Sub-grid scale model with structure effects incorporated
through the helicityNobumitsu YOKOI
Institute of Industrial Science, University of Tokyo
In collaboration with Akira YOSHIZAWA
turbulent electromotive force
Reynolds (+ turb. Maxwell) stress
: mean velocity strain : mean magnetic strain
FlowLarge-scale structure
Turbulence
Transportcoefficients
Productionrates
Intensity of turbulence:energy
Structure of turbulence:helicities
Transport suppression
Eddyviscosity
Velocityshear
Magneticshear
Turbulent magneticdiffusivity
Electriccurrent
Vorticity
1
Mean velocity
: Time scale of turbulence
laminar turbulent turbulent mean
Swirling flow and turbulence (Yokoi & Yoshizawa, PoF, 1993)
2
Mean velocity
: Time scale of turbulence
laminar turbulent turbulent mean
Uz
Uz
Uθ
Uθ
r
r
z
θ
θ
turbulent swirling
Swirling flow and turbulence (Yokoi & Yoshizawa, PoF, 1993)
2
Mean velocity
: Time scale of turbulence
laminar turbulent turbulent mean
Uz
Uz
Uθ
Uθ
r
r
z
θ
θ
turbulent swirling
Swirling flow and turbulence (Yokoi & Yoshizawa, PoF, 1993)
2
Mean velocity
: Time scale of turbulence
laminar turbulent turbulent mean
Uz
Uz
Uθ
Uθ
r
r
z
θ
θ
turbulent swirling
Swirling flow and turbulence (Yokoi & Yoshizawa, PoF, 1993)
2
Mean velocity
: Time scale of turbulence
laminar turbulent turbulent mean
Uz
Uz
Uθ
Uθ
r
r
z
θ
θ
turbulent swirling
Swirling flow and turbulence (Yokoi & Yoshizawa, PoF, 1993)
2
Smagorinskyconstant CS
Isotropic flow
Mixing-layer flow
Channel flow
Classical Smagorinsky model
Problem of constant adjustment
SGS viscosity
: Smagorinsky constant
Structure effect
3
Smagorinskyconstant CS
Isotropic flow
Mixing-layer flow
Channel flow
Dissipativenature
more
less
Classical Smagorinsky model
Problem of constant adjustment
SGS viscosity
: Smagorinsky constant
Structure effect
3
Smagorinskyconstant CS
Isotropic flow
Mixing-layer flow
Channel flow
Fluctuating vorticity(Robinson, Kline & Spalart 1988)
Vorticalstructures
weak
intermediate
strong
Dissipativenature
more
less
Classical Smagorinsky model
Problem of constant adjustment
SGS viscosity
: Smagorinsky constant
Structure effect
3
Smagorinskyconstant CS
Isotropic flow
Mixing-layer flow
Channel flow
Fluctuating vorticity(Robinson, Kline & Spalart 1988)
Vorticalstructures
weak
intermediate
strong
Coherent vortical structures may be related to the less dissipative nature
Dissipativenature
more
less
Classical Smagorinsky model
Problem of constant adjustment
SGS viscosity
: Smagorinsky constant
Structure effect
3
Grid-Scale (GS) velocity equation
SGS stress
SGS viscosity Helicity-related coefficient
Two-equation model
SGS K equation
SGS HS equation
Helicity SGS model
4
One-equation model
SGS viscosity
Helicity-related coefficient
SGS turbulent energy KS
SGS turbulent helicity (HS) equation
SGS Reynolds stress
Local equilibrium of the SGS energy
Production ~ Dissipation
Production ~ Dissipation
5
Zero-equation model (Same level as Smagorinsky model)
Local equilibrium of the SGS helicity Production ~ Dissipation
with
requires testusing DNS
6
Grid-Scale (GS) velocity equation
SGS stress
GS strain rate
Magnetohydrodynamic Case
Grid-Scale (GS) magnetic-field equation
SGS electromotive force
7
MHD Counterpart of the Smagorinsky Model
Local equilibrium of the SGS energy
Production ~ Dissipation
Production
Dissipation
Turbulent magneticPrandtl number
8
Smagorinsky model for MHD
Local equilibrium
9
Local equilibrium of the SGS cross helicity
Production
Dissipation
Production ~ Dissipation
10
Smagorinsky model for MHD
Turbulent magneticPrandtl number
Local equilibrium
11
Helicity-related Termsin MHD Case
Turbulent MHD residual helicity
HR equation
12
Local equilibrium
Equipartition
13
14
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