Appendix A: Nomenclature

A.1 Symbols

A ₁, A ₂	subgrid stress tensors in the compressible momentum equation
B ₁, , B ₇	subgrid stress tensors in the compressible energy equation
c	speed of sound
C	cross-stress tensor
C _f	skin friction coefficient
E	total energy
G	convolution filter kernel
J ^?1	Jacobian of the curvilinear grid transform
k	wave number
k _c= ?/ ?	LES cutoff wave number
L	Leonard tensor
M	Mach number
M _sgs	subgrid-scale Mach number
M _t	turbulent Mach number
p	pressure
q _T	heat flux
R	subgrid Reynolds stress tensor
Re	Reynolds number
T	temperature
T _?	Kolmogorov time scale
u	velocity vector
U ^k	kth component of the contravariant flux
u _?	friction velocity

?	LES cutoff length
	test filter cutoff length
? x, ? y, ? z	mesh size in direction x, y, z
? t	time step of the computation
?	kinetic energy dissipation rate
? _num	numerical dissipation rate
? _sgs	subgrid dissipation rate
?	Kolmogorov length scale
?	molecular diffusivity
	dynamic viscosity
?	kinematic viscosity
?	frequency
?	density
?	subgrid stress tensor
? _?	viscous stress tensor
?	LES cutoff time

u _i	ith component of the velocity vector
	filtered part of
	subgrid part of
	mass-weighted filtered part of
	Fourier transform of
	expressed in boundary layer wall units
	synthetic filtered total energy
	synthetic filtered viscous stress tensor
	synthetic filtered heat flux
	tensorial...