a	amplitude envelope of lateral motion
$a_{max}$	maximum amplitude
A	maximum lateral excursion of the tail over a cycle
$C_f$	force coefficient
$C_p$	pressure force coefficient
${\overline{C}}_f$	mean axial force coefficient
$C_v$	viscous force coefficient
D	drag
f	tail-beat frequency
F	force exerted on the fish body by the flow
h	lateral excursion of the body
$\dot{h}$	velocity of the lateral undulations
k	wave number of the body undulations
L	fish length
PIV	particle image velocimetry
${\overline{P}}_{side}$	mean power loss
$Re$	Reynolds number
$St$	Strouhal number
t	time
T	thrust
$\overline{T}$	mean thrust force
U	swimming speed
V	speed of the backward undulatory body wave
z	axial flow direction measured along the fish axis from the tip of the fish’s snout
$\beta$	slip velocity
$\eta$	Froude propulsive efficiency
$\lambda$	wavelength
$\nu$	kinematic viscosity of water
$\rho$	fluid density
$\tau$	tail-beat period
${\tau }_{ij}$	viscous stress
$\omega$	angular frequency