Coherent motions and time scales that control heat and mass transfer at wind-swept water surfaces

Abstract

Forecast of the heat and chemical budgets of lakes, rivers, and oceans requires improved predictive understanding of air‐water interfacial transfer coefficients. Here we present laboratory observations of the coherent motions that occupy the air‐water interface at wind speeds (U10) 1.1–8.9 m/s. Spatiotemporal near‐surface velocity data and interfacial renewal data are made available by a novel flow tracer method. The relative activity, velocity scales, and time scales of the various coherent interfacial motions are measured, namely for Langmuir circulations, streamwise streaks, nonbreaking wind waves, parasitic capillary waves, nonturbulent breaking wind waves, and turbulence‐generating breaking wind waves. Breaking waves exhibit a sudden jump in streamwise interfacial velocity wherein the velocity jumps up to exceed the wave celerity and destroys nearby parasitic capillary waves. Four distinct hydrodynamic regimes are found to exist between U10 = 0 and 8.9 m/s, each with a unique population balance of the various coherent motions. The velocity scales, time scales, and population balance of the different coherent motions are input to a first‐principles gas transfer model to explain the waterside transfer coefficient (kw) as well as experimental patterns of temperature and gas concentration. The model mixes concepts from surface renewal and divergence theories and requires surface divergence strength ( β), the Lagrangian residence time inside the upwelling zone ( tLu), and the total lifetime of new interface before it is downwelled ( tLT). The model's output agrees with time‐averaged measurements kw, patterns of temperature in infrared photographs, and spatial patterns of gas concentration and kw from direct numerical simulations. Several nondimensional parameters, e.g. βtLu and τstLT where τs is the interfacial shear rate, determine the effectiveness of a particular type of coherent motion for affecting kw.

Turbulence in a small arctic pond

“…5, day 171.64 and 172.3). At higher winds speeds, white capping and breaking of surface waves increase e above predictions from law of the wall scaling in larger water bodies (Terray et al 1996;Turney 2016;Moghimi et al 2016). It is not known whether the fetch is sufficient in small ponds for sufficient wave development for a similar intensification of turbulence.…”

Chemical hydrodynamics of a downward microbubble flow for intensification of gas‐fed bioreactors

“…Therefore, for the sake of simplicity and flexibility, we discuss models of k L separate to those for a . Four methods exist for predicting k L , as follows: (1) Dimensional analysis of a speculative collection of parameters; (2) Empirical least‐squares regression fit to a speculated equation that isn't dimensionally correct; (3) Assumption that Higbie‐Danckwert's surface renewal events dominate the process and then speculating a calculation of renew frequency, such as done in the “small eddy” model or the “large eddy” model; (4) Asymptotic analysis of the advection‐diffusion equation such as in Deen (Chapter 10, page 420) and in “surface divergence” models …”

“…Turbulence consists of a spectrum of scales for velocity, length, and time, and thus it is not immediately clear which scales should be entered into Re . This ambiguity is still not settled after many decades of work …”

“…Surface renewal theory is falling out of favor during the past decade due to the search for models that match the true hydrodynamics in the concentration boundary layer. Recent quantitative analysis shows a method to determine when the interfacial fluid may be considered stagnant …”

“…Its predictive capabilities are generally better than the other methods, therefore it is receiving more attention from researchers in recent years. In the case of free gas – liquid interface, it leads to the surface divergence theory – wherein the advection‐diffusion equation is paired with realistic fluid mechanics for the concentration boundary layer (i.e., stagnation flow quantified by the surface divergence strength ) to create the following equation …”