About

Krishnan Mahesh is a Professor of Mechanical Engineering and the Richard B. Couch Professor of Naval Architecture and Marine Engineering at the University of Michigan. He is also the Director of the Center for Naval Research and Education. His research interests focus on high-fidelity simulation of complex, multi-physics, turbulent flows relevant to various applications including marine propulsors, multiphase flows, cavitation, hydroacoustics, superhydrophobic surfaces, biofouling, fluid/structure interaction, flow stability, and moving-body flows. Dr. Mahesh has received numerous honors and awards for his contributions to fluid mechanics, including the 2026 ASME Freeman Scholar Award, the Best Paper Award at the Fifth International Symposium on Marine Propulsors, and the Fulbright Scholar award. He holds a Ph.D. in Mechanical Engineering from Stanford University, an M.S. from Stanford, and a B.Tech. from the Indian Institute of Technology, Bombay.

Research topics

• Mechanics
• Physics
• Computer science
• Materials science
• Statistical physics

Selected publications

• Effects of spanwise streamline curvature on a spatially developing boundary layer

  Journal of Fluid Mechanics · 2026-01-05

  articleOpen accessSenior author

  Direct numerical simulation is performed to study the effects of spanwise curvature on transitioning and turbulent boundary layers. Turbulent transition is induced with an array of resolved cuboids. Spanwise curvature is prescribed using a novel approach with a body force that is applied orthogonally to the bulk flow to curve the mean free-stream streamlines at a set radius. The flows are analysed in a streamline-aligned coordinate system. Although the radius of curvature is large compared with the size of the boundary layer, its effects on the development of the boundary layer are appreciable. The results indicate that spanwise curvature induces a non-uniform mean secondary flow and alters the structure of turbulence within the boundary layer. Analytical expressions for the crossflow are derived in the viscous sublayer and log layer. These alterations are visible as changes in the distribution of the turbulent stresses and alignment of the vortical structures with the mean flow. These modifications are responsible for a misalignment between the Reynolds stress tensor and the velocity gradient tensor, which has important consequences for the validity of the widely used Boussinesq turbulent viscosity hypothesis in Reynolds-averaged Navier–Stokes models. Spanwise curvature was observed to decrease turbulent kinetic energy. These results have important implications on the development of turbulence in general applications, such as the flow over a prolate spheroid.

  PublisherDOI

• Cavitation inception mechanisms during the interaction between a pair of counter-rotating vortices

  Journal of Fluid Mechanics · 2026-01-14

  articleOpen accessSenior author

  Cavitation inception in the wake of propulsor systems often arises from the interaction between multiple vortices. We use large-eddy simulation (LES) to study cavitation during the canonical interaction of a pair of unequal strength counter-rotating vortices generated in the wake of a hydrofoil pair at a chord-based Reynolds number ( $ \textit{Re}$ ) of $1.7 \times 10^6$ . The simulations reproduce the experimental observations by Knister et al. (In 33rd Symposium on Naval Hydrodynamics, Osaka, Japan, 2020) of spatially and temporally intermittent inception events occurring in the weaker vortex. Sinusoidal instabilities representing the Crow instability develop on the weaker vortex beyond one chord length downstream of the hydrofoils, causing it to bend and wrap around the stronger vortex. The inviscid stretching causes a significant reduction of the weaker core pressure and inception occurs as it approaches close to the stronger core. These intermittent inception events correspond to $3{-}4$ fold pressure reduction from the unperturbed value, with the instantaneous pressures reaching $40\,\%{-}60\,\%$ lower than the mean minimum pressure. However, the loss of circulation ( ${\gt} 20\,\%$ ) in both cores during the later stages of interaction reduces the possibility of further inception events. Statistical analysis reveals that inception occurs once per Crow cycle and is most likely to occur near the central regions of the Crow wavelength. Conditional averages show that the axial stretching is non-uniform along the weaker vortex axis, with the stretching intensities in the central regions being four times larger than the wavelength-averaged value. Probability distribution analysis shows that only a small portion of the weaker core experiences inception pressures and these regions have relatively lower axial stretching intensities compared with the bulk of the core.

  PublisherDOI

• Vortex topology in the lee of a 6:1 prolate spheroid

  ArXiv.org · 2025-07-03

  preprintOpen accessSenior author

  A large scale parametric study of the flow over the prolate spheroid is presented to understand the effect of Reynolds number and angle of attack on the separation, the wake formation and the loads. Large-Eddy Simulation is performed for six Reynolds numbers ranging from Re = 0.15M to Re = 4M and for eight angles of attack ranging from 10 degrees to 90 degrees. For all the cases considered, the boundary layer separates symmetrically and forms a recirculation region. Several distinct flow topologies are observed that can be grouped into three categories: proto-vortex, coherent vortex and recirculating wake. In the proto-vortex state, the recirculation does not have a distinct center of rotation, instead, a two-layer detached flow structure is formed. In the coherent vortex state, the separated shear layer rolls into a three-dimensional vortex that is aligned with the axis of the spheroid. This vortex has a clear center of rotation corresponding to a minimum of pressure and transforms the azimuthal momentum from the separated shear layer into axial momentum. In the recirculating wake regime, the recirculation is incoherent and the primary separation forms a dissipative shear layer that is convected in the direction of the free-stream. This symmetric pair of shear layers bounds a low-momentum recirculating cavity on the leeward side of the spheroid. The properties of these states are not constant, but evolve along the axis of the spheroid and are dictated by the characteristics of the boundary layer at separation. The variation of the flow with Reynolds number and angle of attack is described, and its connection to the loads on the spheroid are discussed.

  PublisherOA PDF

• A large-eddy simulation study of water tunnel interference effects for a marine propeller in crashback mode of operation

  Flow · 2025-01-01

  articleOpen accessSenior authorCorresponding

  Marine propellers are studied in design and off-design modes of operation like crashback, where the propeller rotates in reverse while the vehicle is in forward motion. Past experiments (Jessup et al. , Proceedings of the 25th Symposium on Naval Hydrodynamics, St John's, Canada , 2004; Proceedings of the 26th Symposium on Naval Hydrodynamics, Rome, Italy , 2006) studied the marine propeller David Taylor Model Basin 4381 in the open-jet test section of the 36-inch variable pressure water tunnel (VPWT). In crashback, a significant discrepancy with unclear sources exists between the mean propeller loads from the VPWT and open-water towing tank (OW) experiments (Ebert et al. , 2007 ONR Propulsor S & T Program Review, October , 2007). We perform large-eddy simulation at $Re=561\,000$ and advance ratios $J=-0.50$ and $-0.82$ with the VPWT geometry included, contrasting to the unconfined (OW) case at those same $J$ and $Re=480\,000$ . We identify and delineate the water tunnel interference effects responsible, and demonstrate that these effects resemble those of a symmetric solid model or bluff body. Solid blockage due to jet expansion and nozzle blockage due to proximity to the tunnel nozzle are identified as the primary interference effects. Their impact varies with the advance ratio $J$ and strengthens for higher magnitudes of $J$ . The effective length scale to assess the severity of interference effects is found to be larger than the vortex ring diameter.

  PublisherOA PDFDOI

• Large-eddy simulation of a non-equilibrium turbulent boundary layer

  Journal of Fluid Mechanics · 2025-07-03 · 2 citations

  articleOpen accessSenior authorCorresponding

  Wall-resolved large-eddy simulation (LES) of a non-equilibrium turbulent boundary layer (TBL) is performed. The simulations are based on the experiments of Volino (2020 a J. Fluid Mech. 897 , A2), who reported profile measurements at several streamwise stations in a spatially developing zero pressure gradient TBL evolving through a region of favourable pressure gradient (FPG), a zero pressure gradient recovery and subsequently an adverse pressure gradient (APG) region. The pressure gradient quantified by the acceleration parameter $K$ was held constant in each of these three regions. Here, $K = -(\nu /\rho U_e^{3}) {\textrm d}P_e/{\textrm d}x$ , where $\nu$ is the kinematic viscosity, $\rho$ is density, $U_e$ is the free stream velocity and ${\textrm d}P_e/{\textrm d}x$ is the streamwise pressure gradient at the edge (denoted by the subscript ‘ $e$ ’) of the TBL. The simulation set-up is carefully designed to mimic the experimental conditions while keeping the computational cost tractable. The computational grid appropriately resolves the increasingly thinning and thickening of the TBL in the FPG and APG regions, respectively. The results are thoroughly compared with the available experimental data at several stations in the domain, showing good agreement. The results show that the computational set-up accurately reproduces the experimental conditions and the results demonstrate the accuracy of LES in predicting the complex flow field of the non-equilibrium TBL. The scaling laws and models proposed in the literature are evaluated and the response of the TBL to non-equilibrium conditions is discussed.

  PublisherOA PDFDOI

• Large-eddy simulation of the tip vortex flow in a ducted propulsor

  Journal of Fluid Mechanics · 2025-05-08 · 5 citations

  articleOpen accessSenior author

  Large-eddy simulation (LES) is performed to study the tip vortex flow in a ducted propulsor geometry replicating the experiments of Chesnakas & Jessup (2003, pp. 257–267), Oweis et al. (2006 a J. Fluids Engng 128 , 751–764) and Oweis et al. (2006 b J. Fluids Engng 128 , 751–764). Inception of cavitation in these marine propulsion systems is closely tied to the unsteady interactions between multiple vortices in the tip region. Here LES is used to shed insight into the structure of the tip vortex flow. Simulation results are able to predict experimental propeller loads and show agreement with laser Doppler velocimetry measurements in the blade wake at design advance ratio, $J=0.98$ . Results show the pressure differential across the blade produces a leakage vortex which separates off the suction side blade tip upstream of the trailing edge. The separation sheet aft of the primary vortex separation point is shown to take the form of a skewed shear layer which produces a complex arrangement of unsteady vortices corotating and counter-rotating with the primary vortex. Blade tip boundary layer vortices are reoriented to align with the leakage flow and produce instantaneous low-pressure regions wrapping helically around the primary vortex core. Such low-pressure regions are seen both upstream and downstream of the propeller blade trailing edge. The trailing edge wake is found to only rarely have a low-pressure vortex core. Statistics of instantaneous low pressures below the minimum mean pressure are found to be concentrated downstream of the blade’s trailing edge wake crossing over the primary vortex core and continue in excess of 40 % chord length behind the trailing edge. The rollup of the leakage flow duct boundary layer behind the trailing edge is also seen to produce counter-rotating vortices which interact with the primary leakage vortex and contribute to strong stretching events.

  PublisherDOI

• Monolithic framework to simulate fluid-structure interaction problems using geometric volume-of-fluid method

  ArXiv.org · 2025-05-28

  preprintOpen accessSenior author

  We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF-based one-continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface-capturing (IC) approach, the PLIC method is used to reconstruct the interface, and the Lagrangian Explicit (LE) method is used in the directionally split advection procedure. To model the hyperelastic behavior of the solid, we consider Mooney-Rivlin material models, where we use the left Cauchy-Green deformation tensor (B) to account for the solid deformation on an Eulerian grid and the fifth-order WENO-Z reconstruction method is utilized to treat the advection terms involved in the transport equation of B. Multiple benchmark problems are considered to verify the accuracy of the approach. Furthermore, to demonstrate the capability of the solver to handle turbulent interactions, we perform direct numerical simulation (DNS) of turbulent channel flow with a deformable compliant bottom wall and a rigid top wall; our observations align well with previous experimental and numerical works. The detailed numerical experiments show that: (i) Despite the discontinuity of the interface across the cell boundaries and stress discontinuity across the interface, a VOF/PLIC-based FSI framework can provide stable and accurate solutions that significantly minimizes numerical artifacts (e.g., flotsam and spurious currents) while maintaining a sharp interface. (ii) The accuracy of a VOF/PLIC-based FSI approach on coarse grids is comparable to the accuracy of a diffusive IC method-based FSI approach on much finer grids.

  PublisherOA PDFDOI

• Vortex topology in the lee of a 6 : 1 prolate spheroid

  Journal of Fluid Mechanics · 2025-12-01 · 2 citations

  articleOpen accessSenior authorCorresponding

  A large-scale parametric study of the flow over the prolate spheroid is presented to understand the effect of Reynolds number and angle of attack on the separation, the wake formation and the loads. Large-eddy simulation is performed for six Reynolds numbers ranging from ${\textit{Re}} = 0.15\times 10^6$ to $4 \times 10^6$ and for eight angles of attack ranging from $\alpha = 10^\circ$ to $\alpha = 90^\circ$ . For all the cases considered, the boundary layer separates symmetrically and forms a recirculation region. Several distinct flow topologies are observed that can be grouped into three categories: proto-vortex, coherent vortex and recirculating wake. In the proto-vortex state, the recirculation does not have a distinct centre of rotation, instead, a two-layer detached flow structure is formed. In the coherent vortex state, the separated shear layer rolls into a three-dimensional vortex that is aligned with the axis of the spheroid. This vortex has a clear centre of rotation corresponding to a minimum of pressure and transforms the transverse momentum from the separated shear layer into axial momentum. In the recirculating wake regime, the recirculation is incoherent and the primary separation forms a dissipative shear layer that is convected in the direction of the free stream. This symmetric pair of shear layers bounds a low-momentum recirculating cavity on the leeward side of the spheroid. The properties of these states are not constant, but evolve along the axis of the spheroid and are dictated by the characteristics of the boundary layer at separation. The variation of the flow with Reynolds number and angle of attack is described, and its connection to the loads on the spheroid are discussed.

  PublisherDOI

• Directionally‐split volume‐of‐fluid technique for front propagation under curvature flow

  International Journal for Numerical Methods in Fluids · 2024-05-23

  articleSenior author

  Abstract A directionally‐split volume‐of‐fluid (VOF) methodology for evolving interfaces under curvature‐dependent speed is devised. The interface is reconstructed geometrically and the volume fraction is advected with a technique to incorporate a topological volume conservation constraint. The proposed approach uses the idea that the role of curvature in a speed function is analogous to the role of viscosity in the corresponding hyperbolic conservation law to propagate complex interfaces where singularities may exist. The approach has the advantage of simple implementation and straightforward extension to more complex multiphase systems by formulating the interface evolution problem using energy functionals to derive an expression for the interface‐advecting velocity. The numerical details of the volume‐of‐fluid based formulation are discussed with emphasis on the importance of curvature estimation. Finally, canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the devised approach and the results are compared with existing work in LS.

  PublisherDOI

• Anomalous pressure–density relations and speed of sound in bubbly water systems

  The Journal of Chemical Physics · 2024-11-22 · 2 citations

  article

  The speed of sound in bubbly water is an important parameter in the wave equations governing pressure-density relations for turbulent multi-phase flow simulations. Recent molecular simulation results indicate that, for bubbles that are thermodynamically stable at finite volume conditions, the derivative of total pressure P with density ρ has a negative sign, complicating the interpretation of the speed of sound. We show that such a negative compressibility is thermodynamically consistent in a single-component two-phase model at finite volume, and identify an empirically derived equation of state to illustrate that this observation is not an artifact of small simulation length scales. To reconcile this thermodynamic relation with measurements of sound propagation, we decompose the derivative ∂P/∂ρ for bubbly water into its constituent phases to identify absorptive and transmissive contributors, both with an equation of state and using molecular simulations. We find that the speed of sound in the liquid phase remains real-valued while the bubble attenuates sound, giving a negative system compressibility. The inclusion of N2 molecules in molecular simulations illustrates that these observations are robust and hold also for mixtures. From these simulations, we also compute scattering functions for bubbly systems to identify oscillations associated with the speed of sound. Finally, the spherical harmonic modes of bubble oscillations are analyzed in the context of resonance with propagating waves.

  PublisherDOI

Recent grants

• CAREER: A Novel Approach for Large Eddy Simulation on Unstructured Grids Applied to Turbulent Jets in Cross-Flow

  NSF · $375k · 2002–2007

• A hybrid subgrid model for large-eddy simulation of compressible wall-bounded flows

  NSF · $140k · 2009–2012

• Direct Numerical and Large-eddy Simulation of Supersonic Transverse Jets Using a Novel Numerical Method

  NSF · $259k · 2008–2012

Frequent coauthors

• Karim Alamé

  University of Minnesota

  31 shared

• Sreevatsa Anantharamu

  31 shared

• Parviz Moin

  Stanford University

  30 shared

• Suman Muppidi

  Ames Research Center

  27 shared

• Sourabh V. Apte

  Oregon State University

  22 shared

• Jerrold Lerman

  22 shared

• Praveen Kumar

  University of Minnesota

  18 shared

• Wyatt Horne

  Sandia National Laboratories

  17 shared

Awards & honors

• Best Paper award, 2021 AIAA Hampton Roads Section (HRS)
• Laurence Bement Young Professional Paper Competition, for J.…
• Fulbright Scholar, Host: Indian Institute of Technology, Kha…
• Best paper Award, Fifth International Symposium on Marine Pr…
• Fellow, American Physical Society (2011)