论文标题
在带有非符号温度温度曲线的BousSinesQ方程式上
On the Boussinesq equations with non-monotone temperature profiles
论文作者
论文摘要
在本文中，我们考虑了二维Boussinesq方程的渐近稳定性，其部分耗散在COUETTE流量和温度曲线的组合$ t（y）$的组合近。作为第一个主要结果，我们表明，如果$ t'$最多是$ν^{1/3} $，则在适当的规范中，则只有垂直散发速度而不是温度稳定的线性化boussinesq方程。因此，在这种线性化情况下，混合增强的耗散可以抑制雷利 - 贝纳德的不稳定性。我们进一步表明，这些结果扩展到温度和速度垂直耗散的（强制）非线性方程。
In this article we consider the asymptotic stability of the two-dimensional Boussinesq equations with partial dissipation near a combination of Couette flow and temperature profiles $T(y)$. As a first main result we show that if $T'$ is of size at most $ν^{1/3}$ in a suitable norm, then the linearized Boussinesq equations with only vertical dissipation of the velocity but not of the temperature are stable. Thus, mixing enhanced dissipation can suppress Rayleigh-Bénard instability in this linearized case. We further show that these results extend to the (forced) nonlinear equations with vertical dissipation in both temperature and velocity.
