论文标题
斯托克斯漂移及其不满
Stokes drift and its discontents
论文作者
论文摘要
Stokes Velocity $ \ Mathbf {U}^\ Mathrm {S} $，大约由Stokes（1847，Trans。Camb。Chimb。Soc。，8，441-455）定义，并且完全通过广义的Lagrangian均值在不可或缺的液体中均匀。我们表明，Stokes速度可以自然分解为螺线管组件，$ \ Mathbf {u}^\ Mathrm {s} _ \ Mathrm {solrm {Solrm {sol} $，其余的对于浪潮的较小而缓慢变化。我们进一步表明$ \ mathbf {u}^\ mathrm {s} _ \ mathrm {sol} $当适当地重新定义Lagrangian平均流程以确保其精确的不可压缩性时，出现了唯一的Stokes速度。该结构是Soward＆Roberts的GLM理论（2010年，J。FluidMech。，661，45-72）的应用，我们专门使用表面重力波，并使用Lie系列扩展有效地实现。我们进一步表明，相应的Lagrangian均值动量方程与Craik-Leibovich方程正式相同，并带有$ \ MathBf {u}^\ Mathrm {s} _ \ Mathrm {Solrm {Sol} $替换$ \ Mathbf {u} $ \ mathbf {u}^\ mathrm {s} $和$ \ mathbf {u}^\ mathrm {s} _ \ mathrm {sol} $。
The Stokes velocity $\mathbf{u}^\mathrm{S}$, defined approximately by Stokes (1847, Trans. Camb. Philos. Soc., 8, 441-455), and exactly via the Generalized Lagrangian Mean, is divergent even in an incompressible fluid. We show that the Stokes velocity can be naturally decomposed into a solenoidal component, $\mathbf{u}^\mathrm{S}_\mathrm{sol}$, and a remainder that is small for waves with slowly varying amplitudes. We further show that $\mathbf{u}^\mathrm{S}_\mathrm{sol}$ arises as the sole Stokes velocity when the Lagrangian mean flow is suitably redefined to ensure its exact incompressibility. The construction is an application of Soward & Roberts's glm theory (2010, J. Fluid Mech., 661, 45-72) which we specialise to surface gravity waves and implement effectively using a Lie series expansion. We further show that the corresponding Lagrangian-mean momentum equation is formally identical to the Craik-Leibovich equation with $\mathbf{u}^\mathrm{S}_\mathrm{sol}$ replacing $\mathbf{u}^\mathrm{S}$, and we discuss the form of the Stokes pumping associated with both $\mathbf{u}^\mathrm{S}$ and $\mathbf{u}^\mathrm{S}_\mathrm{sol}$.
