Nonlinear Studies of Stratified Oceanic and Atmospheric Flows--financed through the European Union-NextGeneration EU within PNRR-III-C9-2022-I8-CF 185/22.11.2022)


This project aims to address topics of current interest concerning atmospheric and ocean flows from the perspective of the nonlinear governing equations and of the associated boundary conditions. Emphasis will be placed on the analysis of exact solutions describing the propagation of surface and internal waves in two-and three-dimensional flows with vorticity.

Project Director-Dr. Calin I. Martin


Team members

Dr.   Nataliia Kolun

Dr.   Ronald Quirchmayr

Dr.   Andrei Stan

Drd.   Cristina Gheorghe

Drd.   Ioan Papuc

Drd.   Rita-Maria Bardocz-Balazsi

Drd.   Mihai-Alexandru Aron

Publications


  1. C.-I. Martin. Heat-source type atmospheric nonlinear flow patterns in zonal cloud bands. J. Differential Equations, vol. 445 (2025) Art. No. 113589.

  2. C.-I. Martin. On the onset of wave-breaking and the time evolution of the maximum of the horizontal velocity in rotational equatorial waves. Nonl. Analysis: Real World Applications, vol. 85 (2025) Art. No. 104367.

  3. C.-I. Martin and E. Parau. Hamiltonian formulation for interfacial waves propagating under an elastic sheet above stratified piecewise constant rotational flow. Wave Motion, vol. 133 (2025) Art. No. 103454.

  4. A. Geyer and C.-I. Martin. Three-dimensional time-dependent water flows with constant non-vanishing vorticity and depth dependent density. Physica D: Nonl. Phenomena, vol. 472 (2025) Art. No. 134523.

  5. C.-I. Martin. A wave-breaking result for azimuthally varying water flows in cylindrical coordinates. J. Differential Equations, vol. 416 (2025), 143-158..

  6. C. Gheorghe and A. Stan. Stratified equatorial flows in cylindrical coordinates with surface tension. Monats. Math. vol. 205 (2024), 497-509.

  7. N. Kolun. Stratified steady inviscid water flows with effects of surface tension and constant non-zero vorticity. Ann. Math. Pura Appl, vol. 204 (2025), 39-52.

  8. N. Kolun. On constant vorticity time-dependent water flows over a variable bottom. Z. Angew. Math. Phys. vol. 76 (2025), Art. No. 170.

  9. A. Stan. Free-Surface Equatorial Flows with Surface Tension in Spherical Coordinates. Applicable Analysis (2025).

  10. A. Stan. Symmetric water waves with surface tension: traveling wave behaviour and maximal horizontal velocity. Water Waves (2025).

  11. R. Quirchmayr. Stratified ocean currents with constant vorticity. J. Math. Fluid Mech. vol. 27 (2025), Art. No. 7.

  12. A. Geyer and R. Quirchmayr. On ocean currents with constant vorticity: explicit solutions and an application to ACC. Stud. Appl. Math. vol. 155 (2025), no. 1, e70081.

  13. C.-I. Martin and E. Parau. Traveling hydroelastic waves in constant vorticity flows with stagnation points and allowing for overhanging profiles. Proc. Royal Society A. Mathematical, Physical and Engineering Sciences vol. 482 (2026) no. 2329, Art. No. 20250372.

  14. C.-I. Martin. Free-surface wave-breaking in the full nonlinear water wave problem with a permanent interface in cylindrical coordinates. J. Evolution Equations vol.26 (2026), no. 1, Art. No. 10.

  15. C.-I. Martin. The deep-atmosphere Euler equations: explicit solutions and perturbation analysis. Physica D: Nonlinear Phenomena. vol. 488 (2026), 135100.

  16. R.-I. Ivanov and C.-I. Martin. Three-layer water flows: Dirichlet-Neumann operators and approximations. J. Fluid Mechanics. (2026), 1029, A2.

  17. C.-I. Martin. On the leading-order dynamics of viscous tropospheric flows. Differential and Integral Equations, vol. 39 (2026), no. 9-10.

  18. N. Kolun. Steady wave propagation in rotational flows with discontinuous vorticity and surface tension. Applicable Analysis, (2026), https://doi.org/10.1080/00036811.2026.2658084.

  19. J. Chu, C.-I. Martin, Q. Ding and F.-F. Liao. On the short-wavelength stability and the Kelvin-Helmholtz instability of some explicit solutions to the two-layer nonlinear three-dimensional water wave problem Ann. Math. Pura Appl. accepted (2026).

  20. I. Papuc. Free surface azimuthal flow on equatorial regions with surface tension and density stratification. Monatshefte Math. (accepted) 2026.

Submitted papers


  1. C. Gheorghe. Dispersion relations for three-layer capillary-gravity water flows with two rotational layers. submitted (2026).