Mastering the Manu—how humans create large splashes

摘要

Manu jumping, a popular water diving style among M <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="u1" overflow="scroll"> <mml:mover> <mml:mtext>a</mml:mtext> <mml:mo stretchy="false" style="math-style:normal;math-depth:0;">¯</mml:mo> </mml:mover> </mml:math> ori people in New Zealand, focuses on creating large splashes. Divers perform aerial manoeuvres such as the ‘utkatasana’ pose, entering the water in a V-shape, and executing underwater manoeuvres to enhance the splash size. Our study explores the underlying fluid dynamics of Manu jumping and demonstrates how two key parameters, the V-angle and the timing of body opening, can enhance Worthington jet formation. To accurately replicate human Manu jumping, we studied water entry of both passive solid objects with varying V-angles and an active body opening robot (Manubot). The analysis revealed that a 45° V-angle enhances Worthington jet formation, consistent with human diving data. This angle balances a large cavity size and a deep pinch-off depth. The body opening within a timing window of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="u2" overflow="scroll"> <mml:mstyle displaystyle="true" scriptlevel="0"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mover> <mml:mi>t</mml:mi> <mml:mo stretchy="false">^</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.1</mml:mn> <mml:mspace width="negativethinmathspace"/> <mml:mo>−</mml:mo> <mml:mspace width="negativethinmathspace"/> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:mstyle> </mml:math> synchronizes the robot’s potential energies to be timely transferred to the cavity formation, producing the strongest and most vertical, i.e. ideal, Worthington jets. Based on our experimental findings, we propose a range of parameters for generating the large Manu splashes. These insights offer engineering perspectives on how to modulate underwater cavity dynamics using both passive and active body formations.