the stokes drift and mean flows induced by two-dimensional internal gravity wave packets
DESCRIPTION
The Stokes Drift and Mean Flows Induced by Two-Dimensional Internal Gravity Wave Packets. Ton van den Bremer 1,2 & Bruce Sutherland 2,3 1. Department of Engineering Science, University of Oxford 2. Woods Hole Oceanographic Institution - PowerPoint PPT PresentationTRANSCRIPT
PowerPoint Presentation
The Stokes Drift and Mean Flows Induced by Two-Dimensional Internal Gravity Wave PacketsTon van den Bremer1,2 & Bruce Sutherland2,31. Department of Engineering Science, University of Oxford2. Woods Hole Oceanographic Institution 3. Depts. Physics and Earth & Atmospheric Sciences, University of Alberta
EUROPEAN GEOSCIENCES UNION, APRIL 2014Motivation: Periodic surface gravity waves
From Wallet & Ruellan (1950)
Orbit doesnt close: net horizontal driftMotivation: Periodic surface gravity waves
From Wallet & Ruellan (1950)
Solution to linearized problem for periodic waves:
Circular motion to leading order O() and net horizontal drift at next order O(2), where =ak (steepness).
Motivation: Surface gravity wave packets
From Longuet-Higgins & Stewart (1962), see also McIntyre (1981).
Motivation: Surface gravity wave packets
A deep return flow below surface waves ensures zero vertically-integrated momentum (at x=cgt).What are internal gravity waves?
Surface gravity wavesInternal gravity wavesFree surfaceGravity is restoring forceFluid has uniform densityStratification: layers of different densityBuoyancy is restoring forceStokes drift for periodic internal gravity waves (igws)x- and z-periodicx-periodic and z compactNo Stokes drift
Horizontal Stokes drift
Problem definitionWhat is the structure of the Stokes drift / induced mean flow for a vertically and horizontally localized internal wave-packet?Assumptions:Uniformly stratified ambient,Boussinesq approximation,No dissipation,Weakly non-linear: no feedback of induced flow on packet propagation,Infinite two-dimensional domain (x,z),Approach:Separation of scales expansion of non-linear governing equations,Fully non-linear numerical simulations.
Governing equationsTwo-dimensional Boussinesq internal waves in linearly stratified fluid (stable): Momentum (x and z), internal energy and incompressibility:
Vertical displacement9Leading-order Induced mean flow
Leading-order Induced mean flow
Requirement: no indefinite growth in x.
O(4)O(2)O( 2 3 )Mean-flow response O(2)
No induced flow in vertical: stratification inhibits all motion,Horizontal velocity cannot vary in horizontal direction: long response.
The non-local response: wave-packet filtered
From numerical simulations: =0.01, =0.05,Induced mean flow not included as initial condition.
The non-local response: the long wave scale
From numerical simulations: =0.01, =0.05,Induced mean flow not included as initial condition.
The non-local response: the long wave scale
ConclusionsA two-dimensional horizontally and vertically compact internal gravity wave packet:No mean flow in the vertical,Horizontally long (>>packet) waves are excited,Contain finite amount of horizontal momentum predicted well by theory.Theoretical and numerical validation of Brethertons (1969) anticipation.
Thank you for your attention!