TY  - EJOU
AU  - Danshi	Liu, 
AU  - 	Jiadong	Wang, Jiadong	Wang
AU  - 	Xuewei	Mao, Xuewei	Mao
AU  - Jian	Deng, 

TI  - Energetic	Benefits	for	Two	Swimmers	in	a	Circular	Runway
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2023
VL  - 27
IS  - 3
SN  - 1933-2815

AB  - The	coordinated	motion	by	multiple	swimmers	is	a	fundamental	component	in	fish	school.	Fish	swimming	
in	 a	 certain	 formation	 (tandem,	 side	 by	 side,	 diamond	 and	 phalanx	 etc.)	 can	 gain	 substantial	 energetic	
benefits.	However,	the	question	whether	the	non-straight	swimming	behaviors	such	as	milling	structure	in	
other	 collective	 patterns	 can	 also	 gain	 energetic	 benefits	 remains	 to	 be	 explored.	 Based	 on	 a	 series	 of	
simulations	on	two	self-propelled	swimmers,	we	provide	a	viewpoint	for	the	energetic	benefits	of	milling	
pattern	 in	 collective	 behaviors.	 The	 trajectory	 and	 velocity	 of	 both	 swimmers	 are	 controlled	 by	 a	 PID	
approach.	First,	we	demonstrate	that	the	influence	of	the	circumferential	effect	on	the	optimal	phase,	as	well	
as	the	energy	saving	resulting	from	the	benefits	of	both	propulsion	and	turning.	Then,	we	study	the	radial	
effect	in	 terms	of	energetic	benefits.	 In	 the	milling	pattern,	 the	swimmers	on	 the	inside can	get	a	certain	
energetic	benefit	(-8%)	easily,	while	their	peers	on	the	outside	have	to	be	close	enough	(≤ 0.1BL)	to	the	
inner	one	with	a	proper	phase	to	gain	the	energetic	benefit	(-14%).	Whatever	the	radial	spacing	becomes	
larger	or	lies	in	an	unmatched	phase,	the	swimming	of	the	outer	ones	tend	to	be	more	laborious	(+16%).	It	
is	 found	 that	 the	 swimmers	 that	 keep	 the	matched	 phase	 and	minimum	 radial	 effect	 obtain	 the	 largest	
energetic	benefits	(-26%).	The	present	results	indicate	the	energetic	benefits	by	swimmers	even	in	a	milling	
pattern,	in	which	the	position	difference	dominates	the	extent	of	benefit.
KW  - Biological	fluid	dynamics;	biomimetic	propulsion;	collective	swimming

DO  - 10.32604/icces.2023.09789