A Kolmogorov‐Brutsaert structure function model for evaporation into a turbulent atmosphere. Issue 5 (2nd May 2017)

• Record Type: Journal Article
• Authors: Katul, Gabriel; Liu, Heping
• Is Part Of: Water resources research. Volume 53:Issue 5(2017)
• Page Start: 3635
• Page End: 3644
• Publication Date: 2017-05-02
• Subjects: evaporation -- turbulent atmosphere -- surface renewal -- Kolmogorov -- structure function; Hydrology -- Periodicals; 333.91
• DOI: 10.1002/2016WR020006
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: In 1965, Brutsaert proposed a model that predicted mean evaporation rate E ¯ from rough surfaces to scale with the 3/4 power law of the friction velocity ( u ∗ ) and the square‐root of molecular diffusivity ( Dm ) for water vapor. In arriving at these results, a number of assumptions were made regarding the surface renewal rate describing the contact durations between eddies and the evaporating surface, the diffusional mass process from the surface into eddies, and the cascade of turbulent kinetic energy sustaining the eddy renewal process itself. The working hypothesis explored here is that E ¯ ∼ D m u ∗ 3 / 4 is a direct outcome of the Kolmogorov scaling for inertial subrange eddies modified to include viscous cutoff thereby bypassing the need for a surface renewal assumption. It is demonstrated that Brutsaert's model for E ¯ may be more general than its original derivation implied. Plain Language Summary: The movement of water vapor molecules from rough surfaces such as soils by eddies into the atmosphere is of primary significance to a plethora of applications including hydrological and meteorological forecasting, irrigation planning, energy partitioning, and subsequent growth of the atmospheric boundary layer, to name a few. In 1965, W. Brutsaert proposed a general model that links the movement of water vapor molecules from the surface to the molecular diffusivity of water vapor in air and the wind‐induced shear stress at the surface. The derivation considered air packets sweeping down and coming in contact with the wet surface. When in contact with the surface, these packets become enriched with water vapor molecules during a finite contact duration, after which these packets are ejected from the surface. Brutsaert made key restrictive assumptions about the statistical properties of the contact duration of these packets with the surface to arrive at the final form of the evaporation equation. The work here demonstrates that the same result can be derived by assuming a turnover velocity of these air packets to follow a universal form based on a widely accepted theory of turbulent flows proposed by A. N. Kolmogorov. Key Points: Mean evaporation rate was shown to scale with the 3/4 power law of the friction velocity and the square‐root of molecular diffusivity The scaling was derived from surface renewal theory with ad hoc specification of contact probability between eddies and the surface A new approach that links these scaling results with the universal structure of the turbulent cascade is derived