arXiv subjects

John Marshall Cooper

Publications and source records attributed to John Marshall Cooper.

3 recordsLinked to original sources

arXiv2026

Mapping the Turn: An Eulerian Binormal-Axis Diagnostic for Recirculating 3D Flows

Three-dimensional (3D) recirculating flows are often interpreted qualitatively from selected streamline visualizations. In separated flows, such recirculating motion is central to the drag modulation, but the local orientation of recirculation remains difficult to quantify in a field-based form. This work introduces an Eulerian binormal-axis diagnostic that locally evaluates the orientation of streamline turning at each point in the velocity field, yielding a spatially resolved field of the recirculating direction. Motivated by the Frenet-Serret binormal direction of a curved streamline, the diagnostic uses the velocity vector and its convective acceleration to extract the local streamline-turning axis without requiring explicit streamline integration. The resulting direction is encoded with barycentric RGB weights to visualize streamwise, spanwise, and wall-normal turning axis contributions. The diagnostic is first applied to Hill's spherical vortex, which provides a controlled analytic example of 3D recirculating motion for interpreting the binormal-axis direction and the associated barycentric RGB encoding. It is then applied to the mean field of a pressure-gradient-induced 3D separation bubble. The resulting visualizations show that the diagnostic reveals orientation changes that are not apparent from streamline visualization. The proposed diagnostic therefore converts qualitative streamline impressions into a spatially resolved measure of local streamline-turning orientation, providing a quantitative complement to conventional 3D flow visualization.

physics.flu-dyn↗

arXiv2024

Separation of a Laminar Boundary Layer Subjected to Pressure Gradients with Spanwise Variations

The characteristics of three-dimensional laminar separation bubbles (LSBs), compared with their quasi-two-dimensional counterparts, are studied using direct numerical simulation. A three-dimensional suction-blowing distribution is applied on the top boundary to induce flow separation. Three levels of suction strength (i.e., adverse pressure gradient (APG) strength) are tested. For each suction level, the spanwise extent of the suction is varied. Two non-uniform suction distributions are compared with uniformly-applied suction across the full span (implying a two-dimensional LSB), totaling nine cases. All cases are performed at $Re_δ= U_{\infty}δ/ν= 1000$ based on the inflow boundary layer thickness ($δ$) and free-stream velocity ($U_{\infty}$). Initial results indicate stark contrast between three-dimensional and two-dimensional LSBs. Most notably, the role of suction width is determining the topology of the LSB and its reattachment mechanism. Meanwhile, APG is responsible for determining the size of the LSB and level of turbulence at reattachment. Streamwise-oriented vortices are identified along the crest of the three-dimensional LSBs.

physics.flu-dyn↗

arXiv2024

Pressure-Induced Separation of a Laminar Boundary Layer over a Partially-Slip Wall

The characteristics of pressure-induced laminar separation bubbles (LSBs) over a partially-slip wall, compared with that over a canonical no-slip wall, are studied using direct numerical simulation. Three cases, two utilizing linear Robin-type slip boundary conditions of differing slip length ($Λ$), and one non-slip are compared. For the partial-slip cases, a streamwise distribution of slip profile is employed ensuring smooth transition between no-slip and partial-slip (transition from no-slip to a constant slip length takes 5$δ$, where $δ$ is the inflow boundary layer thickness). The constant target slip length is maintained for $20δ$ upstream and during the onset of flow separation. The separation is induced by a wall-normal velocity profile applied at the top boundary. All cases are performed at $Re_δ= U_{\infty}δ/ν= 455$. Initial results indicate that as slip length increases, separation and reattachment are delayed. Most notably, the formation and shedding of roller vortices is mitigated as slip length increases, resulting in a less turbulent wake, despite that self-similarity of the plane shear layer is maintained.

physics.flu-dyn↗