<p>A theoretical analysis is presented for Rayleigh–Bénard convection in a fluid layer bounded above by a deformable, evaporating free surface. The study focuses on the mechanical consequences of evaporation-induced interfacial dynamics and their coupling to buoyancy generation. Within the Boussinesq approximation, and neglecting surface-tension-driven effects, a regime is identified in which evaporation couples interfacial deformation directly to the buoyancy field, rendering the upper boundary dynamically active. Linear stability analysis shows that even weak evaporation alters the nature of convective onset, replacing the stationary instability of classical Rayleigh–Bénard convection with an oscillatory Hopf bifurcation. This instability arises from kinematic coupling between vertical velocity and interfacial displacement, which produces phase-lagged, evaporation-induced buoyancy perturbations in the absence of rotation, imposed shear, or Marangoni stresses. In the strongly convective regime, an asymptotic scaling theory for heat transport is developed that is consistent with the instability mechanism. The analysis shows that evaporation does not alter the classical Rayleigh exponent governing the Nusselt number. Instead, evaporation enhances plume-emission efficiency through a multiplicative correction controlled by a dimensionless evaporative coupling parameter. The resulting heat-transfer law preserves the classical scaling, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$Nu \sim {Ra}^{1/3}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mi>u</mi> <mo>∼</mo> <msup> <mrow> <mi mathvariant="italic">Ra</mi> </mrow> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, while introducing an evaporation-induced correction that scales with a fractional power of the coupling strength. These results demonstrate that evaporation modifies buoyancy-driven convection by dynamically renormalizing buoyancy injection at the interface rather than by reorganizing bulk dissipation balances. Evaporation therefore acts as an independent control parameter in Rayleigh–Bénard convection, complementing but not subsumed by existing transport theories based on fixed boundaries.</p>

Evaporation-induced interfacial coupling and instability in Rayleigh–Bénard convection

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发表日期：

2026年5月26日

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Adarsh Saini

摘要

A theoretical analysis is presented for Rayleigh–Bénard convection in a fluid layer bounded above by a deformable, evaporating free surface. The study focuses on the mechanical consequences of evaporation-induced interfacial dynamics and their coupling to buoyancy generation. Within the Boussinesq approximation, and neglecting surface-tension-driven effects, a regime is identified in which evaporation couples interfacial deformation directly to the buoyancy field, rendering the upper boundary dynamically active. Linear stability analysis shows that even weak evaporation alters the nature of convective onset, replacing the stationary instability of classical Rayleigh–Bénard convection with an oscillatory Hopf bifurcation. This instability arises from kinematic coupling between vertical velocity and interfacial displacement, which produces phase-lagged, evaporation-induced buoyancy perturbations in the absence of rotation, imposed shear, or Marangoni stresses. In the strongly convective regime, an asymptotic scaling theory for heat transport is developed that is consistent with the instability mechanism. The analysis shows that evaporation does not alter the classical Rayleigh exponent governing the Nusselt number. Instead, evaporation enhances plume-emission efficiency through a multiplicative correction controlled by a dimensionless evaporative coupling parameter. The resulting heat-transfer law preserves the classical scaling, $Nu \sim {Ra}^{1/3}$ $N u \sim {Ra}^{1 / 3}$ , while introducing an evaporation-induced correction that scales with a fractional power of the coupling strength. These results demonstrate that evaporation modifies buoyancy-driven convection by dynamically renormalizing buoyancy injection at the interface rather than by reorganizing bulk dissipation balances. Evaporation therefore acts as an independent control parameter in Rayleigh–Bénard convection, complementing but not subsumed by existing transport theories based on fixed boundaries.