数学与物理交叉学科学术报告(Prof. Yasuhide Fukumoto,日本九州大学)

发布者:项晓玲   发布时间:2018-02-23  浏览次数:179

报告人:Prof. Yasuhide Fukumoto(Institute of Mathematics for Industry, Kyushu University, Japan)

报告题目:Stability of a free surface of velocity discontinuity of a shallow-water flow

报告时间:201832(周五)10:00-11:00

                    201834(周日)10:00-11:00

报告地点:21427报告厅

  

摘要:We revisit the stability of a free surface of velocity discontinuity in a shallow-water stream. The fluid is moving with a uniform velocity U in a half-region but is at rest in the other. The drag force at the bottom surface, quadratic in velocity, is taken into account. In the absence of the drag, the interface of velocity discontinuity undergoes the instability of the Kelvin-Helmholtz type if the velocity discontinuity U is smaller than 8^{1/2}c, but is stabilized otherwise (U>8^{1/2}c), with c being the propagating speed of the gravity wave. The bottom drag destabilizes the interface in the latter range of the Froude number Fr=U/c. For both small and large values of the drag coefficient, the asymptotic form of the growth rate is written down in tidy form. We find that the instability never ceases however large the drag strength is.

  

We put these results on the ground of the Hamiltonian mechanical system. The necessary ingredient for the dissipation induced instability is negative-energy modes, and the energy of waves is calculated. Besides, we address the dissipation effect on so called the over-reflection, being closely related to the instability.

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