Wave-induced Vertical Mixing Research Articles

The effect of strong nonlinearity on wave-induced vertical mixing

Abstract. A semi-analytical solution to an advection–diffusion equation is coupled with a nonlinear wavemaker model to investigate the effect of strong nonlinearity on wave-induced mixing. The comparisons with weakly nonlinear model predictions reveal that in the case of waves of higher steepness, enhanced mixing affects the subsurface layer of the water column. A fully nonlinear model captures the neglected higher-order terms from a weakly nonlinear solution and provides a reliable estimation of the time-mean velocity field. The corrected wave-induced mass-transport velocity leads to improved estimates of subsurface mixing intensity and ocean surface temperature.

A Modelling Approach for the Assessment of Wave-Currents Interaction in the Black Sea

In this study, we investigate wave-currents interaction for the first time in the Black Sea, implementing a coupled numerical system based on the ocean circulation model NEMO v4.0 and the third-generation wave model WaveWatchIII v5.16. The scope is to evaluate how the waves impact the surface ocean dynamics, through assessment of temperature, salinity and surface currents. We provide also some evidence on the way currents may impact on sea-state. The physical processes considered here are Stokes–Coriolis force, sea-state dependent momentum flux, wave-induced vertical mixing, Doppler shift effect, and stability parameter for computation of effective wind speed. The numerical system is implemented for the Black Sea basin (the Azov Sea is not included) at a horizontal resolution of about 3 km and at 31 vertical levels for the hydrodynamics. Wave spectrum has been discretised into 30 frequencies and 24 directional bins. Extensive validation was conducted using in-situ and satellite observations over a five-year period (2015–2019). The largest positive impact of wave-currents interaction is found during Winter while the smallest is in Summer. In the uppermost 200 m of the Black Sea, the average reductions of temperature and salinity error are about −3% and −6%, respectively. Regarding waves, the coupling enhanced the model skill, reducing the simulation error, about −2%.

Model of Vertical Mixing Induced by Wind Waves

In the Navier-Stokes equations, a current is decomposed into four constituents: the mean flow, wave-orbital motion, wave-induced-turbulent and background-turbulent currents. Under certain statistical assumptions, this allows to separate the wave-induced Reynolds stress from the background one. To close the wave-induced Reynolds stress, the Prandtl approach for the wave-induced fluctuations is used, resulting in the implicit expression for the wave-induced vertical mixing function, B. Expression for B is specified, basing on the author results for the turbulent viscosity, found earlier in the frame of the three-layer concept for the air-sea interface. The explicit expression for function B is linear in both wave amplitude and friction velocity in the air. Due to exponential decay of wave amplitude, the found result means the possibility of the enhanced impact of waves on the vertical mixing and related geophysical processes, compared to the known cubic wave-amplitude dependence for B, found by Qiao et al previously.

On modeling of wave-induced vertical mixing

A theoretical approach is applied to investigate wave-induced mixing. The problem is formulated to describe evolution of temperature in a layer of fluid and is solved by applying eigenfunction expansions. The derived semi-analytical solution is applied to predict temperature changes and evolution of temperature profiles due to mechanically generated waves in a closed flume. The results show that water waves modify the temperature distribution in space and time. The analysis shows that the changes occur in the whole layer of fluid. The results indicate that time is a more important factor in a process of wave-induced mixing than expected. Mixing processes depend on a wave height. The rate of change of temperature distribution is more pronounced for higher waves. Another important parameter in mixing processes is the wavelength. The mixing effects are more distinct for deep water waves. The sensitivity analysis implies a need to conduct more theoretical studies and experimental investigations on wave-induced mixing. the model is verified in the course of the original laboratory experiments that were conducted in the insulated flume. A reasonable agreement between predicted and measured temperature profiles proves the applicability of the present approach even for relatively high gradients of temperature distribution over water depth.

Contribution of surface wave-induced vertical mixing to heat content in global upper ocean

Compared with observations, the simulated upper ocean heat content (OHC) determined from climate models shows an underestimation bias. The simulation bias of the average annual water temperature in the upper 300 m is 0.2°C lower than the observational results. The results from our two numerical experiments, using a CMIP5 model, show that the non-breaking surface wave-induced vertical mixing can reduce this bias. The enhanced vertical mixing increases the OHC in the global upper ocean (65°S–65°N). Using non-breaking surface wave-induced vertical mixing reduced the disparity by 30% to 0.14°C. The heat content increase is not directly induced by air-sea heat fluxes during the simulation period, but is the legacy of temperature increases in the first 150 years. During this period, additional vertical mixing was initially included in the climate model. The non-breaking surface wave-induced vertical mixing improves the OHC by increasing the air-sea heat fluxes in the first 150 years. This increase in air-sea heat fluxes warms the upper ocean by 0.05–0.06°C. The results show that the incorporation of vertical mixing induced by nonbreaking surface waves in our experiments can improve the simulation of OHC in the global upper ocean.

Theoretical and Experimental Investigations of Wave-Induced Vertical Mixing

Theoretical investigations supported by a series of original laboratory experiments are conducted to study a wave-induced vertical mixing process. The derived semi-analytical solution is very efficient and is applied to predict the effects of water waves on the temperature changes and the evolution of temperature profiles. The results indicate that waves increase a mixing process. The rate of change of the temperature is higher when waves contributed to mixing process and this process increases with increasing the wavelength to water depth ratio. The analysis indicates that for typical ocean waves the contribution of water waves to mixing may be several orders of magnitude higher than a corresponding contribution arising from the classical diffusion process. This implies a need to conduct more theoretical studies and experimental investigation on the effect of water waves on mixing processes. A series of original laboratory experiments were conducted in the insulated wave flume to verify the derived model. The comparisons show a reasonable agreement between predicted and measured temperature profiles. A reasonable agreement between theoretical results and experimental data is observed for the whole considered range of initial temperature distributions. The comparisons indicate that the model is applicable even to cases when gradients in temperature distributions over water depth are fairly high.

The effects of the non-breaking surface wave-induced vertical mixing on the forecast of tropical cyclone tracks

The Weather Research and Forecasting model (WRF) is configured for the region of (15°–41°N, 105°–135°E), which covers the same area with the MASNUM (Key Lab. Marine Science & Numerical Modeling, State Oceanic Administration) wave-tide-circulation coupled operational forecast system. Three numerical experiments are implemented to investigate the effects of the real-time forecasted sea surface temperature (SST) and the non-breaking wave-induced vertical mixing (Bv) on the track forecast of all 33 tropical cyclones (TC) in the model domain area during 2008 and 2011. The first experiment employs NCEP FNL (NCEP final analysis) SST as WRF’s bottom condition as the Control run, which is also the default setup of WRF. The second and third experiments use real-time forecasted SST from the MASNUM forecast system with and without Bv, respectively. The forecasted track results are compared with Japan Meteorological Agency’s best track data. For 24-h forecast, the averaged TC position error of Experiment with Bv is reduced by 9 % compared to the Control experiment, while the forecasted track error of Experiment without Bv is reduced by only 2 % compared to the Control experiment. For the 48-h forecast, the averaged track errors are reduced by 10 % and 6 % with Bv and without Bv compared to the Control experiment, respectively. These results suggest that the real-time forecasted SST can improve the performance of WRF in forecasting TC track, and the Bv plays an important role in reducing the forecast error of TC track. Comparatively, Bv can improve more on the track of stronger TC.

The improvement of the one-dimensional Mellor-Yamada and K-profile parameterization turbulence schemes with the non-breaking surface wave-induced vertical mixing

Both the level 2.5 Mellor-Yamada turbulence closure scheme (MY) and K-profile parameterization (KPP) are popularly used by the ocean modeling community. The MY and the KPP are improved through including the non-breaking surface wave-induced vertical mixing (Bv), and the improved schemes were tested by using continuous data at the Papa ocean weather station (OWS) during 1961–1965. The numerical results showed that the Bv can make the temperature simulations fit much better with the continuous data from Papa Station. The two improved schemes overcame the shortcomings of predicting too shallow upper mixed layer depth and consequently overheated sea surface temperature during summertime, which are in fact common problems for all turbulence closure models. Statistical analysis showed that the Bv effectively reduced the mean absolute error and root mean square error of the upper layer temperature and increased the correlation coefficient between simulation and the observation. Furthermore, the performance of vertical mixing induced by shear instability and the Bv is also compared. Both the temperature structure and its seasonal cycle significantly improved by including the Bv, regardless of whether shear instability was included or not, especially for the KPP mixing scheme, which suggested that Bv played a dominant role in the upper ocean where the mean current was relatively weak, such as at Papa Station. These results may provide a clue to improve ocean circulation models.

A comparison of two global ocean-ice coupled models with different horizontal resolutions

A global eddy-permitting ocean-ice coupled model with a horizontal resolution of 0.25° by 0.25° is established on the basis of Modular Ocean Model version 4 (MOM4) and Sea Ice Simulator (SIS). Simulation results are compared with those of an intermediate resolution ocean-ice coupled model with a horizontal resolution of about 1° by 1°. The results show that the simulated ocean temperature, ocean current and sea ice concentration from the eddy-permitting model are better than those from the intermediate resolution model. However, both the two models have the common problem of ocean general circulation models (OGCMs) that the majority of the simulated summer sea surface temperature (SST) is too warm while the majority of the simulated subsurface summer temperature is too cold. Further numerical experiments show that this problem can be alleviated by incorporating the non-breaking surface wave-induced vertical mixing into the vertical mixing scheme for both eddy-permitting and intermediate resolution models.

Sensitive study of the long and short surface wave-induced vertical mixing in a wave-circulation coupled model

The previous studies by the MASNUM research team have shown the effectiveness of the wave-induced mixing (Bv) in improving the simulation of upper-ocean thermal structure. The mechanisms of Bv are further investigated by incorporating different Bv products into the MASNUM wave-circulation coupled model. First, experiments were designed to explore the effects of Bv, which contain the contributions at different wave lengths (l). The results of three experiments, the non-Bv case, the short-wave case (l 300 m) are compared, and it is found that the long waves are the most important component for Bv to generate mixing in the upper ocean. As the swell plays dominant role in mixing, the parameterization of Bv into wind may be not a proper way. Second, Bv effects at different time-scales, including daily and monthly, were examined. The results show that the monthly averaged Bv has larger impact than the daily averaged Bv, especially in summer.

A numerical study of transport dynamics and seasonal variability of the Yellow River sediment in the Bohai and Yellow seas

A sediment numerical model was embedded into a wave-tide-circulation coupled model to simulate the transport processes of the Yellow River-derived sediment considering the wave-induced vertical mixing (Bv) and the wave-current coupled bottom shear stress (BSS). Numerical results show that the main stream of the Yellow River-derived sediment moves first eastward off the northern Shandong Peninsula and then southward into the South Yellow Sea all year round. In spring, the sediment moves northeastward in the Bohai Sea. In summer, there is a northeastward branch of sediment in the Bohai Sea off the west coast of the Liaodong Peninsula, while the main part goes eastward to the Yellow Sea. The Yellow River-derived sediment transport from the Bohai Sea to the North Yellow Sea across the Bohai Strait is mainly limited to the top 10 m, and with a maximum centered at 37.9°N in summer. The transport from the North Yellow Sea to the South Yellow Sea across the transect of 37°N is mainly in the 0–30 m layer with a maximum around 123.7°E in autumn. The simulated Yellow River-discharged sediment deposits along the Shandong Peninsula and between 20 and 30 m isobaths in the Yellow Sea, which is consistent with observation. If surface waves are not considered in the model, the sediment deposits westward to the nearshore area in the South Yellow Sea. The sediment would deposit further southward in the numerical experiment results without wind influence. In the numerical experiment of no tide, there is hardly any sediment deposited on the Yellow Sea floor, while in the Bohai Sea most of the sediment is transported southward and northwestward around the river mouth instead of eastward as in the Control Run, indicating the tides play a key role in forming the deposition pattern.

The correctness to the spuriously simulated semi-annual cycle of the sea surface temperature in the equatorial eastern Pacific

One of the challenges faced by the climate model of the Community Climate System Model version 3 (CCSM3) is the spuriously simulated semi-annual cycle of the sea surface temperature (SST) in the equatorial eastern Pacific. This model bias has limited the performance of the climate simulation and prediction. Based on the surface wave-circulation coupled theory, an atmosphere-wave-ocean coupled model was developed, which incorporates the MASNUM (key laboratory of Marine Sciences and Numerical Modeling) wave number spectral model into CCSM3. The new coupled atmosphere-wave-ocean model successfully removes the spurious semi-annual cycle simulated by the original CCSM3 and reasonably produces an SST annual cycle with warm and cold phases in April and August, respectively. The correlation between the simulated and observed SST in the equatorial eastern Pacific is improved from 0.66 to 0.93. The ocean surface layer heat budget analysis indicates that the wave-induced vertical mixing is responsible for improving the simulation of the SST seasonal cycle in the equatorial eastern Pacific.

INTERNAL TIDE AND ITS ASSOCIATED COOLING SYSTEM IN GENKA BAY, OKINAWA, JAPAN

Poster

Improvement of MOM4 by including surface wave-induced vertical mixing

A parameterized surface wave-induced vertical mixing ( B v) is incorporated into the Modular Ocean Model version 4 (MOM4). A comparison of the two numerical experiments with and without B v shows that B v can significantly improve the upper-ocean (20–100 m) simulation in summer. The simulated upper-ocean temperature errors are reduced in summer due to the surface wave-induced vertical diffusive heat flux. The non-breaking-wave-induced vertical mixing can increase the probability of the simulated SST biases between −1 °C and 1 °C from 64% to 76% in the Southern Hemisphere (60°S–10°S) in January, and from 66% to 75% in the Northern Hemisphere (10°N–60°N) in July. The averaged mixed layer depth (MLD) simulated by the MOM4 without B v is 14.4 m shallower than the observations in 10°S–60°S in January, and 7.2 m shallower than the observations in 10°N–60°N in July. B v can deepen the modeled MLD by 12.4 m in the Southern Hemisphere in January and by 6.3 m in the Northern Hemisphere in July. By including B v, the corresponding MLD biases from the observations are only 2.0 and 0.9 m in the Southern and Northern hemispheres, respectively. These results clearly demonstrate that the incorporation of B v can improve the performance of MOM4 significantly in summer.

Sensitivity study of the effects of wave-induced vertical mixing on vertical exchange processes

The hydrodynamic model COHERENS-SED, developed by the present authors through introducing wave-enhanced bottom stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN to COHERENS, is modified to account for wave-induced vertical mixing. The COHERENS-SED model can also be used for one-dimensional, two-dimensional, three-dimensional current and salinity calculations. One-dimensional model and three-dimensional model are used to study the effects of the wave-induced vertical mixing. The horizontal current velocity profiles obtained by the model are in good agreement with the analytical velocity profiles under the same input conditions. Numerical results show that higher wave height would generally generate larger vertical eddy viscosity and lower horizontal velocity. The results for fresh water in Yellow River Delta show that the wave-induced vertical mixing increases the momentum of fresh water transferring ability downwards to seabed and salt water's mixing with upper fresh water. Fresh water flume length is compressed considerably.

An improvement of the too cold tongue in the tropical Pacific with the development of an ocean-wave-atmosphere coupled numerical model

A common problem in the application of the coupled ocean-atmosphere general circulation models (CGCMs) without flux correction is that the simulated equatorial cold tongue in general tends to be too strong, narrow, and extending too far west. The causes are not well understood yet. One possible reason may be the simulated mixed layer depth (MLD) is too shallow in the tropical Pacific due to insufficient vertical mixing in the OGCM. It is believed that the wave-induced vertical mixing can greatly improve the simulation of the MLD and thermocline structure. In this study, the coupled ocean-atmosphere general circulation model (FGCM-0) incorporated with wave-induced mixing has been employed to simulate the tropical Pacific sea surface temperature (SST). Generally, the wave-induced mixing lowers the SST in the OGCM because the strengthened vertical mixing can bring more cold water upward. However, in the coupled model, the non-uniformity of the space distribution in SST drop generates a horizontal gradient of...

Observational Evidence for Vertical Diffusion Driven by Internal Waves of Tidal Origin in the Oslofjord

In an earlier paper (Stigebrandt, 1976), a model was proposed for internal wave-induced vertical mixing in a sill fjord. The observational evidence for the theory at that time was rather sparse, but the void is materially filled by observations presented in this note. Current measurements show, in accordance with the theory, that progressive internal waves radiate out from the Dröbak sill in the Oslofjord. An experiment with tracer dye below the sill depth in the same fjord showed that the coefficient of vertical diffusion of the tracer was an order of magnitude less than the overall coefficient for vertical diffusion of density during the same period. This finding, indicating large horizontal inhomogeneities in the mixing field, gives strong support to the mixing model proposed in the earlier paper referred to above.

Topographically generated internal waves in the open ocean

The generation of internal waves by the interaction of deep ocean flows with bottom topography is considered. The interaction of quasi-steady currents with the bottom topography is found to produce an internal wave drag and associated momentum flux of roughly ½ dyn/cm2, which is comparable to the average wind stress on the ocean surface. The waves are probably dissipated by critical layer phenomena in the lowest kilometer or so of the ocean, the result being a wave-induced vertical mixing coefficient of order 10 cm2/s in that portion of the water column. The interaction of the barotropic tide with the bottom topography is found to result in a flux of energy of order 1 erg/cm2 s into the internal tide, which may represent a nonnegligible sink of the tidal energy. This mechanism appears to be capable of supplying a significant portion of the observed internal wave energy in the ocean. The internal tide is probably dissipated by inherently nonlinear phenomena: spectral transport by weak interactions and, in the upper oceans, strong interactions manifested by localized instabilities resulting in isolated patches of turbulence.