Zonostrophic Instability
Zonostrophic Instability
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地带性不稳定
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
W. Young
中科院分区：
文献类型：
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作者：
K. Srinivasan;W. Young
分带不稳定性导致无射流基态流在b平面上自发出现纬向射流，该流受底部阻力的阻尼和随机体力的驱动。将正压涡度方程分解为纬向平均和涡旋方程，忽略涡旋-涡旋相互作用，定义拟线性系统。QL系统的数值解显示出与求解非线性（NL）系统得到的射流长度尺度相当的纬向射流。从QL系统出发，可以构造涡度的两点单时间相关函数演化的确定性方程，由此可以得到驱动纬向平均流的雷诺兹应力。该确定性系统具有精确的非线性解，即无射流的各向同性均匀涡场。作者通过在参数空间中计算临界稳定性曲线来表征该无射流解的线性稳定性，并成功地将该解析结果与QL系统的数值解进行了比较。但NL型纬向性不稳定发生所需的临界阻力有时比QL型纬向性不稳定发生所需的临界阻力小6倍。在临界稳定曲线附近，线性稳定性理论预测的射流规模与QL数值计算结果一致。但在减少阻力方面，新兴的QL喷气机仅在短时间内符合线性稳定性预测。随后，射流与邻近的射流合并，直到气流成熟，射流的宽度明显大于线性预测，但间距与NL射流相似。
Zonostrophic instability leads to the spontaneous emergence of zonal jets on a b plane from a jetless basicstate flow that is damped by bottom drag and driven by a random body force. Decomposing the barotropic vorticity equation into the zonal mean and eddy equations, and neglecting the eddy–eddy interactions, defines the quasilinear (QL) system. Numerical solution of the QL system shows zonal jets with length scales comparable to jets obtained by solving the nonlinear (NL) system. Starting with the QL system, one can construct a deterministic equation for the evolution of the two-point single-time correlation function of the vorticity, from which one can obtain the Reynolds stress that drives the zonal mean flow. This deterministic system has an exact nonlinear solution, which is an isotropic and homogenous eddy field with no jets. The authors characterize the linear stability of this jetless solution by calculating the critical stability curve in the parameter space and successfully comparing this analytic result with numerical solutions of the QL system. But the critical drag required for the onset of NL zonostrophic instability is sometimes a factor of 6 smaller than that for QL zonostrophic instability. Near the critical stability curve, the jet scale predicted by linear stability theory agrees with that obtained via QL numerics. But on reducing the drag, the emerging QL jets agree with the linear stability prediction at only short times. Subsequently jets merge with their neighbors until the flow matures into a state with jets that are significantly broader than the linear prediction but have spacing similar to NL jets.