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Open research questions in Fluid Dynamics and Turbulent Flows

131 gap statements mined from Fluid Dynamics and Turbulent Flows papers in our 4.5M-paper local library, which holds 1,822 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.

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What the literature leaves open

  • Finally, active or passive flow control techniques could be investigated to mitigate the strong pressure fluctuations and improve the aerodynamic stability of the configuration. Due to the lack of agreement with the empirical methods, a different mechanism other than purely acoustic is likely the cause of the fluctuations.

    Aerodynamic unsteadiness from a forward-facing door over a cavity at Mach 6 · 2026 · DOI

  • The study of laminar-turbulent transition in subsonic boundary layers is important but challenging. Prior methods have limitations. The paper proposes a new method to address these limitations.

    Infrared thermography in studying the laminar-turbulent transition in the boundary layer · 2026 · DOI

  • The need to control boundary layer transition in hypersonic vehicles. The challenge of establishing a potentially passive and non-intrusive control method for the suppression of second Mack mode instability.

    Stabilisation of second Mack mode in hypersonic boundary layers through spanwise non-uniform surface temperature distribution · 2026 · DOI

  • The study is based on direct numerical simulations, which may not capture all the complexities of real-world scenarios. The range of Mach numbers investigated is limited to 4.8–6.

    Stabilisation of second Mack mode in hypersonic boundary layers through spanwise non-uniform surface temperature distribution · 2026 · DOI

  • The gap is addressed by deriving a two-dimensional Reynolds model that incorporates contributions of the oscillating boundary.

    Two‐Dimensional Carreau Law for a Quasi‐Newtonian Fluid Flow Through a Thin Domain With a Slightly Rough Boundary · 2026 · DOI

  • The analytic derivation of the exponent -3/8 from the ERG flow and the verification of hypothesis (H2) are identified as the central open problems, with a precise mathematical formulation provided for each.

    NXE Program: Cartan-Biot-Savart Inequality and Morphological Scale Law in 3D Navier-Stokes — Data and Code Repository · 2026 · DOI

  • The lack of sufficient resolution close to the wall in experimental measurements introduces significant uncertainty in that region. The sensitivity of resolvent analysis to errors in the mean flow profile is not well understood.

    Uncertainty quantification in resolvent analysis of experimental wall-bounded turbulent flows · 2026 · DOI

  • The paper identifies the need for a more effective method to mitigate mode collapse in normalizing flows. Prior techniques, such as training with a fixed beta value or using a fixed schedule, are shown to be inadequate. The paper highlights the challenge of modeling complex distributions with multiple modes, which requires a more sophisticated approach.

    Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimation · 2026 · DOI

  • The study is limited to the layer mixing problem. The study uses a specific computational grid and software package. The study does not compare the results with other turbulence models.

    Study of the Influence of the Computational Grid on the RSM Turbulence Model in the Layer Mixing Problem · 2026 · DOI

  • Future studies could investigate the effect of computational grid resolution on other turbulence models. Future studies could explore the use of the Reynolds Stress Model in other engineering applications. Future studies could develop new methods for selecting optimal computational grid parameters.

    Study of the Influence of the Computational Grid on the RSM Turbulence Model in the Layer Mixing Problem · 2026 · DOI

  • Further study of the boundary layer and its properties is needed. Further application of Prandl's work to the study of fluid flow is needed. Further analysis of the Navier-Stokes equations and the diffusion equation is needed.

    Diffusion, viscosity, convection and the boundary layer · 2026 · DOI

  • The study identifies a need for a detailed analysis of the boundary layer and its properties.

    Diffusion, viscosity, convection and the boundary layer · 2026 · DOI

  • The lack of a unifying perspective on intermittent cascades operating in space plasma environments. The need for a description of Kolmogorov cascades in terms of continuous-time random walks.

    A Unifying Perspective on Kolmogorov Cascades in Solar Wind Plasma Turbulence · 2026 · DOI

  • The computation of triple correlations is in itself uncertain, as longer averages are usually required for the convergence of higher-order moments (Wyngaard 1973; Lenschow, Mann & Kristensen 1994; Saddoughi & Veeravalli 1994; Huang & Katul 2022), whereas the functional shape of triple correlations with height needed for analytically estimating gradients is also not well known (Wyngaard & Coté 1971).

    Stratification, turbulence organisation and pressure-strain effects on surface-layer turbulence anisotropy · 2026 · DOI

  • Future research directions include the application of the approach to large-scale problems. The development of more efficient numerical methods for the discretisation of the inflated dynamic Laplacian. The exploration of potential applications in fields such as fluid mechanics and dynamical systems.

    An Inflated Dynamic Laplacian to Track the Emergence and Disappearance of Semi-material Coherent Sets · 2026 · DOI

  • The research gap identified in the paper is the limitation of traditional Lagrangian methods in tracking coherent flow features in complex evolving environments. The gap is addressed by the introduction of the inflated dynamic Laplacian.

    An Inflated Dynamic Laplacian to Track the Emergence and Disappearance of Semi-material Coherent Sets · 2026 · DOI

  • Lack of a predictive and analytically tractable description of turbulence. Difficulty in resolving the predicted shell structure in numerical simulations. Need for a geometric description of scalar transport in decaying turbulence.

    Geometric solution of turbulent mixing · 2026 · DOI

  • Traditional error diagnostics for turbulence models have focused on engineering quantities of interest, rather than mechanism-resolved errors.

    Integral-analysis-based diagnostics of turbulence model errors in skin friction · 2026 · DOI

  • The Navier–Stokes equations have a potential problem with finite-time blow-up. The Dual-Field Interface Model (DFIM) has not been extended to macroscopic hydrodynamics before.

    Appendix J: Effective 3-Brane Hydrodynamics and the Regularization of the Navier–Stokes Equations via DFIM · 2026 · DOI

  • Estimating past events in wall turbulence based solely on surface measurements and first principles is an ill-posed problem. The problem is complicated by chaos, which is described by the adjoint Navier-Stokes equations.

    Mitigating adjoint chaos in wall turbulence · 2026 · DOI

  • The traditional approach to studying the impact of flow shear on fluctuations has limitations, - Normal mode stability analyses may not capture nonmodal growth and optimal…

    Nonmodal growth and optimal perturbations in magnetohydrodynamic shear flows · 2026 · DOI

  • Further study of the effects of near-wall uncertainty on resolvent modes and singular values. Application of the sensitivity analysis framework to other types of flows.

    Uncertainty quantification in resolvent analysis of experimental wall-bounded turbulent flows · 2026 · DOI

  • Investigating the application of the annealing scheme to other types of normalizing flows, - Exploring the use of different adaptive annealing schedules, - Applying the NF-based sampling scheme to more complex…

    Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimation · 2026 · DOI

  • To compute C BS, C, and cs from first principles. To use the DFIM to study extreme turbulence. To use the DFIM to reverse-engineer candidate initial data that force a classical blow-up.

    Appendix J: Effective 3-Brane Hydrodynamics and the Regularization of the Navier–Stokes Equations via DFIM · 2026 · DOI

  • Applying the technique to other areas of turbulence research. Refining the stochastic modeling of the dispersion of magnetic field lines guiding energetic particles in the turbulent solar wind.

    A Unifying Perspective on Kolmogorov Cascades in Solar Wind Plasma Turbulence · 2026 · DOI

Most-cited papers in Fluid Dynamics and Turbulent Flows

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Open questions raised by papers listed on this page include: (1) Due to the lack of agreement with the empirical methods, a different mechanism other than purely acoustic is likely the cause of the fluctuations (“Aerodynamic unsteadiness from a forward-facing door over a cavity at Mach 6”, 2026); (2) The lack of sufficient resolution close to the wall in experimental measurements introduces significant uncertainty in that region (“Uncertainty quantification in resolvent analysis of experimental wall-bounded…”, 2026); (3) Future studies could investigate the effect of computational grid resolution on other turbulence models (“Study of the Influence of the Computational Grid on the RSM Turbulence Model in…”, 2026); (4) Further study of the boundary layer and its properties is needed (“Diffusion, viscosity, convection and the boundary layer”, 2026); (5) The lack of a unifying perspective on intermittent cascades operating in space plasma environments (“A Unifying Perspective on Kolmogorov Cascades in Solar Wind Plasma Turbulence”, 2026). 131 gap statements have been mined from Fluid Dynamics and Turbulent Flows papers in our 4.5M-paper local library, which holds 1,822 papers on the topic; the gaps come from whichever of those papers state one. They are mostly the research gaps the authors state and the papers' abstracts, plus future-work, limitations and challenges passages. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one, so you can read the original claim in context.

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