# Presentation: 567919

## Enhanced Energy Loss from Reconnections with a Vortex Mesh

**I.H. Neumann, R.J. Zieve**
**UC Davis Physics                    ****CA-APS October 26, 2007**

## Problem with friction

** ****bulk mutual friction proportional to **
**  ****amount of normal phase in SF; **
**  ****calculate based on temp. & velocity**
**  ****F****friction**** = ************s**** (v****n ****– ****v****vortex****)**
** ****experimentally observed value 10****8**** times **
**  ****larger than expected at low temperatures;**
**  ****more importantly does not scale with ********n**
** ****vortex moves at local SF velocity**
** ****see precession along wall by measuring **
**  ****movement of attachment point on wire**

**Notes:**
Friction equation we use v= v local (ring-nl ring)+ v nonlocal (BS piece) - alpha* v perp

“consider partially trapped vortex on wire with free end precessing along wall

Dissipation due to moving sf vortex core scattering off of normal fluid excitations

## Model

** ****consider mesh of **
**  ****microscopic vortices **
**  ****on wall**
** ****partially trapped vortex **
**  ****on the wire, other end **
**  ****on cylindrical cell wall**
** ****wall end of moving vortex travels through mesh **
**  ****at the local superfluid velocity**

**Questions**

**Does mesh enhance energy dissipation?**
**Do reconnections decrease the length of the moving vortex?**
**Do oscillations of the moving vortex increase its velocity thereby increasing dissipation?**

- Z-axis  position

- Position projected along x-axis

**Notes:**
“after annihilation of most of the bulk rotation in the superfluid, after rotation ceases”

## Simulations

** ****generate random mesh of straight pinned vortices**
** ****vary mesh vortex length and orientation**
** ****vary mesh vortex density **
**  ****(number of vortices & dimensions of mesh)**
** ****measure position of vortex attachment point**
** ****amount of vortex on wire is proportional to**
**  ****energy stored in vortex**

## Method

** ****5****th**** order Runge-Kutta-Fehlberg calculates **
**  ****change in position of moving vortex (circulation)**
** ****fluid flow field (velocity) calculated using **
**  ****Biot-Savart law, image vortices, boundary conditions**
** ****allow moving vortex to recombine with mesh **
**  ****vortices when within certain proximity**
** ****use artificially high friction coefficient to keep **
**  ****simulation stable**
** ****use moving mesh of vortices on wall**

**Notes:**
“trying to keep moving vortex end in middle of wall mesh”
Compare vel diff btwn 4th and 5th order; time step to solve ODE  ~ 25 pts 2.5x10-3
 eqn of motion Eulers eqn for incompressible fluid flow + added friction; core treat as r(1.3Ang)<<curvature of vortex and massless

non-local contrib to vel: integrate over vortex core (using Biot Savart)
Local sf vel “self induced field’ comes from exp values for ring – non local part of ring (fit ring to curve)

v= v local (ring-nl ring)+ v nonlocal (BS piece) - alpha* v perp
Subtract vel tangent to vortex core (antibunching)

Fourier series soln of laplace eqn to cancel remaining perp vel to curved wall- takes too much time so assume good enough cancelation due to images and rest is left to roughness

Vortex on wire semiinfinite –inf to wall image is wall to +inf

## Movie 

- position projected along the x-axis

- Z-axis position

**Notes:**
“plots moving vortex and its reconnections with mesh vortices on wall over time”

Gnuplot plots text file; Put in my real data; bloch aug29 if movie good else glasernov6

## Results

** ****50-200% enhancement of moving vortex energy dissipation rate **
**   ****when allowing interaction with wall mesh vortices**

**1.67**

**Notes:**
Put in my real data; bloch aug29 if movie good else glasernov6

Explain comparison of 1st slope when interacting with mesh to end where slope only due to friction since no mesh

## Conclusions

** ****interaction of moving vortex with wall  **
**  ****mesh vortices causes an increase in **
**  ****energy dissipation rate**
** ****velocity does not change significantly when vortex **
**  ****is allowed to reconnect with mesh**
** ****we believe that reconnections with mesh shorten **
**  ****the vortex on the wire thereby causing it to lose **
**  ****line energy**

**Notes:**
Vel important for mutual friction since goes as v cubed (?) but also there is a critical vel for sf at which it actually has viscosity

--run on the sim using here and have some print outs to show for vel spectrum

## Experiment

** ****vibrating wire cell filled with ****4****He (at ~350mk) **
** ****rotate cryostat to create circulation**
** ****stop rotation, wait for vortex to pin on cell wire**
** ****circulation around wire changes the vibrational **
**  ****modes **

## Measurement Technique

** ****pluck wire with current pulse    **
** ****circulation around the wire from a **
**  ****vortex splits frequency degeneracy**
** ****cell in magnetic field **
** ****observe beats in emf, **
**  ****proportional to circulation**