Kelvin-Helmholtz Instability Waves

Kelvin-Helmholtz Instability Waves are formed when one fluid layer is on top of another fluid layer moving with a different velocity. These instabilities take the form of small waves that can eventually grow into vortex rollers. This is a purely potential flowirrotational) phenomenon. The following Mathematica code was adapted from Zheming Zheng’s Fortran program. It uses vortex blobs to simulate smooth rollers and periodic point vortices to simulate the far field. A simple predictor-corrector scheme is used to integrate the differential equations:

(* runtime: 9 minutes *) n = 40; dt = 0.05; L = 2Pi; gamma = L/n; rcore = 0.5; plist = Table[{x, 0.01 Sin[2Pi x/L]}, {x, 0, L(1 - 1/n), L/n}]; vcalc[plist_] := Table[Sum[{x, y} = plist[[j]] - plist[[i]]; gamma/(2Pi) Sum[If[i == j && k == 0, 0, r2 = (x + k L)^2 +y^2; {-y, x + k L}/r2(1 - Exp[-r2/rcore^2] - 1)], {k, -3, 3}] + If[i ==j, 0, gamma/(2L) {-Sinh[2Pi y/L], Sin[2Pi x/L]}/(Cosh[2Pi y/L] - Cos[2Pi x/L])], {j, 1, n}], {i, 1, n}]; Do[vlist = vcalc[plist]; vlist0 =vlist; vlist = vcalc[plist + dt vlist]; plist += dt(vlist0 + vlist)/2; ListPlot[plist, PlotJoined -> True, PlotRange -> {-2, 2}, AspectRatio -> Automatic], {i, 1, 400}];

Here is some Mathematica code to plot streamlines assuming periodic point vortices: (* runtime: 2 seconds *) Clear[psi]; psi[x_, y_] := Plus @@ Map[-gamma/(4 Pi) Re[Log[Cos[2Pi(x – #[[1]])/L] – Cosh[2Pi (y – #[[2]])/L]]] &, plist]; ContourPlot[psi[x, y], {x, 0, L}, {y, -L/3, L/3}, PlotRange -> All, ContourShading -> False, PlotPoints -> 20, AspectRatio -> Automatic]

Link: Kelvin-Helmholtz waves in the clouds

Here is another variation showing vortex pairing and pathlines.

Link: movie – famous experiment by Bernal


0 Responses to “Kelvin-Helmholtz Instability Waves”

  1. Leave a Comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Welcome !

You will find here some of my favorite hobbies and interests, especially science and art.

I hope you enjoy it!

Subscribe to the RSS feed to stay informed when I publish something new here.

I would love to hear from you! Please feel free to send me an email : bugman123-at-gmail-dot-com


Blog Stats

  • 553,072 hits

%d bloggers like this: