A new similarity model for the stratified under-ice boundary layer in lakes and its application to ice-covered Lake Baikal

2020 ◽  
Author(s):  
Georgiy Kirillin ◽  
Ilya Aslamov ◽  
Nikolai Granin ◽  
Roman Zdorovennov
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Lake Baikal ◽  
Strong Dependence ◽  
Shear Velocity ◽  
Ice Cover ◽  
Heat Fluxes ◽  
Solid Boundary ◽  
Buoyancy Frequency ◽  
Ice Water

<p>Seasonal ice cover on lakes and polar seas creates seasonally developing boundary layer at the ice base with specific features: fixed temperature at the solid boundary and stable density stratification beneath. Turbulent transport in the boundary layer determines the ice growth and melting conditions at the ice-water interface, especially in large lakes and marginal seas, where large-scale water circulation can produce highly variable mixing conditions. Since the boundary mixing under ice is difficult to measure, existing models of ice cover dynamics usually neglect or parameterize it in a very simplistic form. We propose a model of the turbulent energy budget in the stably stratified boundary layer under ice, based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty-Ozmidov scaling). The model was verified on fine-scale measurements in Lake Baikal and demonstrated a good agreement with data. The measured ice-water heat fluxes in were among the largest reported in lakes (up to 40 W m<sup>−2</sup>) and scaled well against the proposed relationship. The model yields a scaling relationship for the ice-water heat flux as a function of the shear velocity squared that suggests the traditional bulk parameterizations may significantly underestimate the ice-water heat flux, especially at strong under-ice current velocities. The ultimate result consists in a strong dependence of the water-ice heat flux on the shear velocity under ice. </p>

scholarly journals Turbulence in the stratified boundary layer under ice: observations from Lake Baikal and a new similarity model

2019 ◽  
Author(s):  
Georgiy Kirillin ◽  
Ilya Aslamov ◽  
Vladimir Kozlov ◽  
Roman Zdorovennov ◽  
Nikolai Granin
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Lake Baikal ◽  
Dissipation Rate ◽  
Strong Dependence ◽  
Shear Velocity ◽  
Ice Cover ◽  
Solid Boundary ◽  
Buoyancy Frequency ◽  
Ice Water

Abstract. Seasonal ice cover on lakes and polar seas creates seasonally developing boundary layer at the ice base with specific features: fixed temperature at the solid boundary and stable density stratification beneath. Turbulent transport in the boundary layer determines the ice growth and melting conditions at the ice-water interface, especially in large lakes and marginal seas, where large-scale water circulation can produce highly variable mixing conditions. Since the boundary mixing under ice is difficult to measure, existing models of ice cover dynamics usually neglect or parameterize it in a very simplistic form. We present first detailed observations on mixing under ice of Lake Baikal, obtained with the help of advanced acoustic methods. The dissipation rate of the turbulent kinetic energy (TKE) was derived from correlations (structure functions) of current velocities within the boundary layer. The range of the dissipation rate variability covered 2 orders of magnitude, demonstrating strongly turbulent conditions. Intensity of mixing was closely connected to the mean speeds of the under-ice currents, the latter being of geostrophic origin and having lake-wide scales. Mixing developed on the background of stable density (temperature) stratification, which affected the vertical structure of the boundary layer. To account for stratification effects, we propose a model of the turbulent energy budget based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty-Ozmidov scaling). The model agrees well with the observations and yields a scaling relationship for the ice-water heat flux as a function of the shear velocity squared. The ice-water heat fluxes in the field were the largest among all reported in lakes (up to 40 W m−2) and scaled well against the proposed relationship. The ultimate result consists in a strong dependence of the water-ice heat flux on the shear velocity under ice. The result suggests large errors in the heat flux estimations, when the traditional bulk approach is applied to stratified boundary layers. It also implies that under-ice currents may have much stronger effect on the ice melt than estimated by traditional models.

scholarly journals Turbulence in the stratified boundary layer under ice: observations from Lake Baikal and a new similarity model

2020 ◽  
Vol 24 (4) ◽  
pp. 1691-1708 ◽  
Author(s):  
Georgiy Kirillin ◽  
Ilya Aslamov ◽  
Vladimir Kozlov ◽  
Roman Zdorovennov ◽  
Nikolai Granin
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Lake Baikal ◽  
Dissipation Rate ◽  
Large Scale ◽  
Shear Velocity ◽  
Ice Cover ◽  
Solid Boundary ◽  
Buoyancy Frequency ◽  
Ice Water

Abstract. Seasonal ice cover on lakes and polar seas creates seasonally developing boundary layer at the ice base with specific features: fixed temperature at the solid boundary and stable density stratification beneath. Turbulent transport in the boundary layer determines the ice growth and melting conditions at the ice–water interface, especially in large lakes and marginal seas, where large-scale water circulation can produce highly variable mixing conditions. Since the boundary mixing under ice is difficult to measure, existing models of ice cover dynamics usually neglect or parameterize it in a very simplistic form. We present the first detailed observations on mixing under ice of Lake Baikal, obtained with the help of advanced acoustic methods. The dissipation rate of the turbulent kinetic energy (TKE) was derived from correlations (structure functions) of current velocities within the boundary layer. The range of the dissipation rate variability covered 2 orders of magnitude, demonstrating strongly turbulent conditions. Intensity of mixing was closely connected to the mean speeds of the large-scale under-ice currents. Mixing developed on the background of stable density (temperature) stratification, which affected the vertical structure of the boundary layer. To account for stratification effects, we propose a model of the turbulent energy budget based on the length scale incorporating the dissipation rate and the buoyancy frequency (Dougherty–Ozmidov scaling). The model agrees well with the observations and yields a scaling relationship for the ice–water heat flux as a function of the shear velocity squared. The ice–water heat fluxes in the field were the largest among all reported in lakes (up to 40 W m−2) and scaled well against the proposed relationship. The ultimate finding is that of a strong dependence of the water–ice heat flux on the shear velocity under ice. The result suggests large errors in the heat flux estimations when the traditional “bulk” approach is applied to stratified boundary layers. It also implies that under-ice currents may have much stronger effect on the ice melt than estimated by traditional models.

scholarly journals A Study of Critical Heat Flux During Flow Boiling in Microchannel Heat Sinks

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Tailian Chen ◽  
Suresh V. Garimella
Keyword(s):  
Heat Flux ◽  
Critical Heat Flux ◽  
Flow Rate ◽  
Heat Input ◽  
Heat Sink ◽  
Flow Boiling ◽  
Strong Dependence ◽  
Heat Fluxes ◽  
Abrupt Decrease ◽  
Parallel Microchannels

The cooling capacity of two-phase transport in microchannels is limited by the occurrence of critical heat flux (CHF). Due to the nature of the phenomenon, it is challenging to obtain reliable CHF data without causing damage to the device under test. In this work, the critical heat fluxes for flow boiling of FC-77 in a silicon thermal test die containing 60 parallel microchannels were measured at five total flow rates through the microchannels in the range of 20–80 ml/min. CHF is caused by dryout at the wall near the exit of the microchannels, which in turn is attributed to the flow reversal upstream of the microchannels. The bubbles pushed back into the inlet plenum agglomerate; the resulting flow blockage is a likely cause for the occurrence of CHF which is marked by an abrupt increase in wall temperature near the exit and an abrupt decrease in pressure drop across the microchannels. A database of 49 data points obtained from five experiments in four independent studies with water, R-113, and FC-77 as coolants was compiled and analyzed. It is found that the CHF has a strong dependence on the coolant, the flow rate, and the area upon which the heat flux definition is based. However, at a given flow rate, the critical heat input (total heat transfer rate to the coolant when CHF occurs) depends only on the coolant and has minimal dependence on the details of the microchannel heat sink (channel size, number of channels, substrate material, and base area). The critical heat input for flow boiling in multiple parallel microchannels follows a well-defined trend with the product of mass flow rate and latent heat of vaporization. A power-law correlation is proposed which offers a simple, yet accurate method for predicting the CHF. The thermodynamic exit quality at CHF is also analyzed and discussed to provide insights into the CHF phenomenon in a heat sink containing multiple parallel microchannels.

The Importance of Relative Wind Speed in Estimating Air–Sea Turbulent Heat Fluxes in Bulk Formulas: Examples in the Bohai Sea

2020 ◽  
Vol 37 (4) ◽  
pp. 589-603 ◽  
Author(s):  
Xiangzhou Song
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Wind Speed ◽  
Bohai Sea ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Surface Currents ◽  
The Bohai Sea ◽  
Turbulent Heat Fluxes ◽  
Relative Wind

AbstractSea surface currents are commonly neglected when estimating the air–sea turbulent heat fluxes in bulk formulas. Using buoy observations in the Bohai Sea, this paper investigated the effects of near-coast multiscale currents on the quantification of turbulent heat fluxes, namely, latent heat flux (LH) and sensible heat flux (SH). The maximum current reached 1 m s−1 in magnitude, and a steady northeastward current of 0.16 m s−1 appeared in the southern Bohai Strait. The predominant tidal signal was the semidiurnal current, followed by diurnal components. The mean absolute surface wind was from the northeast with a speed of approximately 3 m s−1. The surface winds at a height of 11 m were dominated by the East Asian monsoon. As a result of upwind flow, the monthly mean differences in LH and SH between the estimates with and without surface currents ranged from 1 to 2 W m−2 in July (stable boundary layer) and November (unstable boundary layer). The hourly differences were on average 10 W m−2 and ranged from 0 to 24 W m−2 due to changes in the relative wind speed by high-frequency rotating surface tidal currents. The diurnal variability in LH/SH was demonstrated under stable and unstable boundary conditions. Observations provided an accurate benchmark for flux comparisons. The newly updated atmospheric reanalysis products MERRA-2 and ERA5 were superior to the 1° OAFlux data at this buoy location. However, future efforts in heat flux computation are still needed to, for example, consider surface currents and resolve diurnal variations.

Effects of spatial resolution and temporal offset of air-sea boundary-layer variables on turbulent heat flux estimates

2021 ◽  
Author(s):  
Tong Lee ◽  
Chelle Centemann ◽  
Carol Anne Clayson ◽  
Mark Bourassa ◽  
Shannon Brown ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
High Resolution ◽  
Surface Wind ◽  
Turbulent Heat Flux ◽  
Heat Fluxes ◽  
Sea Surface ◽  
Turbulent Heat ◽  
Input Variables ◽  
Temporal Offset

<p>Air-sea turbulent heat fluxes and their spatial gradients are important to the ocean, climate, weather, and their interactions. Satellite-based estimation of air-sea latent and sensible fluxes, providing broad coverage, require measurements of sea surface temperature, ocean-surface wind speed, and air temperature and humidity above sea surface. Because no single satellite has been able to provide simultaneous measurements of these input variables, they typically come from various satellites with different spatial resolutions and sampling times that can be offset by hours. These factors introduce errors in the estimated heat fluxes and their gradients that are not well documented. As a model-based assessment of these errors, we performed a simulation using a Weather Research and Forecasting (WRF) model forced by high-resolution blended satellite SST for the Gulf Stream extension region with a 3-km resolution and with 30-minute output. Latent and sensible heat fluxes were first computed from input variables with the original model resolutions and at coincident times. We then computed the heat fluxes by (1) decimating the input variables to various resolutions from 12.5 to 50 km, and (2) offsetting the “sampling” times of some input variables from others by 3 hours. The resultant estimations of heat fluxes and their gradients from (1) and (2) were compared with the counterparts without reducing resolution and without temporal offset of the input variables. The results show that reducing input-variable resolutions from 12.5 to 50 km weakened the magnitudes of the time-mean and instantaneous heat fluxes and their gradients substantially, for example, by a factor of two for the time-mean gradients. The temporal offset of input variables substantially impacted the instantaneous fluxes and their gradients, although not their time-mean values. The implications of these effects on scientific and operational applications of heat flux products will be discussed. Finally, we highlight a mission concept for providing simultaneous, high-resolution measurements of boundary-layer variables from a single satellite to improve air-sea turbulent heat flux estimation.</p>

An Explicit Algebraic Model for Turbulent Heat Transfer in Wall-Bounded Flow With Streamline Curvature

2006 ◽  
Vol 129 (4) ◽  
pp. 425-433 ◽  
Author(s):  
B. A. Younis ◽  
B. Weigand ◽  
S. Spring
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Algebraic Model ◽  
Heat Fluxes ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Streamline Curvature ◽  
Turbulent Heat Fluxes ◽  
The Mean

Fourier’s law, which forms the basis of most engineering prediction methods for the turbulent heat fluxes, is known to fail badly in capturing the effects of streamline curvature on the rate of heat transfer in turbulent shear flows. In this paper, an alternative model, which is both algebraic and explicit in the turbulent heat fluxes and which has been formulated from tensor-representation theory, is presented, and its applicability is extended by incorporating the effects of a wall on the turbulent heat transfer processes in its vicinity. The model’s equations for flows with curvature in the plane of the mean shear are derived and calculations are performed for a heated turbulent boundary layer, which develops over a flat plate before encountering a short region of high convex curvature. The results show that the new model accurately predicts the significant reduction in the wall heat transfer rates wrought by the stabilizing-curvature effects, in sharp contrast to the conventional model predictions, which are shown to seriously underestimate the same effects. Comparisons are also made with results from a complete heat-flux transport model, which involves the solution of differential transport equations for each component of the heat-flux tensor. Downstream of the bend, where the perturbed boundary layer recovers on a flat wall, the comparisons show that the algebraic model yields indistinguishable predictions from those obtained with the differential model in regions where the mean-strain field is in rapid evolution and the turbulence processes are far removed from local equilibrium.

Estimate of heat flux at the ice-water interface in Lake Baikal from experimental data

2014 ◽  
Vol 457 (2) ◽  
pp. 982-985 ◽  
Author(s):  
I. A. Aslamov ◽  
V. V. Kozlov ◽  
I. B. Misandrontsev ◽  
K. M. Kucher ◽  
N. G. Granin
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Lake Baikal ◽  
Water Interface ◽  
Ice Water

scholarly journals Turbulent mixing and heat fluxes under lake ice: the role of seiche oscillations

2018 ◽  
Author(s):  
Georgiy Kirillin ◽  
Ilya Aslamov ◽  
Matti Leppäranta ◽  
Elisa Lindgren
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
Turbulent Mixing ◽  
Ice Cover ◽  
The Arctic ◽  
Small Scale ◽  
Conductive Heat ◽  
Strong Wind ◽  
Dissipation Rates ◽  
Ice Water

Abstract. We performed a field study on mixing and vertical heat transport under ice cover of an Arctic lake. Mixing intensities were estimated from small-scale oscillations of water temperature and turbulent kinetic energy dissipation rates derived from current velocity fluctuations. Well-developed turbulent conditions prevailed in the stably stratified interfacial layer separating the ice base from the warmer deep waters. The source of turbulent mixing was identified as whole-lake (barotropic) oscillations of the water body driven by strong wind events over the ice surface. We derive a scaling of ice-water heat flux based on dissipative Kolmogorov scales and successfully tested against measured dissipation rates and under-ice temperature gradients. The results discard the conventional assumption of nearly conductive heat transport within the stratified under-ice layer and suggest contribution of the basal heat flux into the melt of ice cover is higher than commonly assumed. Decline of the seasonal ice cover in the Arctic is currently gaining recognition as a major indicator of climate change. The heat transfer at the ice-water interface remains the least studied among the mechanisms governing the growth and melting of seasonal ice. The outcomes of the study find application in heat budget of seasonal ice on inland and coastal waters.

Investigation of the Dynamics of Nucleate Boiling in Subcooled Falling Liquid Films

2014 ◽  
Vol 9 (2) ◽  
pp. 145-155
Author(s):  
Vladimir Serdyukov ◽  
Anton Surtaev ◽  
Oleg Volodin
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Strong Dependence ◽  
Pool Boiling ◽  
Nucleate Boiling ◽  
Liquid Films ◽  
Heat Fluxes ◽  
Nucleation Frequency ◽  
Water Films ◽  
Falling Liquid Films

This paper deals with the features of nucleation dynamics at boiling in falling water films at different subcooling, Reynolds number and heat fluxes. With the use of high-speed infrared and digital video the local parameters of nucleate boiling in falling liquid films such as: bubbles’ diameter before condensation, frequency of nucleation and temperature of onset of bubble appearance were received. Analysis of the experimental data showed that bubbles’ diameter before condensation has strong dependence on initial temperature and increases with the rise of heat flux. The main influence on nucleation frequency has the variation of heat flux density. At the same time the experimental data on nucleation frequency in falling water films are close to the frequency of nucleation at pool boiling. To identify the main features the comparison of received data on the local characteristics at boiling in subcooled falling liquid film with existing models for pool boiling was made

scholarly journals Influences of a Winter Wheat Belt on the Evolution of the Boundary Layer

2005 ◽  
Vol 133 (8) ◽  
pp. 2178-2199 ◽  
Author(s):  
Renee A. McPherson ◽  
David J. Stensrud
Keyword(s):  
Boundary Layer ◽  
Land Use ◽  
Heat Flux ◽  
Soil Moisture ◽  
Winter Wheat ◽  
Latent Heat ◽  
Planetary Boundary Layer ◽  
Heat Fluxes ◽  
Scale Transformation ◽  
Sensible Heat

Abstract Evidence exists that a large-scale alteration of land use by humans can cause changes in the climatology of the region. The largest-scale transformation is the substitution of native landscape by agricultural cropland. This modeling study examines the impact of a direct substitution of one type of grassland for another—in this case, the replacement of tallgrass prairie with winter wheat. The primary difference between these grasses is their growing season: native prairie grasses of the U.S. Great Plains are warm-season grasses whereas winter wheat is a cool-season grass. Case study simulations were conducted for 27 March 2000 and 5 April 2000—days analyzed in previous observational studies. The simulations provided additional insight into the physical processes involved and changes that occurred throughout the depth of the planetary boundary layer. Results indicate the following: 1) with the proper adjustment of vegetation parameters, land-use type, fractional vegetation coverage, and soil moisture, the numerical simulations were able to capture the overall patterns measured near the surface across a growing wheat belt during benign springtime conditions in Oklahoma; 2) the impacts of the mesoscale belt of growing wheat included increased values of latent heat flux and decreased values of sensible heat flux over the wheat, increased values of atmospheric moisture near the surface above and downstream of the wheat, and a shallower planetary boundary layer (PBL) above and downstream of the wheat; 3) in the sheared environments that were examined, a shallower PBL that resulted from growing wheat (rather than natural vegetation) led to reduced entrainment of higher momentum air into the PBL and, thus, weaker winds within the PBL over and downwind from the growing wheat; 4) for the cases studied, gradients in sensible heat were insufficient to establish an unambiguous vegetation breeze or its corresponding mesoscale circulation; 5) the initialization of soil moisture within the root zone aided latent heat fluxes from growing vegetation; and 6) reasonable specification of land surface parameters was required for the correct simulation and prediction of surface heat fluxes and resulting boundary layer development.

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