A vorticity wave packet breaking within a rapidly rotating vortex. Part II: wave/mean flow interaction

2021 ◽  
Author(s):  
Philippe Caillol
Keyword(s):  
Wave Packet ◽  
Mean Flow ◽  
Flow Interaction

Numerical study on the eddy–mean flow interaction between a cyclonic eddy and Kuroshio

2016 ◽  
Vol 72 (5) ◽  
pp. 727-745 ◽  
Author(s):  
Wu Geng ◽  
Qiang Xie ◽  
Gengxin Chen ◽  
Tingting Zu ◽  
Dongxiao Wang
Keyword(s):  
Numerical Study ◽  
Cyclonic Eddy ◽  
Mean Flow ◽  
Flow Interaction

scholarly journals Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

2019 ◽  
Vol 875 ◽  
pp. 1145-1174 ◽  
Author(s):  
T. Congy ◽  
G. A. El ◽  
M. A. Hoefer
Keyword(s):  
Water Waves ◽  
Large Scale ◽  
Kdv Equation ◽  
Linear Wave ◽  
Mean Flow ◽  
Undular Bore ◽  
Expansion Waves ◽  
Flow Interaction ◽  
The Kdv Equation ◽  
New Type

A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

scholarly journals Mean flows generated by a progressing water wave packert

1981 ◽  
Vol 22 (3) ◽  
pp. 318-347 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Wave Packet ◽  
Boundary Conditions ◽  
Finite Length ◽  
Water Wave ◽  
Wave Train ◽  
Mean Flow ◽  
The Mean

AbstractEquations are derived which describe the evolution of the mean flow generated by a progressing water wave packet. The effect of friction is included, and so the equations are subject to the boundary conditions first derived by Longuet-Higgins [10]. Solutions of the equations are obtained for a wave packet of finite length, and also for a uniform wave train. The latter solution is compared with experiments.

The development of three-dimensional wave-packets in unbounded parallel flows

1968 ◽  
Vol 32 (4) ◽  
pp. 801-808 ◽  
Author(s):  
M. Gaster ◽  
A. Davey
Keyword(s):  
Wave Packet ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Physical Plane ◽  
Parallel Flows ◽  
Flow Velocity Profile ◽  
The Stability ◽  
Special Case ◽  
Dimensional Wave

In this paper we examine the stability of a two-dimensional wake profile of the form u(y) = U∞(1 – r e-sy2) with respect to a pulsed disturbance at a point in the fluid. The disturbed flow forms an expanding wave packet which is convected downstream. Far downstream, where asymptotic expansions are valid, the motion at any point in the wave packet is described by a particular three-dimensional wave having complex wave-numbers. In the special case of very unstable flows, where viscosity does not have a significant influence, it is possible to evaluate the three-dimensional eigenvalues in terms of two-dimensional ones using the inviscid form of Squire's transformation. In this way each point in the physical plane can be linked to a particular two-dimensional wave growing in both space and time by simple algebraic expressions which are independent of the mean flow velocity profile. Computed eigenvalues for the wake profile are used in these relations to find the behaviour of the wave packet in the physical plane.

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