Momentum decomposition of the pressure field

The generative mechanism of the pressure field is fundamental in turbulence research and flow control, especially when subject to turbulent separation at high Reynolds numbers. To this end, we propose a physics-based framework—momentum decomposition of the pressure field—which uses the momentum equations to decompose the spatial pressure gradient into quantifiable momentum budgets. Each momentum budget corresponds to a distinct physical mechanism, enabling a rigorous decomposition and quantitative evaluation of the inherent mechanisms governing pressure generation. Incorporating results of a direct numerical simulation of laminar cylinder flow, this method is first demonstrated, after which the three-dimensional large eddy simulation results of a complex turbulent bluff body wake at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mtext>Re</a:mtext> <a:mi>D</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>1.88</a:mn> <a:mo>×</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>5</a:mn> </a:msup> </a:mrow> </a:math> are analyzed with a comparison of flow control. In the near wake, the bulk of low pressure originates from the streamwise convection of the centripetal flow outside the wake, which manifests as a streamline curvature effect from the term <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mover> <b:mi>u</b:mi> <b:mo>¯</b:mo> </b:mover> <b:mi>∂</b:mi> <b:mover> <b:mi>v</b:mi> <b:mo>¯</b:mo> </b:mover> <b:mo>/</b:mo> <b:mi>∂</b:mi> <b:mi>x</b:mi> </b:mrow> </b:math> , while the pressure variation inside the wake receives main contributions from Reynolds stresses. Under flow control, due to the streamline curvature modification near the base edge, the pulsed jet produces favorable pressure gradients from the mean flow term <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mover> <c:mi>u</c:mi> <c:mo>¯</c:mo> </c:mover> <c:mi>∂</c:mi> <c:mover> <c:mi>v</c:mi> <c:mo>¯</c:mo> </c:mover> <c:mo>/</c:mo> <c:mi>∂</c:mi> <c:mi>x</c:mi> </c:mrow> </c:math> contributing to the bulk of base-pressure recovery. Overall, the proposed framework provides a fundamental flow diagnostic tool and a rigorous foundation for designing and analyzing flow control strategies, since pressure control can be rationally linked to the momentum budgets manipulation, generally applicable to flow regimes governed by the Navier-Stokes equations.