Shear-induced breaking of large internal solitary waves
Shear-induced breaking of large internal solitary waves
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DOI：
10.1017/s0022112008004898
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发表时间：
2009-02-10
影响因子：
3.7
通讯作者：
Davies, Peter A.
中科院分区：
文献类型：
--
作者：
Fructus, Dorian;Carr, Magda;Davies, Peter A.
研究了24个最小Richardson数小于1/4的极大振幅内孤立波(ISW)的稳定性。这项研究还补充了三层流体中的完全非线性计算。波沿着夹在薄的上层(深度hi)和深层(深度h(3))之间的线性分层的跃层(深度h(2))移动，两者都是均匀的。特别是，用粒子图像测速仪(PIV)测量了通过跃层的波浪诱导速度剖面，并通过计算获得了该剖面。发现破裂的ISW的振幅在a(1)>；2.24根h(1)h(2)(1+h(2)/h(1))的范围内，而稳定波则在或低于这一界限。研究了0.27<；h(2)/h(1)<；1和4.14<；h(3)/(h(1)+h(2))<；7.14的破裂波和0.36<；h(2)/h(1)<；3.67和3.22<；h(3)/(h(1)+h(2))<；7.25的稳定波。破裂处可见开尔文·亥姆霍兹样巨浪。它们的长度为7.9h(2)，传播速度是波速的0.09倍。这些实测值与稳定性分析的预测值吻合得很好，假设定常剪切流的U(Z)和Rho(Z)取在波极大处(U(Z)水平速度剖面，p(Z)密度沿垂直z)。只有具有足够强度的波中的不稳定模才有机会增长得足够快，以形成破裂：破裂的波的估计增长率(不稳定模)是最强稳定情况下的3.3-3.7倍。对最小Richardson数(Ri(Min)，在跃层中)，一个可能不稳定的袋子的水平长度，与波诱导的Ri<；14，(L-x)和波长(波长)的评估表明，在(L-x/波长，Ri(Min))平面上，所有的测量结果都落在Ri(Min)=-0.23L(X)/lambda+0.298+/-0.016的范围内。发现了L-x/波长0.86的破裂波和L-x/波长0.86的稳定波。结果表明，在L-x/λ方面，存在一种类似门槛的行为。结果表明，L-x/λ=0.86的破裂阈值比基于最小Richardson数的破裂阈值更尖锐，并揭示了Richardson数在较厚的跃层中几乎是反对称的，最小值出现在跃层的顶部。
The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h(2)) sandwiched between a thin upper layer (depth hi) and a deep lower layer (depth h(3)), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a,) in the range a(1) > 2.24 root h(1)h(2)(1 + h(2)/h(1)), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 < h(2)/h(1) < 1 and 4.14 < h(3)/(h(1) + h(2)) < 7.14 and stable waves for 0.36 < h(2)/h(1) < 3.67 and 3.22 < h(3)/(h(1) + h(2)) < 7.25. Kelvin Helmholtz-like billows were observed in the breaking cases. They had a length of 7.9h(2) and it propagation speed 0.09 times the wave speed. These measured Values compared well with predicted values from a stability analysis, assuming steady shear flow with U(z) and rho(z) taken at the wave maximum (U(z) horizontal velocity profile, p(z) density along the vertical z). Only unstable modes in waves of sufficient strength have the chance to grow sufficiently fast to develop breaking: the waves that broke had an estimated growth (of unstable modes) more than 3.3-3.7 times than in the strongest stable case. Evaluation of the minimum Richardson number (Ri(min), in the pycnocline), the horizontal length of a pocket of possible instability, with wave-induced Ri < 14, (L-x) and the wavelength (lambda), showed that all measurements fall within the range Ri(min) = -0.23L(x)/lambda + 0.298 +/- 0,016 in the (L-x/lambda, Ri(min))-plane. Breaking ISWs were found for L-x/lambda > 0.86 and stable waves for L-x/lambda < 0.86. The results show a sort of threshold-like behaviour in terms of L-x/lambda. The results demonstrate that the breaking threshold of L-x/lambda = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnocline.