$80–110/hr
The role in one line
A physicist with published expertise in convection stability creates, solves, or audits research-level problems in hydrodynamic systems.
Written by Training Turk from the public listing; it may be incomplete or out of date. Read the full posting on Mercor.
What you would do
- Construct or analyze problems on Rayleigh-Benard or Rayleigh-Darcy convection with rigorous mathematical scaffolding
- Apply spectral eigenvalue, normal-mode expansion, and marginal stability techniques to determine critical thresholds
- Solve benchmark problems or verify solutions from other specialists, documenting all analytical steps
- Audit completed work for mathematical rigor and physical plausibility within your subdomain
Who they are looking for
- PhD in fluid mechanics, applied mathematics, or closely related field; postdoc, research scientist, or junior faculty preferred
- Published record on convection stability specifically; journal papers with DOI required as proof
- Fluency in LaTeX, Python, and Jupyter; familiarity with VS Code coding extensions helpful
- English language proficiency at B2 or above for clear written reasoning in deliverables
- 10 hours per week over 8-10 weeks; remote, asynchronous work without fixed hours
What the interview is likely to probe
1.Rayleigh-Benard stability setup
This probes whether you can specify correct boundary conditions and non-dimensional parameters, showing mastery of the phenomenon you claim to study.
Expect something like: “Describe how you would formulate the marginal stability problem for convection between plates with flux-prescribed heating and a stress-free upper boundary, including all relevant non-dimensional numbers and how they determine critical onset.”
2.Spectral method implementation
Spectral eigenvalue solvers are standard in your field; this question tests whether you can translate physical assumptions into a solvable discrete system.
Expect something like: “You have an eigenvalue problem for Rayleigh-Benard convection; explain how you would discretize it using Chebyshev polynomials and what convergence checks you would perform on the critical Rayleigh number.”
3.Porous-medium (Darcy) convection differences
Porous-medium flows differ qualitatively from Newtonian fluids; this tests whether your stability knowledge transfers or whether you conflate distinct phenomena.
Expect something like: “How does the dispersion relation in Rayleigh-Darcy convection differ from classical Rayleigh-Benard, and what effect does Darcy's law have on the neutral stability curve you would compute?”
4.Written mathematical exposition
All deliverables must be independently verifiable by peers; this checks whether you communicate derivations clearly without hand-waving.
Expect something like: “Write a 150-word paragraph deriving the Boussinesq approximation from the full Navier-Stokes equations, stating all assumptions and indicating which terms you dropped and why.”
5.Auditing and error detection
Part of your role is reviewing others' work; this tests whether you catch subtle algebraic or conceptual errors in published-style solutions.
Expect something like: “You receive a completed solution claiming the critical Rayleigh number for mixed boundary conditions is 1708; what checks would you perform to validate or refute this claim?”
Exercise you may get
Formulate a complete Rayleigh-Benard convection stability problem with mixed boundaries and solve for the critical Rayleigh number using a sketch of your method, showing all boundary conditions and non-dimensional scaling.
How to prepare
- Gather three recent papers from your own publication record demonstrating convection stability expertise and review the key results, methods, and boundary conditions you used.
- Prepare clear explanations of the Boussinesq approximation and normal-mode perturbation analysis as you have used them in your own work.
- Review one recent spectral eigenvalue method or finite-element study in your subdomain and be ready to discuss its solution strategy and convergence behavior.
- Write a 200-word technical summary of the key differences between Rayleigh-Benard and Rayleigh-Darcy stability problems.
Facts
- Pay
- $80–110/hr
- Commitment
- hourly
- Hours
- 10 per week
- Work arrangement
- remote · Remote
- Domain
- Life, Physical, and Social Science
- Posted
- 9/25/2026
- Open slots
- 3