Modelling Marine and Coastal Processes PROGRAM OVERVIEW: Physical Oceanography

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1 Modelling Marine and Coastal Processes PROGRAM OVERVIEW: Physical Oceanography - Motivation - General Introduction to marine and coastal geophysical processes - Physical properties of seawater: temperature, salinity, density - Vertical structure, stratification and stability of the ocean - Main mechanisms generating motion in the ocean - Scales of circulation in the ocean - Hydrostatic equilibrium - Barotropic and baroclinic conditions - Geostrophic currents - Wind induced circulation - the Ekman solution - Convergence and divergence - Dynamics of the coastal regions - coastal upwelling

2 BIBLIOGRAPHY Open University, Seawater: its Composition, Properties and Behavior (volume 2); Ocean Circulation (volume 3), Oceanography Course Team, Oceanographic Series, 2nd edition, Butterworth Heinemann. Introductory Dynamical Oceanography, 1983, S. Pond e G. Pickard, Pergamon Press, 2nd edition. Introduction to Physical Oceanography, 2007, R. H. Stewart, Department of Oceanography, Texas A&M University.

3 INTRODUCTION The ocean is part of our Planet s integrated physical system

4 INTRODUCTION Interaction Ocean Atmosphere and physical processes in the ocean

5 INTRODUCTION Hydrological Cycle The Hydrological Cycle showing the annual movement of the water and the quantity of accumulated water in each reservoir (10 3 km 3 ~ kg of water)

6 TEMPERATURE, SALINITY AND DENSITY The physical properties of the pure water relevant for the study of fluid dynamics are pressure and temperature. For the sea water we have to join salinity. Temperature and salinity are two of the most important physical properties of the sea water because: they help to identify particular water masses in the ocean; together with pressure they determine the density of the sea water (ρ(s,t,p)). The density is the most important factor in the vertical movement of the waters in the ocean, because it determines the depth at which a water mass reaches the equilibrium in the gravity field. Conservative properties of the sea water are properties that change only through mixing of the water masses, after the water have lost contact with the atmosphere and other external influencies. Examples: potential temperature and salinity. Non-Conservative Properties of the sea water are those that can change through processes other than water masses mixing. Examples: in situ temperature, dissolved oxigen and nutrients concentration.

7 TEMPERATURE, SALINITY AND DENSITY The temperature is a measure of the mean kinetic energy of the particles that constitute a given material macroscopic property. Two systems are in thermal equilibrium if and only if their temperatures are the same. Adiabatic processes are processes that fluids experiment as a consequence of their compressibility, without exchanging heat with the surrounding environment: when a fluid expands loses internal energy and it temperature decreases; when it is compressed the internal energy grow and the temperature increases. Potential Temperature As the water is slightly compressible, a parcel of water transported from the deep ocean to the surface, expands and tends to cool. The temperature of a parcel of sea water transported adiabaticaly to the surface is lower than it in situ temperature. This thermodynamic property is called potential temperature and is used to compare water masses at different depths, or to study vertical movements over a large depth range. Compute the potential temperature here

8 TEMPERATURE, SALINITY AND DENSITY To dissolve salts in pure water changes it properties: small variations in compressibility, thermal expation, and refraction index; large variation in the density, temperature of the freezing point and of the maximum density, and electric conductivity. pure water mean sea water temperature (ºC) temperature of maximum density freezing temperature salinity Temperature of maximum density and temperature of the freezing poin of the sea water as a function of the salinity.

9 TEMPERATURE, SALINITY AND DENSITY Salinity is the measure of the quantity of salts dissolved in sea water. Until 1980 slainity was expressed as parts per thousands (ppt or ). The mean salinity of the oceans is 35. Methods to measure salinity: Gravimetric measurement: time consuming and imprecise due to the decomposition of some salts during the process of heating to evaporation. Chemical measurement: based on the levels of chlorine used until the mid 1960s. Physical measurement: based on the electric conductivity. The method uses an imperical formula to convert contuctivity fractions into salinities. Actual definition of salinity based on the imperical formulae which envolve a fraction of conductivity pattern, R 15 =C(S,15,0)/C(35,15,0). The salinity is determined from measurements of electric conductivity and termperature. Conductivity sensors (C), temperature (T) and pressure (D from depth) are usually assembled in the same device, the CTD.

10 TEMPERATURE, SALINITY AND DENSITY The importance in the knowledge of the density, ρ, is that the movement of the deeper water masses is controlled by the density, that means the gravitiational stability. As the density depends on the T and S the vertical circulation is controlled by these two parameters and for this reason is known as thermohaline circulation. The density of the water at the surface is controlled by the temperature and salinity only; but in the interior of the ocean the density depends also on the pressure, because the water is slightly compressible. The density decrease with the temperature and increases with salinity and pressure. Units of density are expressed in kg/m 3. The range of values: 1021 kg/m 3 at the surface 1070 kg/m 3 at metres of depth. The mean value is approx kg/m 3. In Oceanography we use from time to time the specific volume, α=1/ρ, and nearly always a quantity called σ t (sigma-t), σ t =ρ(s,t,p 0 )-1000, where P 0 is the pressure at the sea level (1 atmosphere).

11 TEMPERATURE, SALINITY AND DENSITY As the density varies in the two last digits only, and we normaly compare water masses at similar depths (same pressure), the use of σ t is consensual. σ t has units but usually we omit them. Example: T=10ºC, S=35 e P=0 ρ=1026,96 kg.m -3 σ t =26.96 Range of values for σ t : 21 (surface) 28,3 (10000 m depth). Associated with potential temperature, θ, we define potential density, sigma-θ, represented by σ θ. There is no quick, pratical, and safe method to measure in situ density. It can be measured in laboratories but is a hard task. In practice, density is calculated from temperature, salinity and pressure, which are measured directly. The relation between the density, temperature, salinity and pressure is represented by the sea water equation of state, which is rather complicated...

12 International Equation of State of Seawater (IES80) where: and: Compute density (sigma-t) from T, S and P here The new Thermodynamic Equation Of Seawater (TEOS-10)

13 TEMPERATURE, SALINITY AND DENSITY The temperature of the open ocean is comprised between 2ºC and 30ºC and the salinity between 30 and 40. About 90% of the open ocean is comprised between 2ºC and 10ºC and between 34 and 35, representing subsurface water. The remaining is surface water. The density (sigma-t) as a funtion of the temperature and salinity. A range for all the ocean is represented. Note that 90% of all the ocean water fall inside the dashed area. Note that the relation between density, temperature and salinity in not linear, more in the temperature than in the salinity. The density is less sensitive to temperature variations at lower temperatures than at high temperature.

14 TEMPERATURE, SALINITY AND DENSITY In Oceanography we consider the hydrostatic pressure, that means, the pressure caused by the water column above a given level (depth). That implies to consider P=0 at the surface. However, the pressure there is the atmospheric pressure. The Fundamental Equation of the Hydrostatic describes the pressure variation, p, with the depth, z, in a column of the fluid: p=ρgz. Considering ρ constant, the hydrostatic equation show a linear relation between pressure and depth. Units of pressure: 1 Pa=1 N.m 2; 10 5 Pa=10 5 N.m 2 =1 bar 1 atmosphere. In the ocean we can use the relation: Z=1 m p 1 decibar (db).

15 VERTICAL STRUCTURE OF THE OCEAN Typical vertical profiles of temperature at different latitudes. The seasonal thermocline ocurr due to the strong surface heating of the ocean during Summer in the mean latitudes. Vertical profiles of temperature at different month showing the development (solid line) and the decay (dashed lines) of the seasonal thermocline in the mean latitudes of the North Hemisphere.

16 VERTICAL STRUCTURE OF THE OCEAN Typical mean salinity profiles for different latitudes of the oceans. Typical mean density profiles for different latitudes of the world ocean.

17 VERTICAL STRUCTURE OF THE OCEAN The upper layer of the ocean (meters or tens of meters) correspond to the mixed layer where the ocean is well mixed due to the direct influence of the wind. In this region, temperature, salinity and thus density show only small variations with depth. Below follows a region with strong vertical gardient of temperature (thermocline), salinity (halocline) and as a consequence density (picnocline). In the deeper ocean those parameter show again small variations with depth. Typical vertical structure of the ocean

18 VERTICAL STRUCTURE OF THE OCEAN Mean zonal North-South vertical transect of temperature in the world ocean Mean zonal North-South vertical transect of density in the world ocean

19 STRATIFICATION AND STABILITY IN THE OCEAN If a denser water mass lies above e less dense water mass there is instability and the sinking of the denser water occurs. If a lighter water (less dense) lies over a heavier water (denser water), the interface between the two waters is in a stability condition. The stability increases with the difference of density between the two waters. The static stability is important in the flow of a stratified fluid where ρ increases with depth. The criterium to determine the importance of the static stability is given by the stability parameter that cames out from the Stability Equation: (valid for E>50x10-8 m -1 ) 1 dρ E ρ dz Stability is defined by: E>0, stability condition E=0, neutral stability, E<0, instability condition.

20 STRATIFICATION AND STABILITY IN THE OCEAN The influence of the stability is expressed through a frequency of stability, N, called Frequency of Brunt-Väisälä or Frequency of Stratification, N 2 = ge N = ge ( cycles / second, Hz ) The Frequency of Brunt-Väisälä quantifies the importance of the stability and is a fundamental parameter in the dynamics of flows with stratification. The frequency of Brunt-Väisälä can be interpreted as the frequency of the vertical movement that a parcel of water suffers when it is displaced from it equilibrium position by a vertical disturbance the frequency of Brunt-Väisälä is the maximum frequency of the internal waves in the Ocean and has typical values of some cycles/houre.

21 STRATIFICATION AND STABILITY IN THE OCEAN Frequency of stratification observed in the Pacific Ocean. Left: stability of the deep termocline, east of the Kuroshio current. Right: stability of the upper termocline, characteristic of the tropical regions. Note the different scales.