4:15 PM - 4:30 PM
[ACG40-09] Wave Parameter Dependence of Influence of Langmuir Turbulence on the Surface Mixed Layer Under Surface Heating
Keywords:Ocean surface mixed layer, Langmuir turbulence
There is the mixed layer (ML) in the upper ocean where water temperature, salinity, and density are uniform due to the turbulent mixing. Since the amount of change in water temperature depends on the mixed layer depth (MLD), accurate estimation of the MLD is essential for predicting SSTs and atmospheric phenomena. Shear turbulence caused by wind stress (wind forcing) and Langmuir turbulence (LT) associated with Langmuir circulation caused by the interaction of surface waves and currents (wave forcing) are dominant in deepening the ML under surface heating. Ocean and coupled general circulation models have shallow biases in the simulated MLD in the summer Southern Ocean (e.g., Belcher et al. 2012). Belcher et al.2012 calculated the frequency of the occurrence of Lat < 0.35, where Lat = (U*/US0)1/2 (U* is the wind friction velocity and US0 is the surface Stokes drift velocity), which is a measure of wind forcing relative to wave forcing, and suggested that LT, whose effects were not represented by the conventional general circulation models at that time, intensifies the surface mixing to the make the actual MLD greater in the Southern Ocean. However, it has not been quantified how much LT deepens ML. Furthermore, other previous studies (e.g., Van Roekel et al. 2012) have shown that wavelength λ and angle between wind and wave direction (wind-wave misalignment) θww also affect the intensity of LT, but their impact on ML deepening is also unknown.
Therefore, we performed large-eddy-simulations (LES) using the parameters of wind friction velocity (U*), surface Stokes drift velocity (US0,) wavelength λ, wind-wave misalignment (θww), surface heating (B0), and Coriolis parameter (f) to quantify the effects of the LT contribution to MLD under surface heating. We focused on the value D/Dwind, which is the ratio of the MLD (D) reproduced with wind, wave, and thermal forcing to the MLD (Dwind) under wind and thermal forcing. This indicates how much the wave forcing (LT) deepens the ML formed by wind and heat alone. A number of experiments were conducted with four different dimensionless numbers, Lat-1 = (US0/U*)1/2 , the strength of wave forcing relative to wind forcing, Z = B0/U*2 f, the strength of thermal forcing relative to wind forcing, R = λ/4πDwind , the dimensionless wavelength, and θww , the wind-wave misalignment. In this presentation, we will mainly discuss the dependence on R.
In all experiments with wave forcing, even under surface heating, wave forcing (LT) deepens the ML(D/Dwind > 1). However, D/Dwind also changes with wavelength (R), with D/Dwind reaching a maximum around R = 0.4 - 0.6. To further investigate this characteristic dependence, we evaluated the turbulent kinetic energy (TKE) budget terms and found that the generation term due to waves decreases with longer wavelengths (larger R). This is because the vertical shear of the Stokes drift velocity is inversely proportional to wavelength. It was also found that shorter wavelengths (smaller R) result in larger TKE generation terms due to waves, but these larger values are concentrated in shallow depth in the ML and do not contribute to ML deepening. In fact, evaluation of the vertical turbulent velocity weighted by depth showed that the maximum value is around R = 0.4 - 0.6, and revealed the turbulence contributing to ML deepening is greatest around R = 0.4 - 0.6.
We further calculated four dimensionless numbers using observed and reanalysis data and globally estimated D/Dwind in the real spring ocean based on the numerical experiment results. The results showed, for example, as suggested by Belcher et al. 2012, that the frequency of wave forcing is higher and D/Dwind is larger actually in the spring Southern Ocean, but because wavelength is shorter than the Dwind (R is smaller), the value of D/Dwind varied greatly depending on whether R is considered.
Finally, the Hoenikker number Ho, a dimensionless number used in previous studies to represent the strength of surface heating, was examined. Ho=B0H/U*2US0, where H is the length scale. When wavelength λ is used for H as in Min and Noh 2004 and others, D and wave effect D/Dwind could differ significantly even for the same Ho, due to the different Coriolis parameter f. In other words, Ho defined in this way is an inappropriate parameter to classify the turbulences under surface heating.
It is also shown that to classify turbulences with the Hoenniker number, using a length scale incorporating f, such as H=Dwind, is appropriate.
Therefore, we performed large-eddy-simulations (LES) using the parameters of wind friction velocity (U*), surface Stokes drift velocity (US0,) wavelength λ, wind-wave misalignment (θww), surface heating (B0), and Coriolis parameter (f) to quantify the effects of the LT contribution to MLD under surface heating. We focused on the value D/Dwind, which is the ratio of the MLD (D) reproduced with wind, wave, and thermal forcing to the MLD (Dwind) under wind and thermal forcing. This indicates how much the wave forcing (LT) deepens the ML formed by wind and heat alone. A number of experiments were conducted with four different dimensionless numbers, Lat-1 = (US0/U*)1/2 , the strength of wave forcing relative to wind forcing, Z = B0/U*2 f, the strength of thermal forcing relative to wind forcing, R = λ/4πDwind , the dimensionless wavelength, and θww , the wind-wave misalignment. In this presentation, we will mainly discuss the dependence on R.
In all experiments with wave forcing, even under surface heating, wave forcing (LT) deepens the ML(D/Dwind > 1). However, D/Dwind also changes with wavelength (R), with D/Dwind reaching a maximum around R = 0.4 - 0.6. To further investigate this characteristic dependence, we evaluated the turbulent kinetic energy (TKE) budget terms and found that the generation term due to waves decreases with longer wavelengths (larger R). This is because the vertical shear of the Stokes drift velocity is inversely proportional to wavelength. It was also found that shorter wavelengths (smaller R) result in larger TKE generation terms due to waves, but these larger values are concentrated in shallow depth in the ML and do not contribute to ML deepening. In fact, evaluation of the vertical turbulent velocity weighted by depth showed that the maximum value is around R = 0.4 - 0.6, and revealed the turbulence contributing to ML deepening is greatest around R = 0.4 - 0.6.
We further calculated four dimensionless numbers using observed and reanalysis data and globally estimated D/Dwind in the real spring ocean based on the numerical experiment results. The results showed, for example, as suggested by Belcher et al. 2012, that the frequency of wave forcing is higher and D/Dwind is larger actually in the spring Southern Ocean, but because wavelength is shorter than the Dwind (R is smaller), the value of D/Dwind varied greatly depending on whether R is considered.
Finally, the Hoenikker number Ho, a dimensionless number used in previous studies to represent the strength of surface heating, was examined. Ho=B0H/U*2US0, where H is the length scale. When wavelength λ is used for H as in Min and Noh 2004 and others, D and wave effect D/Dwind could differ significantly even for the same Ho, due to the different Coriolis parameter f. In other words, Ho defined in this way is an inappropriate parameter to classify the turbulences under surface heating.
It is also shown that to classify turbulences with the Hoenniker number, using a length scale incorporating f, such as H=Dwind, is appropriate.