长寿命和孤立涡旋，具有势涡度和流函数之间线性关系的最小涡量平衡状态（Bretherton & Haidvogel, J. Fluid Mech., 第78卷，第1期，1976年，第129-154页）通常无法描述最终状态。我们发现这些涡旋可以通过一个“$\sinh$”涡度-流函数关系来描述，该关系对应于Joyce & Montgomery（J. Plasma Phys., 第10卷，第1期，1973年，第107-121页）和Montgomery & Joyce（Phys. Fluids, 第17卷，第6期，1974年，第1139-1145页）为二维平坦底部湍流提出的最大熵平衡状态。受最近观察结果的启发，即线性PV-流函数关系描绘了二维地形湍流的背景流，我们提出通过额外叠加一个“$\sinh$”关系来模拟总流的最终状态，以解释孤立涡旋。我们将经验性的“$\sinh$”关系和组合模型与配置了两种简单大尺度地形的二维湍流模拟中的最终状态进行验证：正弦形凸起加凹陷，以及纬向山脊加沟槽。只要经验理论适应后者纬向平均流状态，这两种地形都获得了良好的一致性。首次，我们的经验理论正确描述了最终流结构，并揭示了二维地形湍流中两种平衡状态的共存。 显示英文摘要

摘要： In recent numerical simulations of two-dimensional (2D) topographic turbulence, the minimum-enstrophy equilibrium state (Bretherton \& Haidvogel,J. Fluid Mech., vol. 78, issue 1, 1976, pp. 129-154) with an underlying linear relation between potential vorticity and streamfunction cannot generally describe the final state, due to the presence of long-lived and isolated vortices above topographic extrema. We find that these vortices can be described by a ``$\sinh$'' vorticity-streamfunction relation that corresponds to the maximum-entropy equilibrium state proposed by Joyce \& Montgomery (J. Plasma Phys., vol. 10, issue 1, 1973, pp. 107-121) and Montgomery \& Joyce (Phys. Fluids, vol. 17, issue 6, 1974, pp. 1139-1145) for 2D flat-bottom turbulence. Motivated by recent observations that a linear PV-streamfunction relation depicts the background flow of 2D topographic turbulence, we propose to model the final state of the total flow by additionally superposing a ``$\sinh$'' relation to account for isolated vortices. We validate the empirical ``$\sinh$'' relation and composition model against the final states in 2D turbulence simulations configured with two simple domain-scale topographies: a sinusoidal bump plus a dip, and a zonal ridge plus a trench. Good agreements are obtained for both topographies, provided that the empirical theory must be adapted to the zonally averaged flow states over the latter. For the first time, our empirical theory correctly describes the final flow structures and uncovers the coexistence of two equilibrium states in 2D topographic turbulence.