The long-wave vorticity dynamics of rotating buoyant outflows
The long-wave vorticity dynamics of rotating buoyant outflows
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DOI：
10.1017/jfm.2017.291
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发表时间：
2017-06
影响因子：
3.7
通讯作者：
E. Johnson;O. Southwick;N. R. McDonald
中科院分区：
文献类型：
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作者：
E. Johnson;O. Southwick;N. R. McDonald
本文通过考虑相对于旋转框架，将浮力流体注入由固体壁限制的静止流体时的流动发展来讨论沿岸流的演变。初始快速响应由科里奥利力-压力梯度平衡确定，开尔文波以长波速度快速传播，边界壁位于其右侧（正旋转）。然而，流体柱可以拉伸或挤压喷射从沿海流出，使喷出的流体获得正或负的相对涡度。根据它的符号，这种涡度在固体壁中的图像可以加强或对抗由开尔文波（KW）建立的零位涡度异常（PVa）流。本文提出了一个简单的、完全非线性的、色散的准地转模式，讨论了涡旋与KW驱动的相对强度变化时沿岸外流的形式。该模型保留了足够的物理捕捉在有限振幅的影响，从而基本的非线性的流量，但足够简单，以便允许高精度的数值积分的完整的问题，也明确，完全非线性的解决方案，在水力极限的均匀PVa流出的演变。外流演变强烈依赖于被驱逐流体的PVa的符号，这决定了涡和KW驱动是加强还是相反，以及内部Rossby半径与涡源尺度的比值，|V_{0}/D^{2}\unicode[STIX]{x1D6F1}_{0}|^{1/2}$，（其中$D$测量流出深度，$\unicode[STIX]{x1 D 6 F1}_{0}$测量流出的PVa，$V_{0}$测量流出的体积通量），它测量两个驱动器的相对强度。显式水力解与数值积分的比较表明，解析解预测的流动发展以及与分散Rossby波在当前边界上的差异，并在源区域的变化捕获的完整方程，但不存在的水力解决方案。
This paper discusses the evolution of coastal currents by considering, relative to a rotating frame, the flow development when buoyant fluid is injected into a quiescent fluid bounded by a solid wall. The initial rapid response is determined by the Coriolis force–pressure gradient balance with a Kelvin wave propagating rapidly, at the long-wave speed, with the bounding wall to its right (for positive rotation). However fluid columns can stretch or squash on ejection from coastal outflows so that the ejected fluid gains positive or negative relative vorticity. Depending on its sign, the image in the solid wall of this vorticity can reinforce or oppose the zero potential-vorticity-anomaly (PVa) current set up by the Kelvin wave (KW). This paper presents a simple, fully nonlinear, dispersive, quasi-geostrophic model to discuss the form of coastal outflows as the relative strength of vortex to KW driving is varied. The model retains sufficient physics to capture both effects at finite amplitude and thus the essential nonlinearity of the flow, but is sufficiently simple so as to allow highly accurate numerical integration of the full problem and also explicit, fully nonlinear solutions for the evolution of a uniform PVa outflow in the hydraulic limit. Outflow evolutions are shown to depend strongly on the sign of the PVa of the expelled fluid, which determines whether the vortex and KW driving are reinforcing or opposing, and on the ratio of the internal Rossby radius to the vortex-source scale, $|V_{0}/D^{2}\unicode[STIX]{x1D6F1}_{0}|^{1/2}$ , of the flow (where $D$ measures the outflow depth, $\unicode[STIX]{x1D6F1}_{0}$ the PVa of the outflow and $V_{0}$ the volume flux of the outflow), which measures the relative strengths of the two drivers. Comparison of the explicit hydraulic solutions with the numerical integrations shows that the analytical solutions predict the flow development well with differences ascribable to dispersive Rossby waves on the current boundary and changes in the source region captured by the full equations but not present in the hydraulic solutions.